Create longest_increasing_subsequence.py

The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 50, 41, 60, 80} is 6

Author: dhruvsaini

dynamic_programming/longest_increasing_subsequence.py

@@ -0,0 +1,12 @@
+"""
+The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 50, 41, 60, 80} is 6 
+"""
+def LIS(arr):
+    n= len(arr)
+    lis = [1]*n
+
+    for i in range(1, n):
+        for j in range(0, i):
+            if arr[i] > arr[j] and lis[i] <= lis[j]:
+                lis[i] = lis[j] + 1
+    return max(lis)