PIQ39: Longest Common Subsequence

最新推荐文章于 2022-09-20 20:59:37 发布

原创最新推荐文章于 2022-09-20 20:59:37 发布 · 335 阅读

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本文介绍了一种求解两个字符串间最长公共子序列的问题，并提供了一个详细的Python实现方案。通过动态规划方法，不仅计算出最长公共子序列的长度，还重构了具体的子序列。

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Problem Statement

Given two string s1 and s2. Find the longest common subsequence between s1 and s2.

Link@HackerRank: The Longest Common Subsequence

def longest_common_subsequence(s1, s2):
    """Find the longest common subsequence between s1 and s2.
    """
    # Corner cases.
    if not s1 or not s2:
        return None

    # DP.
    n, m = len(s1), len(s2)
    dp = [[0 for i in xrange(m + 1)] for j in xrange(n + 1)]
    for i in xrange(1, n + 1):
        for j in xrange(1, m + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i][j] = 1 + dp[i - 1][j - 1]
            else:
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])

    # Construct the longest common subsequence.
    lcs = []
    i, j = n, m
    while i and j:
        if s1[i - 1] == s2[j - 1]:
            lcs.append(s1[i - 1])
            i -= 1
            j -= 1
        elif dp[i][j] == dp[i - 1][j]:
            i -= 1
        else:
            j -= 1
    lcs.reverse()

    return "".join(lcs)