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[LeetCode] Edit Distance(很好的DP)

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

用m*n的矩阵vector中的(i,j)存储从word1中(0...i)到word2中(0...j)的最小变化次数

矩阵中,从上到下对应删除操作,从左到右对应插入操作,从左上到右下对应Replace操作。

class Solution {public:    int minDistance(string word1, string word2) { //1->2        if(word1==word2)            return 0;        int len1 = word1.size();        int len2 = word2.size();        vector<int> temp(len2+1,0);        vector<vector<int> > vec(len1+1,temp);        for(int i=1;i<=len1;i++){            vec[i][0] = i;        }        for(int j=1;j<=len2;j++){            vec[0][j] = j;        }        for(int i=1;i<=len1;i++){            for(int j=1;j<=len2;j++){                int tem1,tem2;                tem1 = min(vec[i-1][j]+1,vec[i][j-1]+1);                tem2 = word1[i-1]==word2[j-1] ? vec[i-1][j-1]:vec[i-1][j-1]+1;                vec[i][j] = min(tem1,tem2);            }//end for        }//end for        return vec[len1][len2];    }};