From 758def814afbbfcf6026495cfb8e80c0465a7ee0 Mon Sep 17 00:00:00 2001
From: jaynilshah <36128751+jaynilshah@users.noreply.github.com>
Date: Thu, 31 Oct 2019 01:30:12 +0530
Subject: [PATCH] Longest Increasing Subsequence

Longest Increasing Subsequence in O(nlogn)
---
 .../LongestIncreasingSubsequence.java         | 42 +++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 Dynamic Programming/LongestIncreasingSubsequence.java

diff --git a/Dynamic Programming/LongestIncreasingSubsequence.java b/Dynamic Programming/LongestIncreasingSubsequence.java
new file mode 100644
index 0000000..e1821e7
--- /dev/null
+++ b/Dynamic Programming/LongestIncreasingSubsequence.java	
@@ -0,0 +1,42 @@
+import java.util.ArrayList;
+import java.util.List;
+
+public class LIS {
+    public static int lowerBound(List<Integer> a, int low, int high, int element){
+        while(low < high){
+            int middle = low + (high - low)/2;
+            if(element > a.get(middle))
+                low = middle + 1;
+            else
+                high = middle;
+        }
+        return low;
+    }
+
+    public static int upperBound(List<Integer> a, int low, int high, int element){
+        while(low < high){
+            int middle = low + (high - low)/2;
+            if(a.get(middle) > element)
+                high = middle;
+            else
+                low = middle + 1;
+        }
+        return low;
+    }
+
+    public static int longestIncreasingSubsequence(List<Integer> a){
+        //equals included then upperbound
+        // else lower bound use as required
+        ArrayList<Integer> ans = new ArrayList<>();
+        for(int i=0;i<a.size();i++){
+            int x = lowerBound(ans,0,ans.size(),a.get(i));
+            if(x+1>ans.size()){
+                ans.add(a.get(i));
+            }
+            else
+            ans.set(x,a.get(i));
+        }
+        return ans.size();
+    }
+
+}
\ No newline at end of file