Sync LeetCode submission Runtime - 113 ms (56.57%), Memory - 32.3 MB (57.58%)

Author: jimit105

2249-count-the-hidden-sequences/README.md

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+<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>differences</code>, which describes the <strong>differences </strong>between each pair of <strong>consecutive </strong>integers of a <strong>hidden</strong> sequence of length <code>(n + 1)</code>. More formally, call the hidden sequence <code>hidden</code>, then we have that <code>differences[i] = hidden[i + 1] - hidden[i]</code>.</p>
+
+<p>You are further given two integers <code>lower</code> and <code>upper</code> that describe the <strong>inclusive</strong> range of values <code>[lower, upper]</code> that the hidden sequence can contain.</p>
+
+<ul>
+	<li>For example, given <code>differences = [1, -3, 4]</code>, <code>lower = 1</code>, <code>upper = 6</code>, the hidden sequence is a sequence of length <code>4</code> whose elements are in between <code>1</code> and <code>6</code> (<strong>inclusive</strong>).
+
+	<ul>
+		<li><code>[3, 4, 1, 5]</code> and <code>[4, 5, 2, 6]</code> are possible hidden sequences.</li>
+		<li><code>[5, 6, 3, 7]</code> is not possible since it contains an element greater than <code>6</code>.</li>
+		<li><code>[1, 2, 3, 4]</code> is not possible since the differences are not correct.</li>
+	</ul>
+	</li>
+</ul>
+
+<p>Return <em>the number of <strong>possible</strong> hidden sequences there are.</em> If there are no possible sequences, return <code>0</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> differences = [1,-3,4], lower = 1, upper = 6
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> The possible hidden sequences are:
+- [3, 4, 1, 5]
+- [4, 5, 2, 6]
+Thus, we return 2.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> differences = [3,-4,5,1,-2], lower = -4, upper = 5
+<strong>Output:</strong> 4
+<strong>Explanation:</strong> The possible hidden sequences are:
+- [-3, 0, -4, 1, 2, 0]
+- [-2, 1, -3, 2, 3, 1]
+- [-1, 2, -2, 3, 4, 2]
+- [0, 3, -1, 4, 5, 3]
+Thus, we return 4.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> differences = [4,-7,2], lower = 3, upper = 6
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> There are no possible hidden sequences. Thus, we return 0.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>n == differences.length</code></li>
+	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
+	<li><code>-10<sup>5</sup> &lt;= differences[i] &lt;= 10<sup>5</sup></code></li>
+	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
+</ul>

2249-count-the-hidden-sequences/solution.py

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+# Approach: Determine the Difference Between the Hidden Array's Upper and Lower Bounds
+
+# Time: O(n)
+# Space: O(1)
+
+class Solution:
+    def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
+        x = y = curr = 0
+
+        for d in differences:
+            curr += d
+            x = min(x, curr)
+            y = max(y, curr)
+
+            if y - x > upper - lower:
+                return 0
+
+        return (upper - lower) - (y - x) + 1
+