Leetcode Edit Distance 72

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
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题目链接

dp[i][j] 表示从word1［i］到 word2［j］需要操作的最小次数
考虑从dp[i-1][j-1] 怎么到dp[i][j]
word1［i］和word2［j］：
如果 word1［i］＝＝ word2［j］：
dp[i][j]＝ dp[i-1][j-1]
否则：
若删除, dp[i][j]＝ dp[i-1][j]+1
若插入, dp[i][j]＝ dp[i][j-1]+1
若替换, dp[i][j]＝ dp[i-1][j-1]+1
取最小

class Solution {public:    int minDistance(string word1, string word2) {        int len1=word1.length();        int len2=word2.length();        if(len1==0 || len2==0) return (len1!=0) ? len1:len2;        int dp[1000][1000];        for(int i=0;i<=len1;i++)                dp[i][0]=i;        for(int j=0;j<=len2;j++)                dp[0][j]=j;        for(int i=1;i<=len1;i++){                for(int j=1;j<=len2;j++){                        if(word1[i-1]==word2[j-1]){                                dp[i][j]=dp[i-1][j-1];                        }                        else{                                dp[i][j]=min(dp[i-1][j],min(dp[i][j-1],dp[i-1][j-1]))+1;                        }                }        }        return dp[len1][len2];    }};