Create Longest_Common_Subsequence.py

code/dynamic_programming/src/longest_common_subsequence_substring/Longest_Common_Subsequence.py

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+# The longest common subsequence in Python
+
+
+# Function to find lcs_algo
+def lcs_algo(S1, S2, m, n):
+    L = [[0 for x in range(n+1)] for x in range(m+1)]
+
+    # Building the mtrix in bottom-up way
+    for i in range(m+1):
+        for j in range(n+1):
+            if i == 0 or j == 0:
+                L[i][j] = 0
+            elif S1[i-1] == S2[j-1]:
+                L[i][j] = L[i-1][j-1] + 1
+            else:
+                L[i][j] = max(L[i-1][j], L[i][j-1])
+
+    index = L[m][n]
+
+    lcs_algo = [""] * (index+1)
+    lcs_algo[index] = ""
+
+    i = m
+    j = n
+    while i > 0 and j > 0:
+
+        if S1[i-1] == S2[j-1]:
+            lcs_algo[index-1] = S1[i-1]
+            i -= 1
+            j -= 1
+            index -= 1
+
+        elif L[i-1][j] > L[i][j-1]:
+            i -= 1
+        else:
+            j -= 1
+
+    # Printing the sub sequences
+    print("S1 : " + S1 + "\nS2 : " + S2)
+    print("LCS: " + "".join(lcs_algo))
+
+
+S1 = "ACADB"
+S2 = "CBDA"
+m = len(S1)
+n = len(S2)
+lcs_algo(S1, S2, m, n)