Edit Distance

LeetCode #72

Description:

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

Example:

Note

Idea:

DP[i+1][j+1]就是代表word1[i]和word2[j]之间的distance。

Code:

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m=word1.size(), n=word2.size();
        // consider all operations on word1
        vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
        for(int i=0; i<=m; ++i)
            dp[i][0]=i;
        for(int i=0; i<=n; ++i)
            dp[0][i]=i;

        for(int i=1; i<=m; ++i){
            for(int j=1; j<=n; ++j){
                if(word1[i-1]==word2[j-1])
                    dp[i][j]=dp[i-1][j-1];
                else{
                    dp[i][j]=1+std::min(std::min(dp[i][j-1], // Insert on word1
                        dp[i-1][j]),  // delete on word1
                        dp[i-1][j-1]); // replace on word1
                }

            }
        }

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