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31 lines
957 B
Python
31 lines
957 B
Python
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"""
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LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them.
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A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
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Example:"abc", "abg" are subsequences of "abcdefgh".
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"""
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def lcs_dp(x, y):
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# find the length of strings
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m = len(x)
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n = len(y)
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# declaring the array for storing the dp values
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L = [[None] * (n + 1) for i in xrange(m + 1)]
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seq = []
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for i in range(m + 1):
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for j in range(n + 1):
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if i == 0 or j == 0:
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L[i][j] = 0
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elif x[i - 1] == y[ j - 1]:
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L[i][j] = L[i - 1][j - 1] + 1
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seq.append(x[i -1])
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else:
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L[i][j] = max(L[i - 1][j], L[i][j - 1])
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# L[m][n] contains the length of LCS of X[0..n-1] & Y[0..m-1]
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return L[m][n], seq
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if __name__=='__main__':
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x = 'AGGTAB'
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y = 'GXTXAYB'
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print lcs_dp(x, y)
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