Merge pull request #203 from erdenezul/refactor_longest_common_subsequence

refactor longest common subsequence problem

dynamic_programming/longest common subsequence.py

@@ -1,48 +0,0 @@
-"""
-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(x,y):
-    b=[[] for j in range(len(x)+1)]
-    c=[[] for i in range(len(x))]
-    for i in range(len(x)+1):
-        b[i].append(0)
-    for i in range(1,len(y)+1):
-        b[0].append(0)
-    for i in range(len(x)):
-        for j in range(len(y)):
-            if x[i]==y[j]:
-                b[i+1].append(b[i][j]+1)
-                c[i].append('/')
-            elif b[i][j+1]>=b[i+1][j]:
-                b[i+1].append(b[i][j+1])
-                c[i].append('|')
-            else :
-                b[i+1].append(b[i+1][j])
-                c[i].append('-')            
-    return b,c
-
-
-def print_lcs(x,c,n,m):
-    n,m=n-1,m-1
-    ans=[]
-    while n>=0 and m>=0:
-        if c[n][m]=='/':
-            ans.append(x[n])
-            n,m=n-1,m-1
-        elif c[n][m]=='|':
-            n=n-1
-        else:
-            m=m-1 
-    ans=ans[::-1]
-    return ans                   
-                       
-
-if __name__=='__main__':
-    x=['a','b','c','b','d','a','b']
-    y=['b','d','c','a','b','a']
-    b,c=LCS(x,y)
-    print('Given \nX : ',x)
-    print('Y : ',y)
-    print('LCS : ',print_lcs(x,c,len(x),len(y)))

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)