【重点】【DP】72.编辑距离

题目

法1：DP

二维DP，自底向上，参见《算法小抄》中的解释，更容易理解！！！

class Solution {
    public int minDistance(String word1, String word2) {
        int m = word1.length() + 1, n = word2.length() + 1; // 加1是兼容空串
        int[][] dp = new int[m][n];
        for (int i = 1; i < n; ++i) {
            dp[0][i] = i;
        }
        for (int i = 1; i < m; ++i) {
            dp[i][0] = i;
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {
                    dp[i][j] = Math.min(dp[i - 1][j - 1], Math.min(dp[i][j - 1], dp[i - 1][j])) + 1;
                }
            }
        }

        return dp[m - 1][n - 1];
    }
}