Merge pull request TheAlgorithms#58 from dhruvsaini/patch-1

Create longest common subsequence.py

Author: harshildarji

dynamic_programming/longest common subsequence.py

@@ -0,0 +1,18 @@
+"""
+LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them.
+A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
+Example:"abc", "abg" are subsequences of "abcdefgh". 
+"""
+def LCS(s1, s2):
+    m = len(s1)
+    n = len(s2)
+
+    arr = [[0 for i in range(n+1)]for j in range(m+1)]
+
+    for i in range(1,m+1):
+        for j in range(1,n+1):
+            if s1[i-1] == s2[j-1]:
+                arr[i][j] = arr[i-1][j-1]+1
+            else:
+                arr[i][j] = max(arr[i-1][j], arr[i][j-1])
+    return arr[m][n]