[LeetCode]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

思考：DP。

• dp[i-1][j]+1：删除一个字符
• dp[i][j-1]+1：插入一个字符
• dp[i-1][j-1]+(word1[i-1]==word2[j-1])?0:1：替换一个字符

class Solution {
public:
    int minDistance(string word1, string word2) {
        int len1=word1.size()+1;
        int len2=word2.size()+1;
        vector<vector<int> > dp(len1,vector<int>(len2));
        int i,j;
        for(i=0;i<len1;i++) dp[i][0]=i;
        for(i=0;i<len2;i++) dp[0][i]=i;
        for(i=1;i<len1;i++)
        {
            for(j=1;j<len2;j++)
            {
                dp[i][j]=min(dp[i-1][j-1]+((word1[i-1]==word2[j-1])?0:1),min(dp[i-1][j]+1,dp[i][j-1]+1));
            }
        }
        return dp[len1-1][len2-1];
    }
};