16-WorkingWithList.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第16章 使用列表\n",
    "列表可能是Scala程序中最常使用的数据结构了。本章将对列表做详细的介绍。我们会讲到很多可以对列表好执行的操作。我们还将对使用列表的一些重要的程序设计原则做出讲解。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.1 List字面量\n",
    "我们在前面的章节已经介绍过列表，一个包含元素＇a＇、＇b＇和＇c＇的列表写作List（＇a＇, ＇b＇, ＇c＇）。以下是另外一些例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mfruit\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"apples\"\u001b[39m, \u001b[32m\"oranges\"\u001b[39m, \u001b[32m\"pears\"\u001b[39m)"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val fruit = List(\"apples\", \"oranges\", \"pears\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnums\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val nums = List(1, 2, 3, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mdiags3\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]] = \u001b[33mList\u001b[39m(\u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m))"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val diags3 = List(\n",
    "    List(1,0,0),\n",
    "    List(0,1,0),\n",
    "    List(0,0,1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mempty\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mNothing\u001b[39m] = \u001b[33mList\u001b[39m()"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val empty: List[Nothing] = List()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scala的列表类型是协变（covariant）的。意思是对每一组类型S和T，如果S是T的子类型，那么List[S]就是List[T]的子类型。例如，List[String]是List[Object]的子类型。因为每个字符串列表也都可以被当作对象列表，这很自然。[2]\n",
    "注意，空列表的类型为List[Nothing]。在11.3节我们讲过，在Scala的类继承关系中，Nothing是底类型。由于列表是协变的，对于任何T而言，List[Nothing]都是List[T]的子类型。因此既然空列表对象的类型为List[Nothing]，可以被当作是其他形如List[T]类型的对象。这也是为什么编译器允许我们编写如下的代码：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mxs\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m()"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "//List()也是List[String]类型\n",
    "val xs: List[String] = List()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.3 构建列表\n",
    "所有的列表都构建自两个基础的构建单元：N i l和∷（读作“cons”）。Nil表示空列表。中缀操作符：：表示在列表前追加元素。也就是说，x :: xs表示这样一个列表：第一个元素为x，接下来是列表xs的全部元素。因此，前面的列表值也可以这样来定义：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mfruit\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"apples\"\u001b[39m, \u001b[32m\"oranges\"\u001b[39m, \u001b[32m\"pears\"\u001b[39m)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val fruit = \"apples\" :: (\"oranges\" :: (\"pears\" :: Nil))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnums\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val nums  = 1 :: (2 :: (3 :: (4 :: Nil)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mdiag3\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]] = \u001b[33mList\u001b[39m(\u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m))"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val diag3 = (1 :: (0 :: (0 :: Nil))) ::\n",
    "            (0 :: (1 :: (0 :: Nil))) ::\n",
    "            (0 :: (0 :: (1 :: Nil))) :: Nil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mempty\u001b[39m: \u001b[32mNil\u001b[39m.type = \u001b[33mList\u001b[39m()"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val empty = Nil"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "事实上，之前我们用List（...）对fruit、nums、diag3和empty的定义，不过是最终展开成上面这些定义的包装方法而已。例如，List（1, 2, 3）创建的列表就是 1 :: （2 :: （3 :: Nil））。\n",
    "由于：：以冒号结尾，:：这个操作符是右结合的：A :: B :: C会被翻译成 A :: （B :: C）。因此，我们可以在前面的定义中去掉圆括号。例如：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnums\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val nums = 1 :: 2 :: 3 :: 4 :: Nil"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟之前的nums定义是等效的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.4 列表的基本操作\n",
    "对列表的所有操作都可以用下面这三项来表述：  \n",
    "head 返回列表的第一个元素  \n",
    "tail 返回列表中除第一个元素之外的所有元素  \n",
    "isEmpty 返回列表是否为空列表  \n",
    "这些操作在List类中定义为方法。表16.1给出了一些例子。head和tail方法只对非空列表有定义。当我们从一个空列表调用时，它们将抛出异常：\n",
    "\n",
    "```scala\n",
    "Nil.head\n",
    "\n",
    "java.util.NoSuchElementException: head of empty list\n",
    "  scala.collection.immutable.Nil$.head(List.scala:629)\n",
    "  ammonite.$sess.cmd10$Helper.<init>(cmd10.sc:1)\n",
    "  ammonite.$sess.cmd10$.<clinit>(cmd10.sc:7)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "作为如何处理列表的例子，考虑按升序排列一个数字列表的元素。一个简单的做法是插入排序（insertion sort），这个算法的工作原理如下：对于非空列表x :: xs，先对xs排序，然后将第一个元素x插入到这个排序结果中正确的位置。\n",
    "<center>表16.1 基本的列表操作</center>\n",
    "\n",
    "|操作|这个操作做什么|\n",
    "|-|-|\n",
    "|empty.isEmpty|返回true|\n",
    "|fruit.isEmpty|返回false|\n",
    "|fruit.head|返回\"apple\"|\n",
    "|fruit.tail.head|返回\"oranges\"|\n",
    "|diag3.head|返回List(1,0,0)|\n",
    "\n",
    "对一个空列表排序交出空列表。用Scala代码来表示，这个插入排序算法是这样的："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36misort\u001b[39m\n",
       "defined \u001b[32mfunction\u001b[39m \u001b[36minsert\u001b[39m"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def isort(xs: List[Int]): List[Int] = \n",
    "    if(xs.isEmpty) Nil\n",
    "    else insert(xs.head, isort(xs.tail))\n",
    "\n",
    "def insert(x: Int, xs: List[Int]): List[Int] = \n",
    "    if (xs.isEmpty || x < xs.head) x :: xs\n",
    "    else xs.head :: insert(x, xs.tail)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mlist\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m4\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m0\u001b[39m)"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val list=List(4,6,1,5,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres141\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m6\u001b[39m)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isort(list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.5 列表模式\n",
    "列表也可以用模式匹配解开。列表模式可以逐一对应到列表表达式。我们既可以用List（...）这样的模式来匹配列表的所有元素，也可以用：：操作符和Nil常量一点点地将列表解开。\n",
    "以下是第一种模式的例子：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36ma\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"apples\"\u001b[39m\n",
       "\u001b[36mb\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"oranges\"\u001b[39m\n",
       "\u001b[36mc\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"pears\"\u001b[39m"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val List(a,b,c) = fruit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List（a, b, c）这个模式匹配长度为3的列表，并将三个元素分别绑定到模式变量a、b和c。如果我们事先并不知道列表中元素的个数，更好的做法是用：：来匹配。举例来说，a :: b :: rest匹配的是长度大于等于2的列表："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36ma\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"apples\"\u001b[39m\n",
       "\u001b[36mb\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"oranges\"\u001b[39m\n",
       "\u001b[36mrest\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"pears\"\u001b[39m)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val a::b::rest = fruit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 关于List的模式匹配\n",
    "如果回顾第15章介绍过的可能出现的模式的形式，你会发现不论List（...）还是：：都不满足那些定义。事实上，List（...）是一个由类库定义的**提取器（extractor）**模式的实例。我们将在第26章介绍提取器模式。而x :: xs这样的“cons”模式是中缀操作模式的一个特例。作为表达式，中缀操作等同于一次方法调用。对模式而言，规则是不同的：作为模式，p op q这样的中缀操作等同于op（p, q）。也就是说，中缀操作符op是被当作构造方法模式处理的。具体来说， x :: xs这个表达式相当于∷（x, xs）。\n",
    "这里透露出一个细节，应该有一个名为：：的类与这个模式构造方法相对应。的确有这么一个类，它的名字叫scala.::，并且就是用来构建非空列表的。因此：：在Scala中出现了两次，一次是作为scala包中的一个类的名字，一次是在List类的方法名。:：方法的作用是产出一个scala.:：类的实例。在第22章将会介绍更多关于List类的实现细节。\n",
    "使用模式是用基本方法head、tail和isEmpty来解开列表的变通方式。例如，我们再次实现插入排序，不过这一次，我们用模式匹配：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36misort\u001b[39m\n",
       "defined \u001b[32mfunction\u001b[39m \u001b[36minsert\u001b[39m"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def isort(xs: List[Int]): List[Int] = xs match {\n",
    "    case List()   => List() //如果是空列表则直接返回\n",
    "    case x :: xs1 => insert(x, isort(xs1)) //如果不是空列表，调用insert函数，参数为列表head与tail的递归\n",
    "}\n",
    "\n",
    "def insert(x: Int, xs: List[Int]): List[Int] = xs match {\n",
    "    //如果发现xs为空列表，说明已经是最后一个元素了，返回以该元素组成的List即可\n",
    "    case List()   => List(x) \n",
    "    //如果xs不为空列表，比较传入元素与xs.head的大小，如果传入元素比xs.head小，返回原值，否则\n",
    "    case y :: ys  => if(x <= y) x :: xs else y :: insert(x, ys) \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mlist\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m4\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m0\u001b[39m)\n",
       "\u001b[36mres145_1\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m6\u001b[39m)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val list=List(4,6,1,5,0)\n",
    "isort(list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通常，对列表做模式匹配比用方法来解构更清晰，因此模式匹配应该成为你处理列表的工具箱的一部分。\n",
    "\n",
    "以上是在正确使用Scala列表之前你需要知道的全部内容。不过，Scala还提供了大量方法，捕获了列表操作的通用模式。这些方法让列表处理程序更为精简，通常也更为清晰。接下来的两节，我们将介绍List类中最为重要的方法。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.6 List类的初阶方法\n",
    "本节将会介绍定义在List类里的大部分初阶方法。如果一个方法不接收任何函数作为入参，就被称为初阶（first-order）方法。我们还将用两个例子来介绍如何组织操作列表的程序的一些技巧。\n",
    "\n",
    "### 拼接两个列表\n",
    "跟`::`操作相似的一个操作是拼接，写`:::`。不同`::`,`:::`接收两个列表参数作为操作元。`xs ::: ys`的结果是一个包含了xs所有元素，加上ys所有元素的新列表。\n",
    "\n",
    "这里有一些例子：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres146\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m5\u001b[39m)"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2) ::: List(3,4,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres147\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List() ::: List(1,2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres148\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3) ::: List(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟cons类似，列表的拼接操作也是右结合的。像这样一个表达式：\n",
    "`xs ::: ys ::: zs`\n",
    "会被解读为：\n",
    "`xs ::: (ys ::: zs)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分治（Divide and Conquer）原则\n",
    "拼接（:::）是作为List类的一个方法实现的。我们也可以通过对列表进行模式匹配来“手工”实现拼接。我们建议你自己做一下尝试，因为这个过程展示了用列表实现算法的常用方式。首先，我们明确一下拼接方法（我们叫它append）的签名。为了不把事情搞得过于复杂，我们假定append是在List类之外定义的，这样它就需要接收两个待拼接的列表作为参数。这两个列表必须有相同的元素类型，但这个类型具体是什么并不重要。可以给append指定一个代表两个列表的元素类型的类型参数[3]来表达这层意思：\n",
    "```scala\n",
    "def append[T](xs: List[T], ys: List[T]): List[T]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要设计这样一个append方法，有必要回顾一下对于列表这样的递归数据结构的“分而治之”的程序设计原则。许多对列表的算法都首先会用模式匹配将输入的列表切分成更小的样例。这是设计原则中“分”的部分。然后对每个样例构建对应的结果。如果结果是一个非空的列表，那么这个列表的局部可以通过递归地调用同一个算法来构建出来。这是设计原则中“治”的部分。\n",
    "\n",
    "把这个设计原则应用到append方法的实现，我们要问的第一个问题是匹配哪一个列表。跟其他方法相比，append方法并不简单，因为我们有两个选择。好在后续的“治”的部分告诉我们需要同时包含两个输入列表的所有元素。由于列表是从后往前构建的，ys可以保持不动，而xs则需要被解开然后追加到ys的前面。这样一来，我们有理由选择xs作为模式匹配的来源。匹配列表最常见的模式是区分空列表和非空列表。于是我们得到如下append方法的轮廓：\n",
    "```scala\n",
    "def append[T](xs: List[T], ys: List[T]): List[T] = xs match {\n",
    "    case List() => ???\n",
    "    case x :: xs1 => ???\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "剩下要做的便是填充由???标出的两处。[4]第一处是当输入列表xs为空时的可选分支。这个case当中拼接操作可以直接交出第二个列表：\n",
    "```scala\n",
    "case List() => ys\n",
    "```\n",
    "第二处是当输入列表xs由某个头x和尾xs1组成时的可选分支。这个case中结果也是一个非空列表。要构建一个非空列表，我们需要知道这个非空列表的头和尾分别是什么。我们已经知道结果的第一个元素是x。而余下的元素可以通过将第二个列表ys拼接在第一个列表的剩余部分即xs1之后。\n",
    "这样我们就得到了完整的设计："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mappend\u001b[39m"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def append[T](xs: List[T], ys: List[T]): List[T] = xs match {\n",
    "    case List() => ys\n",
    "    case x :: xs1 => x :: append(xs1,ys)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres150\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "append(List(1,2),List(3,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "第二个可选分支的计算展示了分治原则中“治”的部分：首先思考我们想要的输出的形状是什么，然后计算这个形状当中的各个独立的组成部分，在这个过程中的必要环节递归地调用同一个算法。最后，从这些组成部分构建出最终的输出结果。\n",
    "### 获取列表的长度：length\n",
    "length方法计算列表的长度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres151\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m3\u001b[39m"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3).length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不同于数组，在列表上的length操作相对更耗资源。找到一个列表的末尾需要遍历整个列表，因此需要消耗与元素数量成正比的时间。这也是为什么将xs.isEmpty这样的测试换成xs.length == 0并不是个好的主意。这两种测试的结果并没有区别，但第二个会更慢，尤其当列表xs很长时。\n",
    "### 访问列表的末端：init和last\n",
    "我们已经知道基本的操作head和tail，它们分别获取列表的首个元素和除了首个元素剩余的部分。它们也分别有一个对偶（dual）方法：last返回（非空）列表的最后一个元素，而init返回除了最后一个元素之外剩余的部分：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mabcde\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m)"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val abcde = List('a', 'b', 'c', 'd', 'e')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres153\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m)"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.init"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres154\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'e'\u001b[39m"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.last"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟head和tail一样，这两个方法在应用到空列表的时候也会抛出异常：\n",
    "```scala\n",
    "List().last\n",
    "\n",
    "java.util.NoSuchElementException: last of empty list\n",
    "  scala.collection.immutable.Nil$.last(List.scala:632)\n",
    "  scala.collection.immutable.Nil$.last(List.scala:628)\n",
    "  ammonite.$sess.cmd24$Helper.<init>(cmd24.sc:1)\n",
    "  ammonite.$sess.cmd24$.<clinit>(cmd24.sc:7)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不像head和tail那样在运行的时候消耗常量时间，init和last需要遍历整个列表来计算结果。因此它们的耗时跟列表的长度成正比。\n",
    "最好将数据组织成大多数访问都发生在列表头部而不是尾部。\n",
    "\n",
    "### 反转列表：reverse\n",
    "如果在算法当中某个点需要频繁地访问列表的末尾，有时侯先将列表反转，再对反转后的列表做操作是更好的做法。下面是一个反转的例子：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres155\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.reverse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟所有其他列表操作一样，reverse会创建一个新的列表，而不是对传入的列表做修改。由于列表是不可变的，这样的修改就算想做我们也做不到。现在来验证一下，在reverse操作过后，abcde的原始值并没有变："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres156\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m)"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "reverse、init和last操作满足一些可以用于对计算过程推理，以及让程序变得简化的法则。\n",
    "1. reverse是自己的反转：\n",
    "> `xs.reverse.reverse` 等于 `xs`\n",
    "2. reverse将init变成tail，将last变成head，只不过元素顺序是颠倒的：\n",
    "> `xs.reverse.init` 等于 `xs.tail.reverse`  \n",
    "> `xs.reverse.tail` 等于 `xs.init.reverse`  \n",
    "> `xs.reverse.head` 等于 `xs.last`  \n",
    "> `xs.reverse.last` 等于 `xs.head`  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反转操作也可以用拼接（:::）来实现，就像下面这个方法rev："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mrev\u001b[39m"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rev[T](xs: List[T]): List[T] = xs match {\n",
    "    case List() => List()\n",
    "    case x :: xs1 => rev(xs1) ::: List(x)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres158\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rev(abcde)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不过，这个方法的效率并不高。我们不妨来看一下rev的时间复杂度，假定xs列表长度为n。注意会有n次对rev的递归调用。除了最后一次之外，每次调用都会做列表拼接。xs ::: ys这样的列表拼接所需要的时间跟首个入参xs的长度成正比。因此，rev的整体复杂度为：\n",
    "\n",
    "`n + (n-1) + (n-2) + ... + 1 == （n+1)*n/2`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "换句话说，rev的时间复杂度是入参长度的平方阶。这跟时间复杂度为线性的可变链表的标准反转操作比起来很令人失望。不过，rev当前的实现还能做得更好。在331页的例子中，你将看到如何提高这个方法的执行速度。\n",
    "\n",
    "### 前缀和后缀：drop、take和splitAt\n",
    "drop和take是对tail和init的一般化。怎么说呢？它们返回的是列表任意长度的前缀或后缀。表达式“xs take n”返回列表xs的前n个元素。如果n大于xs.length，那么将返回整个xs列表。操作“xs drop n”返回列表xs除了前n个元素之外的所有元素。如果n大于等于xs.length，那么就返回空列表。\n",
    "\n",
    "splitAt操作将列表从指定的下标位置切开，返回这两个列表组成的对偶。[5]它的定义来自如下这个等式：  \n",
    "`xs splitAt n 等于 (xs take n,xs drop n)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres159\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m)"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde take 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres160\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m)"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde drop 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres161\u001b[39m: (\u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m], \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m]) = (\u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m))"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde splitAt 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 元素选择：apply和indices\n",
    "\n",
    "apply方法支持从任意位置选取元素。不过相对于数组而言，对列表的这项操作并不是那么常用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres162\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'c'\u001b[39m"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde apply 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟其他类型一样，当对象出现在方法调用中函数出现的位置时，编译器会帮我们插入apply。因此上面的代码可以简化为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres163\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'c'\u001b[39m"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对列表而言，从任意位置选取元素的操作之所以不那么常用，是因为xs（n）的耗时跟下标n成正比。事实上，apply是通过drop和head定义的：  \n",
    "`xs apply n 等于 (xs drop n).head`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres164\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'c'\u001b[39m"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(abcde drop 2).head"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从这个定义我们也可以清晰地看到，列表的下标从0开始直到列表长度减1，跟数组一样。Indices方法返回包含了指定列表所有有效下标的列表："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres165\u001b[39m: \u001b[32mRange\u001b[39m = \u001b[33mRange\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 扁平化列表的列表：flatten\n",
    "flatten方法接收一个列表的列表并将它扁平化，返回单个列表："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres166\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m5\u001b[39m)"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(List(1,2),List(3),List(),List(4,5)).flatten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres167\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mArray\u001b[39m[\u001b[32mChar\u001b[39m]] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[33mArray\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'p'\u001b[39m, \u001b[32m'p'\u001b[39m, \u001b[32m'l'\u001b[39m, \u001b[32m'e'\u001b[39m, \u001b[32m's'\u001b[39m),\n",
       "  \u001b[33mArray\u001b[39m(\u001b[32m'o'\u001b[39m, \u001b[32m'r'\u001b[39m, \u001b[32m'a'\u001b[39m, \u001b[32m'n'\u001b[39m, \u001b[32m'g'\u001b[39m, \u001b[32m'e'\u001b[39m, \u001b[32m's'\u001b[39m),\n",
       "  \u001b[33mArray\u001b[39m(\u001b[32m'p'\u001b[39m, \u001b[32m'e'\u001b[39m, \u001b[32m'a'\u001b[39m, \u001b[32m'r'\u001b[39m, \u001b[32m's'\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fruit.map(_.toCharArray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres168\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[32m'a'\u001b[39m,\n",
       "  \u001b[32m'p'\u001b[39m,\n",
       "  \u001b[32m'p'\u001b[39m,\n",
       "  \u001b[32m'l'\u001b[39m,\n",
       "  \u001b[32m'e'\u001b[39m,\n",
       "  \u001b[32m's'\u001b[39m,\n",
       "  \u001b[32m'o'\u001b[39m,\n",
       "  \u001b[32m'r'\u001b[39m,\n",
       "  \u001b[32m'a'\u001b[39m,\n",
       "  \u001b[32m'n'\u001b[39m,\n",
       "  \u001b[32m'g'\u001b[39m,\n",
       "  \u001b[32m'e'\u001b[39m,\n",
       "  \u001b[32m's'\u001b[39m,\n",
       "  \u001b[32m'p'\u001b[39m,\n",
       "  \u001b[32m'e'\u001b[39m,\n",
       "  \u001b[32m'a'\u001b[39m,\n",
       "  \u001b[32m'r'\u001b[39m,\n",
       "  \u001b[32m's'\u001b[39m\n",
       ")"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fruit.map(_.toCharArray).flatten"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个方法只能被应用于那些所有元素都是列表的列表。如果我们尝试将它应用到不满足这个要求的列表，我们会得到一个编译错误：\n",
    "```scala\n",
    "List(1,2,3).flatten\n",
    "\n",
    "cmd42.sc:1: No implicit view available from Int => scala.collection.IterableOnce[B].\n",
    "val res42 = List(1,2,3).flatten\n",
    "                        ^Compilation Failed\n",
    "Compilation Failed\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 将列表zip起来：zip和unzip\n",
    "拉链（zip）操作接收两个列表，返回一个由对偶组成的列表："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres169\u001b[39m: \u001b[32mcollection\u001b[39m.\u001b[32mimmutable\u001b[39m.\u001b[32mIndexedSeq\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mChar\u001b[39m)] = \u001b[33mVector\u001b[39m(\n",
       "  (\u001b[32m0\u001b[39m, \u001b[32m'a'\u001b[39m),\n",
       "  (\u001b[32m1\u001b[39m, \u001b[32m'b'\u001b[39m),\n",
       "  (\u001b[32m2\u001b[39m, \u001b[32m'c'\u001b[39m),\n",
       "  (\u001b[32m3\u001b[39m, \u001b[32m'd'\u001b[39m),\n",
       "  (\u001b[32m4\u001b[39m, \u001b[32m'e'\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.indices zip abcde"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果两个列表的长度不同，那么任何没有配对上的元素将被丢弃："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mzipped\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mChar\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m((\u001b[32m'a'\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m'b'\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m'c'\u001b[39m, \u001b[32m3\u001b[39m))"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val zipped = abcde zip List(1,2,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个有用的特例是将列表和它的下标zip起来。最高效的做法是用zipWithIndex方法，这个方法会将列表中的每个元素和它出现在列表中的位置组合成对偶。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres171\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mChar\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m(\n",
       "  (\u001b[32m'a'\u001b[39m, \u001b[32m0\u001b[39m),\n",
       "  (\u001b[32m'b'\u001b[39m, \u001b[32m1\u001b[39m),\n",
       "  (\u001b[32m'c'\u001b[39m, \u001b[32m2\u001b[39m),\n",
       "  (\u001b[32m'd'\u001b[39m, \u001b[32m3\u001b[39m),\n",
       "  (\u001b[32m'e'\u001b[39m, \u001b[32m4\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.zipWithIndex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "任何元组的列表也可以通过unzip方法转换回由列表组成的元组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres172\u001b[39m: (\u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m], \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]) = (\u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m))"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zipped.unzip"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "zip和unzip方法提供了一种方式让我们同时对多个列表进行操作。在16.9节我们还会讲到另一种更精简的方式。\n",
    "\n",
    "### 显示列表：toString和mkString\n",
    "toString操作返回列表的标准字符串表现形式："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres173\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"List(a, b, c, d, e)\"\u001b[39m"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.toString"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果需要不同的表现形式，可以用mkString方法。xs mkString （pre, sep, post）涉及四个操作元：要显示的列表xs、出现在最前面的前缀字符串pre、在元素间显示的分隔字符串sep，以及出现在最后面的后缀字符串post。\n",
    "\n",
    "这个操作的结果是如下的字符串："
   ]
  },
  {
   "attachments": {
    "f5e402c0-ac1f-4615-a802-4f0f295c9b30.png": {
     "image/png": 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kyJNOOgln7eyzz4bMoIAIFxTDPVdffTU/odafe+45gg8CEZ7h5muvvfajH/3o2GOP/cpXvqL4vfjii6hv4pVXX30VNUdEgm0gIgFrzUWdVzAM0IzpMaiWyedlZe6glM8777xf/vKXxEYgBadynXXWAQtM4eijj0avwY633367VUnYEuCfOnUqWIb71157bf5ijaLwCQw89NBDL7zwwre//e2vfe1r4a+ZqZiWG0jQIVUV8iTUuuuuu9R0Po/Tyq9oKLQkJpBZAJsZgCZ2i35uuOEGoCXgU5hNhuiIafuF0/sEdhdccMGzzz770ksvmZZZbLHFzjnnHDwas8mS8qKLLnr00Udff/117m+11VZbb701j0HBE088EXox99NOO43Or7zySjw7eh6dWyMgbVbcHXnkkVxPnDhRP675K73SwmxHoRpR7zbbbAP+v/GNbyhRriS57A/bWDkmsX7xi1/A1Qi/qf+BAweCE/hkmWWWAX4NPx2efvrp+ExEz+BwxRVX5AGYAeJedtllUJPHkIuf/vSne++9N9wCYjEMROH4Mc0TOE3oq5RCRNTB7373O3jy3nvvxZmgT2AGBiQF1oW9mc7gwYMPPPBAQIIb0WWTJk3CHDLZhRdemHABvbbFFluksmLEX1gCqAgyGFSXheHgkLvvvnvChAkwD2pljTXWGDt2LK+DB3o2btt1111HjBjB0DyJCN98883d4q3JfFMll6PR4l/UggFN5A+irhJlcu211zJ3CMp92BXlg8iIqBVWWIGJoAevuuoqeBX8c40mAXL+6mIyF3ge3sajZwogECLCAFOmTAFgWIULOBZCq+tQXMCgFyt6dct4lwswfOmll0IOut19990BphejLr1GNQlYJQJDR4EZoNUkiLrILUF0/GNIhgjPicTBmaeccgpPIhrW9ZkpiWIfA4np06fD2Ig/c588efLjjz++77774g5+61vfAsPbbrttyvrWzBMmFoZE58Bv6Ldhw4YNHz6c++jMr371qxCR+B41y1zwERmaTtCQJ598solKiIvW0nNi6COOOCJl/wbGg9NMWugidLsG0SxhaHoU7Yz5efnll4GDAR5++GFC2qeeegpuWH311RFX6PrNb36TUANrdP/99zNb7BbzX3bZZRdZZBEMyZ577okmBT6UJjAxT5Qsv95yyy177LEHDIrSNDiIYsWuDU2EGCNsUahqZTMzNIvoUjwgvfLKK0Tc9AMKVNmutGM5UDE8g0Y45phjLrzwwo033hjaAxivwMoPPvgg901NpOw4gFzYFGMD+sRGUBpDiNQttdRSUQUEhbDQRCoYbNe3TacIA+NCWpQL2uonP/lJKvFio9wajIVCgQlc7VeenbuumXJu3SB8sP322zMccggMYPj666+HUyEWMiyf8RPYBiewDmAjhBgbPImLL76YnqEynfDTjTfeeNttt4FS3Do4+KCDDmJQRLoRn7icA18agkTJXJNcWW+1TqYL5kRCmAXG2LViQwHDFDjHvJzkQywRRXQZKnjQoEF4MOAKrQQnINt6oFAK1oUKLlLiFXEBA6MNwcmQIUOwE3ARXV133XU8/+Mf/xhxgLcZlycZq1q71Kk1oa+YNGmBZOGuMalbb70VH8jcr7VejALkP/zhD7EuDASXMgVIjPqAw9GzKB0kC+EFNh5ATiEKkwJRO+20k8rOKA1XbP3114dv4Qd0HKO4rYVnCGFRkcgFpoI76AEwgCg1wlsjYkX5u45XKCNuunxbrajUDd1rr71gRXxiWPexxx7DlqBGMMywNFEI5Pv5z39ODMQ0gQH5ZbJWNxBTmpNH52Kk0QmoSDCGS4EXgu1H70NQc1z/ys06AvgHcUZX8C6EM2jgV1QNSAO3/MRfLCVQLbHEEjvvvHMv8HFuerqiIpJsAGCkZbFb1I6CIiwcfj/6FhbCVBvENAm5ICioAy2x4FTFtqlCXse0oJBxF5555hlUOmocJYkrAw8QYwwYMADzAyYBBrRjtwhUjj/+eDrBkOPc8C4WCDKBRrCEGwf+sV5QBO4dN24cQgQC0T/wA34h8wLnUAHYIDHKE8pqriLtYZDXgwpD4xiTjNtttx3TQCH+5je/YQDrGjGzMNY999zDBdyAgMG+wA0bMQxgqet5mAhDGcZ/h/VBClxO57irsMU+++yDH7f55pu7Tuvo7mtxD4p1Vv5r/jflVBvKKLJbamf6hIorr7wyr+NNY3hWXXVVUIZ8ghr4GCtipQOCB50QOUvtUXa41USHZuGNZ2EUSAhUeBBRTW7JdcoynHKqwdpxIAfvrhVxh+f9N2JeukXFcA1+dIRTqRPTy3Y9MyqFXMawRFNRt/NYfJaJZW7cf0Qd99PqR9CC7wmjuM3FBMgBBxxAh4xujdyYMWNQVehZOAmkIQYoOwbFRcWnxr3iRWwtCpquYMpUVrxD0uB+kG+RtDQKr1m7FYUbqezdUfx0UCwtic008mvciboy3YIoaXHhutNKskOAB/cY8W+sNoVw6tlYNwR+YF2GgOKofv79fm7oI1+3EvWoo47CB8IyEU9wf7/99oORUH8EAdgD2GDTTTdFqyLeoAt3TWcFHYF8uvypz9RT+pqCM0/CHaINfB3sIq4epoIQRwsEg11yySU6VVacY+fQICkn1lAW0BqBFW/mDHnsvvvu45qYzOVAF9LVeoRoSPEqq6yCAcBlUcyZIFPDXPkYr6MHmLJ4wwD84Ac/QHlBF/pXTJRWgAzLbcpO7aNQA4lQmQCMkkigFWNoElwE/HqYkCdXW201pBX2RhEROKK4ESIsx5tvvokDwTTBId4bNhgPG45NeXUHl4v+cciwstxBmUJKAgv8ANPawM9EGBelDDYwfpDYUmrdr8hAQvR1110XkLhmykBC4KvpikKbKsM3bzJquFYpRxuWQigaoqi1bHWy4izUowyD48UD8CdhgKxe3VJpctXndRcgjWle8wF6Er7oEPYAYtEkRCA4tXj2zBpIUKQYIZQD6KUHlCo6B34DpQyEHgAzWCw4AZwAmJkbgMTmWdmA7sUBIpKxgJPp4GwBBq9DzeWWWw4zLBtYMae2CRvWtTUrBot4DbUOv0J1oIm6Uty0SbmttdZa3jQnjhWBt3gXNkKfMnODU2wegdrgwYNxi1JZYgFi4CbccX2Cx7BD4BG2M3ONTXZ/EsgyJU2f3LS4yCjbsMZ8qMU56CCcEUIcnAhYk2DrhhtuMLOXcpqRCyaF5KN9TObihzJo2C2XlBlLmxS+T3iOyp5DxwYgXl966aWJDglAEVoJIGfwKxSFbAibrq68GPW+yjZkM4XCX7PbeMFWrNGhVsf1fC900FxfYTrQCH41fcy/6K/Zec8WJgrM4ATFBm2wiriC0ilTpsD6dqibggpQ/LC1GHWYmIDSclB9UotIQf7TTz/NpEy1G/gyd4sz8Z7gbO4wrjnuVLzCENfQ7CGWsU5mqGRlP3SpLoGYL1LS6BmMAR6I0gsBS7gpUpBraOd6iUqTh3kGyJkXDyBXeJEmN1JOSjMdSAYOMRKEUOhxUJryYgO0xpAjnES0aFIQ4lZZWJp+ImjABCLPSDI61xr9HtFXG2DdUOx8AGbCOBQ0Ti5QoXwh7lNPPWV8Zm0UgkPMhD5FTRsz4RQiBa6KMWX3bDhQe95DJjO3le2ljEvwfdFFF2299dabbbYZ1hHRRkCw027tEg8g57TTTgNphB0yP5aASMh9cmrPqEARfvMEVk5ZzRH6yF1i8pt/LfxBeOEx9SYPAzOEYAqgi1f416wXRMENdaUHTQLHvvTSSzJPR95YyTRBCP+iIulwvfXWw7EAUcipaR6LGGloFUkjNmLPk/UITBCDnbLTDFfwK52oCnREUim9geEZN4r7OzX6BGbgl6XDtbUSJBbbqqc9KBG6gxohZd8QHLAtWTIhRAMACKFriz/KBZ7KX3NjvvCJS/uxnteoabcMD/BpuIO2ly3x+cA2+iS2/APw7rvvvueee1544YWEKHCs9w/PTSMEVLCx7C25QTggMfGoh0hl65SHV5hJ7rbIsJnp0tVlgAUXXFDCgCxDaRCNzIM+GCXQ7VvQmJ+0TIg3jCXGkTcLOojWFTk6R7QQBphAfcfNqDCE/ONzM8/jgjkRlZsDaAQHxGqpsiTIbJ02OMJ8IoG4w8gY7jOBhXypHsF3w56NGjUKTYQPhSaCNji2sVnPvwwdEuUdQ1eX0N0ZLueZkIEM6G4R5SwslLKQ0vjMvfGiS8hTqQ6Cz1AK6A5NrI0INaJ7l09dJ4iFVq7xARFLNC9OMYIKSyFdRPqpbEUi4uQvsOHpqDcZ+tlnn+UBburamBXBsdBmQzsQtfjii2OfiKfdDOReTlGBhcDI4fTxL7/iCnBz9dVXp0MuUHmwKZaAnhn6g9yiuEvf0C0TWq/Y1uPhBdYm8KKqJNKP/fNpJrFDAEVw5plnIkgAHxiDlNy38AE9hRYWn5ZKWkkPV8ASv84N+QSBa6yxBroYVke2edFsBggh2BI83nrnnXfcCKXnZNE5b+kKaMJxFwCSiNZgUZs95/SNY2Jml1MPXAzABl966aXYkm222QZM4vxin+h/Vjm2AH1B5/zKfaaGvVlppZXg7ZBNBkUqXUYKJo8UvUUc3IFwOCunn366i0k42m7HlldhLSw3toppBt4wGIAH3qwNi91mwl/dUZRKabX4dPeCU3adX/lCyZgwOOGEE1COSJahNqgg+jFQaynnfeCFmAMI/R4aiRZF/K4uo68QQOxWdWdFaznrQF+zrWxIV8k6d9w7ON+wEgbQR5eOskcs10EdRIAhulWqd955J1Lg1qPwwPQt9GyiVD2yFEZjUeEiYLyLbTC0TR+u2IoaUZgQCSUc977Vc5YdpFyvcc899zSKEY1btEx0iKHCE0VjWP+CQoCXxEnK/gd45kl6Q3Cscd9hhx0w9sTKiBghBKwIcxIhuGvWVQZLW5UU93VpgON0iyZlk80OgjLJkIqGFWUGoRZSW1StJwVecIhSNhsWaGlFXdHR56JPl+xC7/AiooL0WjQFIqCTmRMQtOOOO4Jfa+txJ88++2yE02MpQBPyKSTu7Y0jpuiBVwgpCGCfe+45+Iwh1IAGHNzZaqutsIJjxowh4MME4sMC4V577fWzn/0M5aXn684YXoEwqsswGHQF2WDfZ555RnVjCQ0N1xi7teiii/Yp21ZSSXNZeR+6OGr3FWaehzl22203LKhbHAiucd6POOIId+8b26VsP9Q+bl2A/OgRHCIUCg8T3d577708RriJOsOG+aTI110Vw2B16NChWBezczzmnk2aVGZE9yoxcRgrVuY0ObyIWqcTYGBq6Dju77vvvvbA8zwglSOGMAciz7h7w4DDHJo10BF4RQWXwEf1v7gySmMuWCZcJRMgIB83BWlx4ZpfiYFSCe/iYBsmteKKKz7wwAN4iBgSeOCWW27hJ3Q9wgbYFpKlbEvwq5ysvjAeD3ba1JZ74VvzEQAR2OnH6DJbftlT+sZuk+rqtJ4vM8ULwb2Q+dXdEAuWZuIoCMwbkvL8889fddVV2FQ0F76w6KIHyw0YOmrMotJH51ceQL9guhgI/09Hx90/ujI4o8jLlVdeef/994M3OkSULr/8clBkQblq1Iyuo/CiHpuaKIrjUzkzQg3j86ACK2jlOioy5dqEtry/FbFlFiAqzoLhFdMkliPOygfZRBoZ7YlnA4ZhS+DBbBCq6tLxjNgwdyc7OX0T7LKomx1TWXnSykJrI9c4EqKjnM3WljdTwyE33nhjt3oVLKnutdzV4+icjppBqCJ56LtqHovFQZrxdLUQUf0W1zgxRDxudIFDTj75ZK4POeQQOozET0T2nRoYwMgJqjuI8U2jJpPpC7BsrycXzO9GJrhi6tSpMAbyCM9ce+21aNcRI0aMHTsWxzG8du2IlYepbF13x1TMelY5z6jaGpquavbT6iB9KCUf84geND+GksKQuNwqjd3G7wqQGooZggj+xUqhL9wyoulSH0khqRVF/fhTMEEkhU899VTEHqxVT8GClausoB/KM7fddtsNN9wwfPjwCy64gPCLawkGbAxN/1gX0MrDRH6IKLKK8w6xR44cmUoKmGdQYfgR4Dow4FjqZYuCrJBRCJmIG0H6lmMPnRpPYrNBDl1p1PUvOsrZUdIedQMMpu+wRryFq6L0MlNL8NsqhyiKB/BJsLvddtsRhuLREHsR8eDsgCh8ZDhJXsETJ9z0sAxXfWJ9Re8Y7Bm+6BbB8fzLMxCCTkLTWRsCPMOGDQtaTJw4kX4gUKoU04sc1wCU84j9jSpMo0WdQhQ7pZwM1CS4g0KZEW/aWjcI4/IzO1dKIBaSAwzS2k3uFt06O+GhTybIzZ/nhn+DmsYxQhfjG+JaMhx+D8PBtIic+yWs8optvymbE/VX/3y2FrNDho0+gUqU9pS+iJKa3b1ZJr7M76F0wPaoUaPQBUcfffSuu+7qogINliZS2Sw3XiFQhtAwAA8zI0ymkssU0GueJ2RUOrOcKya9jHhwejCxeEL4joMHD2Yu0qVvPqcKTtg7NwykeMMJWHvttfEbrI5xibdaMmBdideR+dFK8YpOZ+yZA0JTkbAfwsugHtLm1rfY9MaLYA+r31HOADMtb2RsTDZ+/HiQj1HHnCMjCCAmH2FP5WQpXYRUNjl5SKmxIB26PcBdPUpEyo5j/3zcERGJ6dNZ5QDJWJ7ElcTJ6FavSlYVdJ98dp3Lq9o/AXAgvaLIt0fZkTEK2MBvBhjTJKlU9zB39aECQkwcZ4yhP6EylJKvwnh021xo4F3rYtx6C2xofkXVbRVvvvmmJ5/1zwf0uIyqauIn6Eh4sP/++xPVwCQw1XXXXUdQAfNYBSNuY0Rop9qpbhSpbnSptmamK17TAVQR0KwtRieCMqvDUw4sjM0xaYbYhlxxXAVihoq5/fbbYfflllsuzuTVHrixQK+tfzni1sBWNlIjqATpH75BTXjukb6SOkWPAz96gw02wMtAMSGoaB/YF2svlhXChx56yKJ8cM2TuOF4BGixmeVkIwRjyJAhDz/8ML3pvItrCx/gD5iA+Oall17C21VWcXUhwGqrrWYP8nGMiNPHi+4lNASJreNGih5hEDGy3qupdh1Sff84OMCHUdaWqJ5//vl0CHKYCNoHe4MNEyEoIDrBU8YP1eja1BdKoMoFNgWNXk+fPh19hBy6gS/yG6o5PfE4kShqUkSgNu9juQEzQKJlVBMoEeblELHW5aYl0/EL5JbK7j3DWZ587bXXAN5duu+XU55T2fnBv1iFiNU8iK8j7+jUMPTLB4NpaYgXmTXRQ8opOzgThkHFo46BDQjxGWFsJA3PcZlllgl3Suq4d5Xe1Kqugas48Jm4HjRokDnPVGz2HNJ3VtmlHkt6khtxO+aYYwCP5x999NFx48Zhk0ywQIJXX30VjeA+LWBAvoiH9tlnHx6DgsyLfsAtSGAu99xzz5QpU1y9CD8g5bSPdZLLL788ZnL99ddfd911iTKJDqGdUKF0oAXSBIGWWmopBgVvIHDatGkp76bysBK6RUIRBzoHGEL/VI5YNEESZAJmbVJbORvaKgncLMbF48QYt5XzSCFZnD1oM8vnUeCgHYTgaKqgIDp8hTuC8K611lp4IZgTS6V0nT36yLhNdrKEJ1b1PECrNR/tEVuhDfskjXrcmEDbE35SI72aSlbcLI5eY2TLI6Ou+p1VjrOJF+UZWQIi8i+mSzNsHGnA4OZfHQJTOx68aTZCgUolWdoITlQuAuVeZrgazEAL6bj66qvj9+MQgFiVPzdxmIDZnZ30jN8zdOhQAmVohzcP5mEYtB8uEap4RjlbTnEwu+PKlMvb4N/Qua3BoQ0NTdescppvyiUVjmFkB4WuueYatPaqq66KXkt5TQikYFrFjlkdK81kBS6wwKNHj95pp51233338847Dyj1tiAAvEg/ppXb8qEb6sH5y7HBTMa1FimNYxgbBnW+UtbCBnmAgdDik2K3cBkAFXE98cQTETCCklgffvzxx92dp5MCnZA6RNF9P8Z/W265JT7aTTfdRG+eXiqTASSGk5tQlHDtzDPP5CeL/pEQRjEPFnEu10B19913M03F2DUGU9iqp3A0UIi66vzEKGZ+uYlRwZGJqqHwRFryUTqo9ahk07MDV4xl4QlCu/322zMXvPV9990Xq8YQbuDFfmsYrA92uQ48oMhwl3iXMN8HojBXM6aHERFklJC15wOOXfnT0MaarZmNc889Fwpuu+22QKV1iawI8QTqD1DRtpYI6h4CAP4H6hiNtuGGG2reTMCaY6QHCAcSBM8MoW6j+2e1r+3laBUgwTCDAWBzvxcv8u+aa64JPK6LHHTQQQceeCDsetxxx6200kqmi++66y74Gfz0zecs9MtH5bpwgtOGqQMGwl/nq0buEX3jfLXI/DAvKILPcdZZZ8E/zO6yyy7Dumy66ab4VUaHrmbxGKwO5t0vgXQgNZ7Tql9Mn5gijDGhEr6aGI6lYoDBOhKaXHrppTgW6J3DDz8cJBx55JEnnXSStOAvbAxglvWaKQFsVAFIQIJkbJ584YUXDjjgACDB19a3S5Xj5QAPjJkXojdkh97iRA+egevcnABaUKCLLrqoxxhid6EFj8FCKftJMhWzw1hyAZdCiIUWWgi8EXcSmiCeHphkNA+B6G1WORTNc4ncGIelxCFAEHARUBcKlETxTAYtgRwVJzBFzi1Sf0ZIjVRrNQfYkg9vM0NowSdIAHuMKFczlikcfaM4+gvNg4RuvPHG1hnG0p2OvvmAVJbhuelxrAYhaEX+1bdrtJikg+41jtHBBx/MEOjVlL1w/BuEAuuFjsUgpbyICFOBNHRmyptZIRBO/y677KKZ93BzfrJIok/ltEmA4WHCBl4HNrrCNMYZYKnyjZEPQdgIv1Gqru8MTmUaQyVdUTQ1iANK4okJEybAfyAaNQqjABxiw8QAQrcOKIcNGwZb4NChmKwzRKHTG2KJbMTQsa4ra7blY3xBNM/onMLlrpA7t/nK+ehuL0CecUuRQyYMeAyBAWd0hAEzwyxa88mEe+211xFHHGGBA0SFa/HOANhx6Z9BgZMQ6sYbbySmQcWrLlVzjLjOOutAS4wizM2U6QFLgJzwpGvLguRCFw4+PISzb6bUpIQhtgvaKTsHSpT8hF/saTefzA2BRIyVE2k5K39IAjgJGi6++GKsGtEVaAdCOJv7xx57rHWDoAhWAxjUH7aciQAeXIICwiSY5XPJEHuMGM/OB6OgCvE2Ro0aFWfE6a4KXp/KN1+AGZ0YCydmVDRaqfJtGuUBFDGXgbn1LWfha/CIEmBi9KDyMKt8hgNyQAVUtjuQrMDuyOf387qKj2uoCTnMQ9JcZAYGponYzChH6XPB/SeeeIKZ8orFk1dffTVzwXaq6AGGifOwRypj7PnVImw4B50O5mF1HiA4wJEEAG3nGmusQfjr3iBPu+gRfVM5RE7ZhgRoBIw9/ZgSAJOPPfYYFISxiXgYDo/EM9iWXXZZesAR5tcXX3wRQYAoHpsZH55ABuGKiRMnnnzyyR4Ab+AFh0P6hx56CPODG2fZxSuvvAKbAQB+HpHW2muvDfD0DAzrrbeeJ3kSyjNNaFqdmhlIfcq2vJc/ss0ICwYeh13jx1vMa+TIkR6jsMceewwZMgRSMgt4FXnB/cKR12EFGwSCN998M68gzsBPjDVixAhCUlgRdfTAAw8wBP7+8ccfLwvBighFKtXI4BmhZjiigT5l2wbDgSWUhj4TkwUhOuJQFssN2xO9wQ8oEH4Ch7AcrwMbGGstH05qLecixiFGXVvUxVgE1F4+0gQRMdVwrLIACSA6IEFZzCRUxiGGuLGweuGFF4LYLbbYor0c+q6E6ou4NOjiZaQ34GSnjAgbh5m47hZOpjl8+HDDeviczhnRYjeuER8UPt4nFgF55BmIgheFr6Cu4EWog0yhbwcNGoSxgL3RkGAMCTXVZF0CFOEmeMYr1Z/GU4F1xaRAdrtfrVmFoV2bBYYzMIlMBgsMpeFj5FleZBp4MdZxMZl++ZMzMETUlLeVo8dBJQyHssCpue+++1wWQk+hwmaXDfad4SuxxbK5xf3quUSRxoG5ccnpDd6K1VqAAVqNhIEgf/HFUEMoL1gfIoGsp556ynBVxWGigH9RpmgKGJ0HXA12q4cKDuOHYFxxxRVWEp966qn8G0cgx/mVUALvFYlCzFJOeKpA4+i/mGY1sTs0t5gm+Eyl7kMfpK18SGLMmDFMHO1jITsjoltBLOhNpbKLJ7H9wAAwOJhw9s4772wiJeW4GQmBs6EO7Dh58mSMMWYbtot4K5Uzl1MJ8/WRlYdNNtnEn/y3ym0xI9865ZRTkEy8/pQlyvPoUlYip512GhqNQU0hhnKBFkCOCgO2PmUDQ5TaxzoKfIhdiXGj9tcH+paPM4GQsWPHIvZoQMjq8WBABcaMR10s4RVUJxJ17733TpkyhfuQg3/hQ11jKYKK5D5KByyh0FdYYQUz7e6U1/TOOX1du4qEB4AhaNARfSQtuE/sRfQM2G46hOIMikm444478HMhJRMETtjeyv5ILdghlhXi4q8gg7HRHo4ivsQW4u0BiZlMUAQP8Ay6Uhph8NDvjzzyCEGVACAggTc/eBHnDaLswCRgV6WbvyDQTZncZMRYC0RmmWnsXESKiYFQ35gHRBtGRQWZuucVQlvAA9VAC4SwIoIP/5gasU6doeEBrN1iuRFQIvhYOIjuWfXt5XQlzBKhIXqWDhF2RvGEMDQD7uxGG23EY24AoOett94a+wq0qrXws0N9NSrbS5WTBg3HvaZPvCiUBrQTUcYupkMBe+WVV3abhz4Zdg6PATdd/lFLxxB226k0F5BM9wU3xmqfDmKUFKSyYRm/B3jALf4rRstcq84fvcEYmHP4DdGAE4jAwDZASms6xCeePn06UQ1OAAYJyuKywKimQLTBYgMjjatNP/RMHIn3oK8T21ossOqEyWZnGLaWT+Ao+QC99957xzqQ1ZMmZ5Zffnl0inrBwirPLG8vHzNMpTyGh+E/qI5oWW8W6d33y2dgGoHUbTPed0kJNgVUnFkBE9QBAwag0XR4dQMZlCdxZGAIhZabaMwQ76gXsMwGQQVa4lzc1W222QZVaw1Myj4dbI3fMbsc5RdHAsZHJnFIDzzwQDQv7KiEW0GQSkFwj+bbqEFvEAt3VsVG/0tmas/b12BBFEccfw4PEZKCNEuGgBk5x72QlJpnVyK77maf6wa6ZpZTsujZFKhfukJbhSXTjY1FZsJ3hEdWnAtgZpePanaUb8GALtgAZ7bTTlJzxeGNLrHEErCQ4moSP2W6xxkQ9IOFmz9/GS/KDUzsNErTN2lugZpRPjqFpMDPKAXzJ0586aWXxl5aGqDUdORPkcGKeDDix5jGVFLUuQgPM8JpQ0egfYjF6Z9ncJmdZvA2boonrqriAz8MDSEs2u6Kt9ZyyAsdWtzUVg58UiHYLY5L24cP+BF7LhmoRvvmI8mZFAratcxYPqRzfkJg+dfCBBCOPUaoTW7Tz9NPP415Ri7Gjx8PAH4fkiEI3dC5liNF/gAmBCH4bS68qTcBg5lGwYUVsCnX7prJiJTa/73R5+x8FJNoaSl7/NXa7seCXd944w0c0PPOO+/QQw/FWQyVZeg2q7tjapu3yBh7zLGWSZFE18HbxpfxzaBYlgNOvBw8DzSGO259a2b5jiWv8LqlsB+UD3jaiZYyhHHhhRfGC0ESQe+7776rjHeUr6HGtrlOrdkZhm6JBxQCFA0VvZhHRk4MSNvzybYWkcfeAlOZFlD4+QZlLMocdN6r35WYXb5e2iO8p7LEpXp1eUmV1y8ftWCEJINaFWOFkn5ZlLelXN/Z8uGzXL12h9PEiRNxK4ixmAihp0voTjDSyh5+6nePZuVzxN955x2iHyIYQvUddtghgoP28u27ntrpJs1o0tqhlvIpL7Gq9VLRyAcml/3ShNIozJYLy6zt5QNgZs+anDHTo/Z++fjyjPyJIBcF/dhKKkoklbrWKJpy10sUmDQvjmrUtDQeVGFtiAm6kHaP0I3CXAGQY+NYGuu7FLmpU6eKPcsXzSdH1cPcGXtDzIi6WvL511HuHGFNLAM4ow/K54+tF4XcsbOwPe/0jzUY8C8f4gKfddZZq6yyCtrQfENEhC429yktYJtZPtnav3yIpCvetNkCE5ap6qmkD4eesa/A5JWW2zL02CQQ6xxWxCjsam23/qgH49OySjTzeu2113Dz1f6uIFx99dWTJk3CeIOEkL4wz3FEdVR1qlKMS/rk3VTqjfBc54LE3Tazyq2V7bd6WnEOgCeeE2nhSeNDo+t1kWMjWipFhj1qSp+FnVoINDzIB73Tpk1DUTNKaz7X0YUxt2lqVMxSyudxcrpIixJWEyQaLddZDCtdJE7lU0RB4uBbc+Ox0NAV8oamS4XFAMgnDi+gvPLKK/p9uGzYUutznKRrHnp/EsANCnHeSSqfF4o6NMM1PayOchZnT/FuUyW1lE2OUTkdTO+akHuzuloLEd23nFsYYaI9GwEQ7eLmYH5Udq5UhRPhRpD58odBJYMHIUOGM844Iz4spOrRlP67fEt07qbcbWst33pPle9mxRlLOuAhIYCK9WrLW9zffvvt0aNHT5gwAZCYI1EX3uvFF1+MRrN8o8kxwT1tyn91A4rqTO9HuyKl3H/Wr3xYQDFWrSxQ+TzrHLbgQ9PX4aDoJEY9epy5nsqaa2yySeU8DqSUt8aNG4c7j7NyySWXgCtge/LJJ5dccknQpRNA/3PxAXiNZThPrmO7YNlWDoD2vlBZUxqSP7N83UN9VNURBt8GKChueO/ss88++uijobLflZ1dPqPTXtlCp0zNLh8Zdwhlv1u8teUji1LJo5g76lM29QuezmW41aq5cDqjikF9YiAYOkRnWoX7QfmKjXVJTry1fE0Gl9/j1f1cEa79e++9hwoePHjwVVddZQBtz1Hc2FK+JR/GVddWxRWLCCZOOvK5X82LCee8OevqzoH4SbSLB0Ku2fkrg23lDJT3y8d+05ydQdWptZYvzKVSooWfff311/Ov5WZoA1RfHMUZ5U5KYip7zPWPVTst5eg+DUHIWnXLRKzmtpRdcW78tYJUEgSTdLtw2CxbhZxAbEJ7oi6GnD59+sCBAy0J9YQLq41F5YzyKZcZ5ezB4An5qa1s4RKaEMIIBo2XG51Y1ah9UD5rImpil1j1mVgTij1q1RyIOrG65Sheby0fSpBrrZJQ9XtQQtT4RkmhMXuUtOqNqqxdnjFdHpHHXHBbt819BeEmmyaaXT7eEYsNoZfDILkr6PTTTz/44INdpLH8FypbHWoV+FxYi25ba+UrVjoNMoYbmAJFoXZ9xdXBqpvWU0dHYxlebTUq7frwzPIluVTylkEmcyOgBbVoeQuAuU1+scUWA6umvPzQw1x8AN6zo5xjR6m9bKkcEZkq+978V3ufKv7KzHxYiUVxxvc6ZG6liJ2XLeUwIUg888Mftu6onG8Ud2b8t6+JOpZWJELVlPncrtrLGWC2tsonvtSGcV/R6BT22UJ4hTCW0FR53PRkkAEDBowZM+awww6bPHlyFB8us8wyxg2paAOlOOpjA8PVTGnAECuRvSW21RFby8c2talhVqNe31rByEhrQhRqeWYuoJIxYtyvf/3reNuE43gzljv6KShNdXxDOZWoSAOj9lOgVLCdUkomqPqU7+e5iKVjFMIVBxe0l8/hpnL2Xlt3h8c3W+uy9gkBcEsafz1yKpX1eTMn+nGpZOGquiA85XBwIqOoExE+TmT5eop6Z6uIzi5nBKTyVVad1j7lc0QzP3xSu8+ncvhYeOUCnMr+QXfjyjfm+iJRIOpDX7h2ZUzmNzajvEfRUk2HYPSiAMS8xIaYr0qjzJ1KPsQvk6lq588fCrJgLGU+EzaeV+Z7y26lyhm+8Z3PlrwJX9fbZ7wjwB9UDs9WXDvK6a49Gjf4MFW+z2l0kkoeNRKt/iR7RPm+r3u8t2hE7ysIYjJlb09j7JaUuXBNYgFAuQgKap8iUSO0/jV70VHqICLxECiKt1rzdrdU9I7ru+7r8Iy0MOoBQ6o4l96380Z4UwPOKp9EVy12lG9520880EkzVJ+JrNTs8kFzm9pG/mwvJyybdTSX26dsDfZUQ+gyZMiQllxlzn3Pn3WICK2MG7RSirA9Vz3dWHlNZT1Sju2tnH+V1i2Vc/RTZipdmdgj6xlp5i1FzvvlM549HTeSTLF0ottqDjnmu0D+MrBbOYPWs8opJPrlYknkt5dNQRKrvfKZ7yggrz5pnlmGCTxI8W7tVmr+0ZNYlDZl6b6r6gbAWKicWU5ZbikHwjpqKvFQ2OQQDDPUqv4q1nqK+lQYq6O7rGM1DdhWObkjQEolp9zJ5YzH+pdPgrWU5ev3c4tXtAdm9j0Eq6OckGtwJmbmy0e1pmxjzB235M/0zcV8u22ySEvZSJQKCSLAr+JWlRGrgHJeyqGbaFT++1WOY+mtFlnv1lyhE/SKr6UEnlMlRPPm7FKCPBfjtpTl5U73Oy1XdBvPhR6R1lYAefjejPK1CNckUJQaWsGeC1D1coIbpVRHTrt1fbhaghE3JbebryOJF+udffLH6iA0oTZ+lZW3pjdNmlUjIec7oxyB2recAFvdD94Vb4GuCFz6lqN+A5hGBSyxlJWKhYicZDxj1Bjui+rPs1UVwz754CvzzIiYR82ifGOvsauSsXwQemNWOdPAVs3BaLCrNSmxHtkrbXYp6qkuWFhAnyoSanLCXWXxTOscfOezUdMXjIONUl618jQJS6BjGcJ8tSsdkQSOFi5I3Fc0ZACnpl6NpGvVd5dDOkpOa2blG/eNWKWh6dKRcYXTcKEln7XDGP3Lp8S9n4rLr+8sOkLFyP1VjRMorjoX4ab1FPWzy0HjHZXmsuqM8hEBIx53UYSLkSoerp3MLKedtlSaghpnTakRYsE2lY+7h/cRasLYSyCNjt3fbuJLBdeLCcPwUiPbIMABw+xSqaHItebiJTnGjISQh4WYWbZVxkdmewVOHbGICeKgrEgLdJQE+uxSWQ4AutiR/uqoZM/msIWf1EkSqh59lXZVaxHJtLa8XcZr1bdaIwIRg2zXcQ3ZGwleoxYsavCUMmVbyumu1fhGTWEZsbnB1vIRjY684Br9qNxDBj1pnngaaN3spe8YeTAFp5O3K/LtKpz9rnirplJiiUsz01FOKog5RjIzwrKOsl4Va+HVLLH21aRZNcPWnj/p25rrre3BFDfIUTZN4FtBF/XSqQhF6EcFpOrRpqKa1OaBCmHrEWWbtzBXVT0ZZdLejMyh5Zqp5I2krMvYjXK5jZpirj89s5xinEqVdWs5btRquxnleGhtkpo28vCzylHa0W0guasVkENm5MMz9YrkhAjiw2HqyPm/rj50w3lG6VSqFHiEHmzprvCj2xRwV1QG9FXt01OMN+9NrurqijbvqtEz1VnHEl3otSo9qhdVeMK/6JRh6N2MedeIpPpvp6FbKovhsQYbqzvpw4e19yKQnTBc3eYSgHV6LACICXYNjP5ra6RoqnFq3OnKS/FTeOVCVX23ExpTBYdz3qqxS3XoJqxSjVO7tkYTj01vXR/odqzWyiJlmgO8Ve9H6NwJIeEQdH2r04yCH+Lh1rLyHx5kqqTNqxtdooqha957TuQxJtVbFRndtm51SKeF/1A+cb8q8nOnQqtvVRVgFc8xbnVhMnUnKfFWtdsmmZJOJqNq2ALbLQ3K2XpnU1Hd6la3utWtbv/PWm266la3utWtbvNYq01X3epWt7rVbR5rtemqW93qVre6zWOtNl11q1vd6la3eaz9D9eqIsJYCPLoAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![图片.png](attachment:f5e402c0-ac1f-4615-a802-4f0f295c9b30.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mkString有两个重载的变种，让我们不必填写部分或全部入参。第一个变种只接收一个分隔字符串：  \n",
    "`xs mkString sep equals xs mkString(\"\",sep,\"\")`  \n",
    "第二个变种可以什么入参都不填：  \n",
    "`xs.mkString equals xs mkString \"\"`  \n",
    "下面是一些例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres174\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"[a,b,c,d,e]\"\u001b[39m"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde mkString (\"[\",\",\",\"]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres175\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"abcde\"\u001b[39m"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde mkString \"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres176\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"abcde\"\u001b[39m"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde.mkString"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres177\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"List(a, b, c, d, e)\"\u001b[39m"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde mkString (\"List(\",\", \",\")\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mkString方法还有别的变种，比如addString，这个方法将构建出来的字符串追加到一个StringBuilder对象，[6]而不是作为结果返回："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mbuf\u001b[39m: \u001b[32mStringBuilder\u001b[39m = \u001b[33mStringBuilder\u001b[39m()"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val buf = new StringBuilder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres179\u001b[39m: \u001b[32mStringBuilder\u001b[39m = \u001b[33mStringBuilder\u001b[39m(\n",
       "  \u001b[32m'('\u001b[39m,\n",
       "  \u001b[32m'a'\u001b[39m,\n",
       "  \u001b[32m';'\u001b[39m,\n",
       "  \u001b[32m'b'\u001b[39m,\n",
       "  \u001b[32m';'\u001b[39m,\n",
       "  \u001b[32m'c'\u001b[39m,\n",
       "  \u001b[32m';'\u001b[39m,\n",
       "  \u001b[32m'd'\u001b[39m,\n",
       "  \u001b[32m';'\u001b[39m,\n",
       "  \u001b[32m'e'\u001b[39m,\n",
       "  \u001b[32m')'\u001b[39m\n",
       ")"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde addString (buf, \"(\",\";\",\")\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mkString和addString这两个方法继承自List的超特质Traversable，因此它们也可以用在所有其他集合类型上。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 转换列表：iterator、toArray、copyToArray\n",
    "为了在扁平的数组世界和递归的列表世界之间做数据转换，可以使用List类的toArray和Array类的toList方法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36marr\u001b[39m: \u001b[32mArray\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mArray\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m)"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val arr = abcde.toArray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres181\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'e'\u001b[39m)"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.toList"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还有一个copyToArray方法可以将列表中的元素依次复制到目标数组的指定位置。如下操作：  \n",
    "`xs copyToArray (arr, start)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将列表xs的所有元素复制至数组arr，从下标start开始。我们必须确保目标数组足够大，能够容纳整个列表。参考下面的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36marr2\u001b[39m: \u001b[32mArray\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mArray\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m)"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val arr2 = new Array[Int](10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "List(1,2,3) copyToArray(arr2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres184\u001b[39m: \u001b[32mArray\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mArray\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m)"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后，如果要通过迭代器访问列表元素，可以用iterator方法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mit\u001b[39m: \u001b[32mIterator\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[32mnon-empty iterator\u001b[39m"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val it = abcde.iterator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres186\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'a'\u001b[39m"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "it.next"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres187\u001b[39m: \u001b[32mChar\u001b[39m = \u001b[32m'b'\u001b[39m"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "it.next"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "例子：归并排序\n",
    "\n",
    "之前我们介绍的插入排序写起来很简洁，不过效率并不是很高。它的平均复杂度跟输入列表的长度的平方成正比。更高效的算法是归并排序（merge sort）。\n",
    "\n",
    "快速通道\n",
    "\n",
    "这个例子是对分治原则和柯里化的另一次展示，同时也用来探讨算法复杂度的问题。不过，如果你想在初读本书时更快完成，可以安全地跳到16.7节。\n",
    "\n",
    "归并排序的机制如下：首先，如果列表有零个或一个元素，那么它已然是排好序的，因此列表可以被直接返回。更长一些的列表会被切分成两个子列表，每个子列表各 含约一半原列表的元素。每个子列表被递归地调用同一个函数来排序，然后两个排好序的子列表会通过一次归并操作合在一起。\n",
    "\n",
    "要实现一个通用的归并排序实现，要允许被排序列表的元素类型和用来比较元素大小的函数是灵活可变的。通过参数将这两项作为参数传入，就得到了最灵活的函数。最终的实现参考示例16.1。\n",
    "\n",
    "msort 的复杂度为（n log（n）），其中n为输入列表的长度。要搞清楚为什么，注意我们将列表切分成两个子列表，以及将两个排好序的列表归并到一起，这两种操作消耗的时间都 跟列表长度成正比。每次对msort的递归调用都会对输入的元素数量减半，因此差不多需要log（n）次连续的递归调用直到到达长度为1的列表这个基本 case。不过，对更长的列表而言，每次调用都会进一步生成两次调用。所有这些加在一起，在log（n）层的调用当中，原始列表的每个元素都会参与一次切 分操作和一次归并操作。\n",
    "\n",
    "这样一来，每个调用级别的总成本也是跟n成正比的。由于有log（n）层调用，我们得到的总成本为n log（n）。这个成本跟列表中预算的初始分布无关，因此最差情况的成本跟平均成本相同。归并排序的这个性质让它成为很有吸引力的算法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mmsort\u001b[39m"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def msort[T](less: (T, T) => Boolean)(xs: List[T]): List[T] = {\n",
    "    def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match {\n",
    "        case (Nil, _) => ys\n",
    "        case (_, Nil) => xs\n",
    "        case (x :: xs1, y :: ys1) =>\n",
    "            if(less(x,y)) x :: merge(xs1, ys)\n",
    "            else y :: merge(xs, ys1)\n",
    "    }\n",
    "    val n = xs.length / 2\n",
    "    if(n==0) xs\n",
    "    else {\n",
    "        val (ys, zs) = xs splitAt n\n",
    "        merge(msort(less)(ys), msort(less)(zs))\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres189\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m7\u001b[39m)"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msort((x: Int,y: Int) => x < y) (List(5,7,1,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "msort函数是我们在9.3节讨论的柯里化概念的经典案例。柯里化让我们可以很容易将函数定制为一种采用特定比较函数的特例。参考下面的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mintSort\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] => \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = ammonite.$sess.cmd190$Helper$$Lambda$3461/1571120022@10115ae"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val intSort = msort((x: Int, y: Int) => x < y) _"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres191\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m7\u001b[39m)"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intSort(List(5,7,1,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里的intSort变量指向一个接收整数列表并以数值顺序排列的函数。我们在8.6节曾经介绍过，下画线表示一个缺失的参数列表。在本例中，缺失的参数是应该被排序的列表。再来看另一个例子，我们可以这样来定义对整数列表按数值倒序排列的函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mreverseIntSort\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] => \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = ammonite.$sess.cmd192$Helper$$Lambda$3471/1754539477@c03a604"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val reverseIntSort = msort((x: Int, y: Int) => x > y) _"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres193\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m7\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m1\u001b[39m)"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverseIntSort(List(5,7,1,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于我们已经通过柯里化给出了比较函数，接下来只需要在调用intSort或reverseIntSort函数时给出要排序的列表即可。参考下面的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mmixedInts\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m4\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m9\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m8\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m7\u001b[39m)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val mixedInts = List(4, 1, 9, 0, 5, 8, 3, 6, 2, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres195\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m7\u001b[39m, \u001b[32m8\u001b[39m, \u001b[32m9\u001b[39m)"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intSort(mixedInts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres196\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m9\u001b[39m, \u001b[32m8\u001b[39m, \u001b[32m7\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m)"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverseIntSort(mixedInts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.7 List类的高阶方法\n",
    "许多对列表的操作都有相似的结构，有一些模式反复出现。例如：以某种方式对列表中的每个元素做转换，验证列表中所有元素是否都满足某种性质，从列表元素中提取满足某个指定条件的元素，或用某种操作符来组合列表中的元素。在Java中，这些模式通常要通过固定写法的for循环或while循环来组装。而Scala允许我们使用高阶操作符[7]来更精简、更直接地表达，这些高阶操作是通过List类的方法实现的。本节我们将对这些高阶操作进行探讨。\n",
    "### 对列表作映射：map、flatMap和foreach\n",
    "\n",
    "xs map f这个操作将类型为List[T]的列表xs和类型为T => U的函数f作为操作元。它返回一个通过应用f到xs的每个元素后得到的列表。例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres197\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1, 2, 3) map (_ + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mwords\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"the\"\u001b[39m, \u001b[32m\"quick\"\u001b[39m, \u001b[32m\"brown\"\u001b[39m, \u001b[32m\"fox\"\u001b[39m)"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val words = List(\"the\", \"quick\", \"brown\", \"fox\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres199\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m3\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m3\u001b[39m)"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words map (_.length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres200\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"eht\"\u001b[39m, \u001b[32m\"kciuq\"\u001b[39m, \u001b[32m\"nworb\"\u001b[39m, \u001b[32m\"xof\"\u001b[39m)"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words map (_.toList.reverse.mkString)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "flatMap操作符跟map类似，不过它要求右侧的操作元是一个返回元素列表的函数。它将这个函数应用到列表的每个元素，然后将所有结果拼接起来返回。下面的例子展示了map和flatMap的区别："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres201\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m]] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m't'\u001b[39m, \u001b[32m'h'\u001b[39m, \u001b[32m'e'\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m'q'\u001b[39m, \u001b[32m'u'\u001b[39m, \u001b[32m'i'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'k'\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m'b'\u001b[39m, \u001b[32m'r'\u001b[39m, \u001b[32m'o'\u001b[39m, \u001b[32m'w'\u001b[39m, \u001b[32m'n'\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m'f'\u001b[39m, \u001b[32m'o'\u001b[39m, \u001b[32m'x'\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words map (_.toList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres202\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[32m't'\u001b[39m,\n",
       "  \u001b[32m'h'\u001b[39m,\n",
       "  \u001b[32m'e'\u001b[39m,\n",
       "  \u001b[32m'q'\u001b[39m,\n",
       "  \u001b[32m'u'\u001b[39m,\n",
       "  \u001b[32m'i'\u001b[39m,\n",
       "  \u001b[32m'c'\u001b[39m,\n",
       "  \u001b[32m'k'\u001b[39m,\n",
       "  \u001b[32m'b'\u001b[39m,\n",
       "  \u001b[32m'r'\u001b[39m,\n",
       "  \u001b[32m'o'\u001b[39m,\n",
       "  \u001b[32m'w'\u001b[39m,\n",
       "  \u001b[32m'n'\u001b[39m,\n",
       "  \u001b[32m'f'\u001b[39m,\n",
       "  \u001b[32m'o'\u001b[39m,\n",
       "  \u001b[32m'x'\u001b[39m\n",
       ")"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words flatMap (_.toList)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以看到，map返回的是列表的列表，而flatMap返回的是所有元素拼接起来的单个列表。\n",
    "下面这个表达式也体现了map和flatMap的区别与联系，这个表达式构建的是一个满足 1≤ j＜i＜5 的所有对偶（i, j）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres203\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres204\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m((\u001b[32m2\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m3\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m3\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m3\u001b[39m))"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(1, 5) flatMap (i => List.range(1, i) map (j => (i, j)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres205\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)]] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[33mList\u001b[39m(),\n",
       "  \u001b[33mList\u001b[39m((\u001b[32m2\u001b[39m, \u001b[32m1\u001b[39m)),\n",
       "  \u001b[33mList\u001b[39m((\u001b[32m3\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m3\u001b[39m, \u001b[32m2\u001b[39m)),\n",
       "  \u001b[33mList\u001b[39m((\u001b[32m4\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m3\u001b[39m))\n",
       ")"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(1, 5) map (i => List.range(1, i) map (j => (i, j)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List.range 是一个用来创建某个区间内所有整数的列表的工具方法。在本例中，我们用到了两次：一次是生成从1（含）到5（不含）的整数列表，另一次是生成从1到i的整 数列表，其中i是来自第一个列表的每个元素。表达式中的map生成的是一个由元组（i, j）组成的列表，其中j ＜ i。外围的flatMap对1到5之间的每一个i生成一个列表，并将结果拼接起来。也可以用for表达式来构建同样的列表："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres206\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m((\u001b[32m2\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m3\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m3\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m1\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m2\u001b[39m), (\u001b[32m4\u001b[39m, \u001b[32m3\u001b[39m))"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for(i <- List.range(1, 5); j <- List.range(1, i)) yield(i, j)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你将在第23章了解到更多关于for表达式和列表操作的内容。\n",
    "\n",
    "第三个映射类的操作是foreach。不同于map和flatMap,foreach要求右操作元是一个过程（结果类型为Unit的函数）。它只是简单地将过程应用到列表中的每个元素。整个操作本身的结果类型也是Unit，并没有列表类型的结果被组装出来。参考下面这个精简的将列表中所有数值加和的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"jp-RenderedText\">\n",
       "<pre><code><span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">sum</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span> = <style>@keyframes fadein { from { opacity: 0; } to { opacity: 1; } }</style><span style=\"animation: fadein 2s;\"><span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">15</span></span></span></code></pre>\n",
       "</div>"
      ],
      "text/plain": [
       "\u001b[36msum\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m15\u001b[39m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var sum = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [],
   "source": [
    "List(1,2,3,4,5) foreach (sum += _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres209\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m15\u001b[39m"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 过滤列表：filter、partition、find、takeWhile、dropWhile和span\n",
    "\n",
    "“xs filter p”这个操作的两个操作元分别是类型为List[T]的xs和类型为T => Boolean的前提条件函数p。这个操作将交出xs中所有p（x）为true的元素x。例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres210\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m2\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,4,5) filter (_ % 2 == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres211\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"the\"\u001b[39m, \u001b[32m\"fox\"\u001b[39m)"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words filter (_.length == 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "partition方法跟filter很像不过返回的是一对列表。其中一个包含所有前提条件为true的元素，另一个包含所有前提条件为false的元素。它满足如下等式：  \n",
    "`xs partition p`等于`(xs filter p,xs filter (!p(_)))`  \n",
    "参考下面的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres212\u001b[39m: (\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m], \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]) = (\u001b[33mList\u001b[39m(\u001b[32m2\u001b[39m, \u001b[32m4\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m5\u001b[39m))"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,4,5) partition (_ % 2 == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "find方法跟filter也很像，不过它返回满足给定前提条件的第一个元素，而不是所有元素。xs find p这个操作接收列表xs和前提条件函数p两个操作元，返回一个可选值。如果xs中存在一个元素x满足p（x）为true，那么就返回Some（x）。而如果对于所有元素而言p都为false，那么则返回None。来看一些例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres213\u001b[39m: \u001b[32mOption\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mSome\u001b[39m(\u001b[32m2\u001b[39m)"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,4,5) find(_%2==0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres214\u001b[39m: \u001b[32mOption\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[32mNone\u001b[39m"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,4,5) find(_<=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "takeWhile和dropWhile操作符也将一个前提条件作为右操作元。xs takeWhile p操作返回列表xs中连续满足p的最长前缀。同理，xs dropWhile p操作将去除列表xs中连续满足p的最长前缀。来看一些例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres215\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m)"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,-4,5) takeWhile(_ > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres216\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"quick\"\u001b[39m, \u001b[32m\"brown\"\u001b[39m, \u001b[32m\"fox\"\u001b[39m)"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words dropWhile(_ startsWith \"t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "span方法将takeWhile和dropWhile两个操作合二为一，就像splitAt将take和drop合二为一一样。它返回一堆列表，满足如下等式：  \n",
    "`xs span p` 等于 `xs takeWhile p,xs dropWhile p`  \n",
    "跟splitAt一样，span同样不会重复遍历xs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres217\u001b[39m: (\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m], \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]) = (\u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m-4\u001b[39m, \u001b[32m5\u001b[39m))"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,2,3,-4,5) span (_ > 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对列表的前提条件检查：forall和exists\n",
    "\n",
    "xs forall p这个操作接收一个列表xs和一个前提条件p作为入参。如果列表中所有元素都满足p就返回true。与此相反，xs exists p操作返回true的要求是xs中存在一个元素满足前提条件p。例如，要搞清楚一个以列表的列表表示的矩阵里是否存在一行的元素全为0："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mhasZeroRow\u001b[39m"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def hasZeroRow(m: List[List[Int]]) = m exists (row => row forall (_ == 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres219\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]] = \u001b[33mList\u001b[39m(\u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m))"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diag3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres220\u001b[39m: \u001b[32mBoolean\u001b[39m = false"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hasZeroRow(diag3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mdiag4\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m0\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val diag4 = diag3 ::: List(List(0, 0, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres222\u001b[39m: \u001b[32mBoolean\u001b[39m = true"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hasZeroRow(diag4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 折叠列表：/：和:\\\n",
    "对列表的另一种常见操作是用某种操作符合并元素。例如：  \n",
    "`sum(List(a,b,c))` 等于 `0 + a + b + c`  \n",
    "这是折叠操作的特例："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36msum\u001b[39m"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sum(xs: List[Int]): Int = (0 /: xs) (_ + _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres224\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m9\u001b[39m"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(List(2,3,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "同理：  \n",
    "`product(List(a,b,c))` 等于 ` 1*a*b*c `   \n",
    "这也是折叠操作的一个特例："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mproduct\u001b[39m"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def product(xs: List[Int]): Int = (1 /: xs) (_ * _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres226\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m24\u001b[39m"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "product(List(2,3,4))"
   ]
  },
  {
   "attachments": {
    "4ec2aaed-9970-4dc7-8813-f0e9d53f4e52.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "左折叠（fold left）操作“（z /: xs）（op）”涉及三个对象：起始值z、列表xs和二元操作op。折叠的结果是以z为前缀，对列表的元素依次连续应用op。例如：  \n",
    "`(z /: List(a,b,c))(op)` 等于 `op(op(op(z,a),b),c)`  \n",
    "或者用图形化表示就是：  \n",
    "![图片.png](attachment:4ec2aaed-9970-4dc7-8813-f0e9d53f4e52.png)  \n",
    "还有个例子可以说明/：的用处。为了把列表中的字符串表示的单词拼接起来，在当中和最前面加上空格，可以："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres227\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\" the quick brown fox\"\u001b[39m"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(\"\" /: words) (_ + \" \" + _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里会在最开始多出一个空格。要去除这个空格，可以像下面这样简单改写："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres228\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"the quick brown fox\"\u001b[39m"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(words.head /: words.tail) (_ + \" \" + _)"
   ]
  },
  {
   "attachments": {
    "81c32478-c8c0-48dd-a390-9fb21ce0617b.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "/：操作符产生一棵往左靠的操作树（之所以用斜杠/也是为了体现这一点）。同理，:\\这个操作产生一棵往右靠的操作树。例如：  \n",
    "`(List(a,b,c) :\\ z) (op)` 等于 `op(a,op(b,op(c,z)))`  \n",
    "或者图形化表示就是：  \n",
    "![图片.png](attachment:81c32478-c8c0-48dd-a390-9fb21ce0617b.png)  \n",
    ":\\操作符读作右折叠（fold right）。它涉及跟左折叠一样的三个操作元，不过前两个出现的顺序是颠倒的：第一个操作元是要折叠的列表，而第二个操作元是起始值。\n",
    "对结合性的操作而言，左折叠和右折叠是等效的，不过可能存在执行效率上的差异。可以设想一下flatten方法对应的操作，这个操作是将一个列表的列表中的所有元素拼接起来。可以用左折叠也可以用右折叠来完成："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mflattenLeft\u001b[39m"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def flattenLeft[T](xss: List[List[T]]) =\n",
    "    (List[T]() /: xss) (_ ::: _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mflattenRight\u001b[39m"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def flattenRight[T](xss: List[List[T]]) =\n",
    "    (xss :\\ List[T]()) (_ ::: _)"
   ]
  },
  {
   "attachments": {
    "1c54825b-b64e-4808-9fbe-7e3c3fc0de0a.png": {
     "image/png": 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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于列表拼接xs ::: ys的执行时间跟首个入参xs的长度成正比，用右折叠的flattenRight比用左折叠的flattenLeft更高效。左折叠在这里的问题是 flattenLeft（xss）需要复制首个元素列表xss.head n-1次，其中n为列表xss的长度。\n",
    "\n",
    "注意上述两个flatten版本都需要对表示折叠起始值的空列表做类型注解。这是由于Scala类型推断程序的一个局限，不能自动推断出正确的列表类型。如果漏掉了类型注解，会得到如下结果：\n",
    "```scala\n",
    "def flattenRight[T](xss: List[List[T]]) =\n",
    "    (xss :\\ List()) (_ ::: _)\n",
    "\n",
    "\n",
    "cmd110.sc:2: type mismatch;\n",
    " found   : List[T]\n",
    " required: List[Nothing]\n",
    "    (xss :\\ List()) (_ ::: _)\n",
    "                     ^Compilation Failed\n",
    "\n",
    "Compilation Failed\n",
    "```\n",
    "要搞清楚为什么类型推断程序出了问题，需要了解折叠方法的类型，以及它们是如何实现的。这个留到16.10节再探讨。\n",
    "\n",
    "最后，虽然/：和：\\操作符的一个优势是斜杠的方向形象地表示出往左或往右靠的树形结构，同时冒号的结合性也将起始值放在了表达式中跟树中一样的位置，可能有的人会觉得这并不直观。只要你想，你也可以用foldLeft和foldRight这样的方法名，这两个也是定义在List类的方法。\n",
    "\n",
    "例子：用fold反转列表\n",
    "\n",
    "在本章前面的部分，我们看到了reverse方法的实现，名为rev，其运行时间是待反转列表长度的平方级。现在来看一个reverse的不同实现，运行开销是线性的。原理是基于下面的机制来做左折叠：  \n",
    "`def reverseLeft[T](xs: List[T]) = (startvalue /: xs) (operation)`  \n",
    "剩下需要补全的就是startvalue（起始值）和operation（操作）的部分了。事实上，可以用更简单的例子来推导出来。为了推导出startvalue正确的取值，可以用最简单的列表List（）开始：  \n",
    "![图片.png](attachment:1c54825b-b64e-4808-9fbe-7e3c3fc0de0a.png)  \n",
    "因此，startvalue必须是List（）。要推导出第二个操作元，可以拿仅次于List（）的最小列表作为样例。我们已经知道startvalue是List（），可以做如下的演算：  \n",
    "![图片.png](attachment:9050c588-7687-4fcb-afbd-d11f94f6317b.png)  \n",
    "因此，operation（List（）, x）等于List（x），而List（x）也可以写作x ::List（）。这样我们就发现可以基于：：操作符把两个操作元反转一下来得到operation（这个操作有时被称作“sonc”，即把：：的 “cons”反过来念）。于是我们得到如下reverseLeft的实现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mreverseLeft\u001b[39m"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def reverseLeft[T](xs: List[T]) = \n",
    "    (List[T]() /: xs) {(ys,y) => y :: ys}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "同样地，为了让类型推断程序正常工作，这里的类型注解List[T]（）是必需的。如果我们分析reverseLeft的时间复杂度，会发现它执行这个常量时间操作（即“snoc”）n次。因此，reverseLeft的时间复杂度是线性的。\n",
    "\n",
    "### 列表排序：sortWith\n",
    "\n",
    "xs sortWith before这个操作对列表xs中的元素进行排序，其中“xs”是列表，而“before”是一个用来比较两个元素的函数。表达式x before y对于在预期的排序中x应出现在y之前的情况应返回true。例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres232\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m-3\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m6\u001b[39m)"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List(1,-3,4,2,6) sortWith (_ < _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres233\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"quick\"\u001b[39m, \u001b[32m\"brown\"\u001b[39m, \u001b[32m\"the\"\u001b[39m, \u001b[32m\"fox\"\u001b[39m)"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words sortWith (_.length > _.length)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意，sortWith执行的是跟前一节的msort算法类似的归并排序。不过sortWtih是List类的方法，而msort定义在列表之外。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.8 List对象的方法\n",
    "到目前为止，我们在本章介绍的所有操作都是List类的方法，因此我们其实是在每个具体的列表对象上调用它们。还有一些方法是定义在全局可访问对象scala.List上的，这是List类的伴生对象。某些操作是用于创建列表的工厂方法，另一些是对特定形状的列表进行操作。这两类方法在本节都会介绍到。\n",
    "\n",
    "### 从元素创建列表：List.apply\n",
    "\n",
    "我们已经看到过不止一次诸如List（1, 2, 3）这样的列表字面量。这样的语法并没有什么特别之处。List（1, 2, 3）这样的字面量只不过是简单地将对象List应用到元素1、2、3而已。也就是说，它跟List.apply（1, 2, 3）是等效的："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres234\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m)"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.apply(1, 2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 创建数值区间：List.range\n",
    "\n",
    "我们在介绍map和flatMap的时候曾经用到过range方法，它创建的是一个包含一个区间的数值的列表。这个方法最简单的形式是 List.rang（from, until），创建一个包含了从from开始递增到until减1的数的列表。所以终止值until并不是区间的一部分。\n",
    "\n",
    "range方法还有两一个版本，接收step作为第三个参数。这个操作交出的列表元素是从from开始，间隔为step的值。step可以是正值也可以是负值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres235\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m)"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres236\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m7\u001b[39m)"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(1,9,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres237\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m9\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m3\u001b[39m)"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.range(9,1,-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 创建相同元素的列表：List.fill\n",
    "fill方法创建包含零个或多个同一个元素拷贝的列表。它接收两个参数：要创建的列表长度和需要重复的元素。两个参数各自以不同的参数列表给出："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres238\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'a'\u001b[39m, \u001b[32m'a'\u001b[39m, \u001b[32m'a'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.fill(5)('a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres239\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mString\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m\"hello\"\u001b[39m, \u001b[32m\"hello\"\u001b[39m, \u001b[32m\"hello\"\u001b[39m)"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.fill(3)(\"hello\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们给fill的参数多于1个，那么它就会创建多维的列表。也就是说，它将创建出列表的列表、列表的列表的列表，等等。多出来的这些参数要放在第一个参数列表中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres240\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m]] = \u001b[33mList\u001b[39m(\u001b[33mList\u001b[39m(\u001b[32m'b'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'b'\u001b[39m), \u001b[33mList\u001b[39m(\u001b[32m'b'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'b'\u001b[39m))"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.fill(2,3)('b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 表格化一个函数：List.tabulate\n",
    "tabulate方法创建的是一个根据给定的函数计算的元素的列表。其入参跟List.fill的一样：第一个参数列表给出要创建列表的维度，而第二个参数列表描述列表的元素。唯一的区别是，元素值不再是固定的，而是从函数计算得来："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36msquares\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m9\u001b[39m, \u001b[32m16\u001b[39m)"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val squares = List.tabulate(5)(n => n * n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mmultiplication\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m]] = \u001b[33mList\u001b[39m(\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m4\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m8\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m9\u001b[39m, \u001b[32m12\u001b[39m),\n",
       "  \u001b[33mList\u001b[39m(\u001b[32m0\u001b[39m, \u001b[32m4\u001b[39m, \u001b[32m8\u001b[39m, \u001b[32m12\u001b[39m, \u001b[32m16\u001b[39m)\n",
       ")"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val multiplication = List.tabulate(5, 5)(_ * _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 拼接多个列表：List.concat\n",
    "concat方法将多个列表拼接在一起。要拼接的列表通过concat的直接入参给出："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres243\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'a'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m)"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.concat(List('a', 'b'), List('c'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres244\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'b'\u001b[39m, \u001b[32m'c'\u001b[39m)"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.concat(List(),List('b'), List('c'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres245\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mNothing\u001b[39m] = \u001b[33mList\u001b[39m()"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "List.concat()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.9 同时处理多个列表\n",
    "元组的zipped方法将若干通用的操作一般化了，它们不再只是针对单个列表而是能同时处理多个列表。其中一个通用操作是map。对两个zip在一起的列表调用map的效果是对元素一组一组地做映射，而不是单个元素。每个列表的第一个元素是一对，第二个元素是一对，以此类推，列表有多长，就有多少对。参考下面的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres246\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m30\u001b[39m, \u001b[32m80\u001b[39m)"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(List(10, 20), List(3, 4, 5)).zipped.map(_ * _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意第二个列表的三个元素被丢弃了。zipped方法只会把所有列表中都有值的元素zip在一起，多出来的元素会被丢弃。\n",
    "同理，exists和forall也有zip起来的版本。它们跟单列表的版本做的事情相同，只不过它们操作的是多个列表而不是一个："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres247\u001b[39m: \u001b[32mBoolean\u001b[39m = true"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(List(\"abc\",\"de\"), List(3, 2)).zipped.forall(_.length == _)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres248\u001b[39m: \u001b[32mBoolean\u001b[39m = false"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(List(\"abc\",\"de\"), List(3, 2)).zipped.exists(_.length != _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "快速通道  \n",
    "在本章的下一节（也是最后一节），我们将介绍Scala类型推断算法的原理。如果你目前对于这样的细节并不关心，可以跳过下一节直接进入结语（339页）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.10 理解Scala的类型推断算法\n",
    "我们之前用到的sortWith和msort的区别在于它们可接收的比较函数语法。\n",
    "我们来比较一下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres249\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msort((x: Char, y: Char) => x > y)(abcde)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres250\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde sortWith (_ > _)"
   ]
  },
  {
   "attachments": {
    "b264fb56-ab2e-4272-b1d1-f0b287218b36.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这两个表达式是等效的，不过前者采用的比较函数字面量版本较长，用到了带名参数和显式类型声明。而后者采用了更精简的写法（_ > \\_），其中带名参数被替换成了下画线。当然，我们也可以在sortWith调用中使用前一种较长的写法来给出比较函数。\n",
    "不过，这个较短的版本并不适用于msort。  \n",
    "![图片.png](attachment:b264fb56-ab2e-4272-b1d1-f0b287218b36.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres251\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcde sortWith ((x: Char, y: Char) => x > y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要搞清楚为什么会这样，我们需要知道Scala类型推断算法的一些细节。Scala的类型推断是基于程序流（flow based）的。对于方法调用m（args），类型推断算法首先检查m的类型是否已知。如果m的类型已知，那么这个类型信息就被用于推断入参的预期类型。 例如，在abcde.sortWith（_ > \\_）中， abcde的类型为List[Char]。因此，类型推断算法知道sortWith是一个接收类型为（Char, Char） => Boolean的入参且产出一个类型为List[Char]的结果的方法。由于该函数入参的参数类型是已知的，并不需要显式地写出来。基于类型推断算法所 了解的关于sortWith的信息，它可以推导出（_ > \\_）应该被展开成（（x: Char, y: Char） => x > y），其中x和y是任意没有被用过的新名称。\n",
    "\n",
    "现在我们来看第二个case,msort（_ > \\_）（abcde）。msort的类型是一个经过柯里化的、多态的[8]方法类型，它接收一个类型为（T, T） => Boolean的入参，产出一个从List[T]到List[T]的函数，其中T是某个当前未知的类型。msort需要先用一个类型参数实例化以后才能被应用到它的入参上。\n",
    "\n",
    "由于msort的确切示例类型暂时未知，类型推断算法不能用这个信息来推断它的首个入参的类型。对于这种情况，类型推断算法会改变策略，它改为先检查方法入参来决定方法的正确实例类型。然而，当它去对（_ > \\_）这个简写的函数字面量做类型检查时，由于我们没有提供任何关于用下画线表示的函数参数类型的信息，类型检查是失败的。\n",
    "解决这个问题的一种方式是给msort传一个显式的类型参数，如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres252\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msort[Char](_ > _)(abcde)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于msort的正确实例类型现在是已知的了，类型推断算法可以用它来推断入参的类型。另一个可能的解决方案是重写msort方法，让它的两个参数交换位置："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mmsortSwapped\u001b[39m"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def msortSwapped[T](xs: List[T])(less: (T, T) => Boolean) : List[T] = {\n",
    "    def merge(xs: List[T],ys: List[T]) : List[T] = (xs, ys) match {\n",
    "        case (Nil, _) => ys\n",
    "        case (_, Nil) => xs\n",
    "        case (x::xs1, y::ys1) => \n",
    "            if(less(x,y)) x::merge(xs1,ys)\n",
    "            else y::merge(xs,ys1)\n",
    "    }\n",
    "    val n = xs.length / 2\n",
    "    if(n == 0) xs\n",
    "    else{\n",
    "        val (xs1,xs2) = xs splitAt n\n",
    "        merge(msortSwapped(xs1)(less),msortSwapped(xs2)(less))\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这样的类型推断也能成功："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mres254\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mChar\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m'e'\u001b[39m, \u001b[32m'd'\u001b[39m, \u001b[32m'c'\u001b[39m, \u001b[32m'b'\u001b[39m, \u001b[32m'a'\u001b[39m)"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msortSwapped(abcde)(_ > _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "怎么做到的？类型推断算法使用了首个参数abcde的已知类型来判定msortSwapped的类型参数。一旦msortSwapped的确切类型已知，它就能被用于推断第二个入参（_ > \\_）的类型。\n",
    "\n",
    "一般来说，当类型推断算法需要推断一个多态方法的类型参数时，它会考虑第一个参数列表里的所有入参的类型，但到此为止。由于msortSwapped是一个柯里化的方法，它有两个参数列表，第二个入参（即函数值）并不会用来判定方法的类型参数。\n",
    "\n",
    "这样的类型推断机制引导出如下的类库设计原则：当我们设计一个接收某些非函数的入参和一个函数入参时，将函数入参单独放在最后一个参数列表中。这样一来，方法的正确实例类型可以从那些非函数入参推断出来，而这个类型又能被继续用于对函数入参做类型检查。这样做的净收益是方法的使用者需要给出的类型信息更少， 因而在编写函数字面量时可以更精简。\n",
    "\n",
    "接下来再看看折叠这个更复杂的操作。为什么我们需要像330页的flattenRight方法的方法体内的那段表达式那样显式地给出类型参数呢？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defined \u001b[32mfunction\u001b[39m \u001b[36mflattenRight\u001b[39m"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def flattenRight[T](xss: List[List[T]]) =\n",
    "    (xss :\\ List[T]()) (_ ::: _)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "右折叠操作的类型以两个类型变量的形式呈现出多态。比如下面这个表达式：  \n",
    "`(xs :\\ z) (op)`  \n",
    "xs 的类型一定是某个任意类型A的列表，比如说xs: List[A]。起始值z可以是某个不一样的类型B。这样一来操作op一定是接收类型分别为A和B的两个入参，返回类型为B的结果，即op: （A, B） => B。由于z的类型跟列表xs的类型不相关，类型推断算法就没有任何关于z的上下文信息。\n",
    "\n",
    "现在我们来看330页的那个错误版本的flattenRight：\n",
    "```scala\n",
    "def flattenRight[T](xss: List[List[T]]) =\n",
    "\n",
    "    (xss :\\ List()) (_ ::: _)\n",
    "\n",
    "cmd129.sc:2: type mismatch;\n",
    " found   : List[T]\n",
    " required: List[Nothing]\n",
    "    (xss :\\ List()) (_ ::: _)\n",
    "                     ^Compilation Failed\n",
    "\n",
    "Compilation Failed\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个折叠操作中的起始值z是一个空列表List（），当没有任何其他额外信息的情况下，它的类型被推断为List[Nothing]。因此，类型推断算法会推断出本次折叠操作的类型B为List[Nothing]。这样一来，折叠操作中的（_ ::: \\_）预期应该满足如下类型：  \n",
    "`(List[T], List[Nothing]) => List[Nothing]`  \n",
    "这的确是本次操作的一个可能的类型，但并不是一个十分有用的版本！它表达的意思是这个操作永远接收一个空列表作为第二个入参，同时永远产出一个空列表作为结果。\n",
    "\n",
    "换句话说，这里的类型推断算法过早地判定了List（）的类型，它应该等看到操作op的类型以后再做决定。**因此这个（本可以很有用的）在柯里化的方法调用中只考虑第一个参数列表来判定方法类型的规则是核心问题所在**。另一方面，即便我们可以放宽这个规则，类型推断算法依然无法推算出op的类型，因为它的参数类型没有给出。因此，一个《二十二条军规》的情况出现了，我们只好通过程序员加上显式的类型注解来解决。\n",
    "\n",
    "这个例子显现出局部的、基于程序流的Scala类型推断机制的局限。在函数式编程语言ML或Haskell中使用的全局的Hindley-Milner风格的类型推断中，并没有这些限制。不过，Scala的局部类型推断对于面向对象的子类型处理相比Hindley-Milner风格要优雅得多。幸运的是，这些局限只在某些边界case出现，且通常很容易通过显式添加类型注解解决。\n",
    "当我们对多态方法相关的错误提示感到困惑时，添加类型注解也是一个有用的调试技巧。如果不确定是什么引起某个特定的类型错误，只管添加你认为正确的类型参数或其他类型注解就好。这样你应该很快就能看到真正的问题所在。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16.11 结语\n",
    "我们见识了很多处理列表的方法。最基本的操作比如head和tail，初阶操作比如reverse，高阶操作比如map，以及List对象中的工具方法。在这个过程中，我们也了解了Scala的类型推断的原理。\n",
    "\n",
    "列表是Scala程序中的真正干活儿的工具，所以知道如何使用它们是有好处的。正因为如此，本章花费大量篇幅深入介绍了列表的用法。不过，列表只是Scala支持的集合类型的一种。下一章范围更宽，相对来说也浅一些，会向你展示如何使用各种Scala集合类型。\n",
    "\n",
    "[1].参考图22.2（473页），一个对列表结构的图形化展示。  \n",
    "[2].第19章将介绍协变和其他型变的更多细节。  \n",
    "[3].第19章将会有更多关于类型参数的细节讲解。  \n",
    "[4].??？这个方法在运行时会抛出scala.NotImplementedError，其结果类型为Nothing，我们可以在开发过程中当作临时实现来用。  \n",
    "[5].正如我们在10.12节指出的，对偶（pair）是Tuple2的非正式名称。  \n",
    "[6].这是scala.StringBuilder类，不是java.lang.StringBuilder类。  \n",
    "[7].这里所说的高阶操作符（high-order operator）指的是用在操作符表示法中的高阶函数。在9.1节提到过，如果一个函数接收一个或多个函数作为参数，那么它就是“高阶”的。  \n",
    "[8].这里指的是参数多态，不是面向对象编程里常见的子类型多态。——译者注"
   ]
  }
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