Leetcode解题-Edit Distance

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描述

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

a) Insert a character
b) Delete a character
c) Replace a character

分析

编辑距离是一个很重要的文本相似度度量标准，比较经典，通常的解法都是二维动态规划。dp[i][j]代表word1中前i个字符和word2前j个字符的编辑距离，则有

dp[i][j] = dp[i - 1][j - 1] (if word1[i] == word2[j])
dp[i][j] = min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]) + 1 (otherwise)

代码

Python

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class Solution(object):
    def minDistance(self, word1, word2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        n1 = len(word1)
        n2 = len(word2)
        if word1 == word2:
            return 0
        dp = [[0] * (n2 + 1) for i in xrange(n1 + 1)]
        for i in xrange(1, n1 + 1):
            dp[i][0] = i
        for j in xrange(1, n2 + 1):
            dp[0][j] = j

        for i in xrange(1, n1 + 1):
            for j in xrange(1, n2 + 1):
                if word1[i - 1] == word2[j - 1]:
                    dp[i][j] = dp[i - 1][j - 1]
                else:
                    dp[i][j] = min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]) + 1
        return dp[n1][n2]

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