edit-distance-动态规划，计算两词之间变换的最小步数

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

动态规划，使用数组记录每一步的步数，注意循环长度为<=length，dp[0][0]表示null的时候

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