refactor longest common subsequence problem

dynamic_programming/longest_common_subsequence.py

@@ -0,0 +1,30 @@
+"""
+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_dp(x, y):
+    # find the length of strings
+    m = len(x)
+    n = len(y)
+
+    # declaring the array for storing the dp values
+    L = [[None] * (n + 1) for i in xrange(m + 1)]
+    seq = []
+
+    for i in range(m + 1):
+        for j in range(n + 1):
+            if i == 0 or j == 0:
+                L[i][j] = 0
+            elif x[i - 1] == y[ j - 1]:
+                L[i][j] = L[i - 1][j - 1] + 1
+                seq.append(x[i -1])
+            else:
+                L[i][j] = max(L[i - 1][j], L[i][j - 1])
+    # L[m][n] contains the length of LCS of X[0..n-1] & Y[0..m-1]
+    return L[m][n], seq
+
+if __name__=='__main__':
+    x = 'AGGTAB'
+    y = 'GXTXAYB'
+    print lcs_dp(x, y)