Edit Distance

leetcode的题目

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

这是一个动态规划的题目

wiki上的递推公式如下

代码如下

　　int minDistance(string word1, string word2) {
        int **dp = new int*[word1.length() + 1];
        for(int i = 0; i < word1.length() + 1; i ++)
            dp[i] = new int[word2.length() + 1];

        for(int i = 0; i < word1.length() + 1; i ++)
            dp[i][0] = i;
        for(int i = 0; i < word2.length() + 1; i ++)
            dp[0][i] = i;
        
        for(int i = 1; i < word1.length() + 1; i ++)
            for(int j = 1; j < word2.length() + 1; j ++)
            {
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + 1;//insert or delete

                if(word1[i - 1] != word2[j - 1])//modify
                {
                    dp[i][j] = min(dp[i][j], dp[i - 1][j - 1] + 1);
                }
                else
                {
                    dp[i][j] = min(dp[i][j], dp[i - 1][j - 1]);
                }
            }

            return dp[word1.length()][word2.length()];
    }

 时间复杂度和空间复杂度都是O(M*N)

如果不要求计算修改过程, 那么空间复杂度可以优化到线性

感觉自己对动态规划还是很不敏感

查阅相关资料后发现, 这个题目属于文本比较算法, 还有很多相关的内容, 比如说LCS和一些其他更加高级的算法, 以后有空再研究一下