Short Problem Definition:
Given two strings a and b of equal length, what’s the longest string (S) that can be constructed such that it is a child of both?
A string x is said to be a child of a string y if x can be formed by deleting 0 or more characters from y.
time complexity is O(N*M)
space complexity is O(N*M)
This is a longest common subsequence problem in disguise. I encourage you to look at a good explanation here.
def lcs(a, b): lengths = [[0 for j in range(len(b)+1)] for i in range(len(a)+1)] for i, x in enumerate(a): for j, y in enumerate(b): if x == y: lengths[i+1][j+1] = lengths[i][j] + 1 else: lengths[i+1][j+1] = \ max(lengths[i+1][j], lengths[i][j+1]) return lengths[-1][-1] def main(): s1 = raw_input() s2 = raw_input() print lcs(s1,s2) if __name__ == '__main__': main()
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