leetcodeOJ 72. Edit Distance

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

思路

//动态规划
//递推式：
// dp[i][0] = i;
// dp[0][j] = j;
// dp[i][j] = dp[i - 1][j - 1], if word1[i - 1] = word2[j - 1];
// dp[i][j] = min(dp[i - 1][j - 1] + 1, dp[i - 1][j] + 1, dp[i][j - 1] + 1), otherwise.

代码如下：

class Solution {public:    int minDistance(string word1, string word2) {        int n = word1.length();        int m = word2.length();        if(m == 0)            return n;        if(n == 0)            return m;        int ans[n+1][m+1] = {0};        for(int i = 0; i <= n; i++){            ans[i][0] = i;        }        for(int j = 0; j <= m; j++){            ans[0][j] = j;        }                for(int i = 1; i <= n; i++){            for(int j = 1; j <= m; j++){                if(word1[i-1] == word2[j-1]){                    ans[i][j] = ans[i-1][j-1];                }                else{                    ans[i][j] = min(min(ans[i-1][j-1], ans[i][j-1]), ans[i-1][j]) + 1;                }            }        }        return ans[n][m];    }};