leetcode------Edit Distance

标题：	Edit Distance
通过率：	26.1%
难度：	难

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

本题是动态规划的经典题目，公式如下：

1、s1.length==0,return s2.length;

2、s2.length==0,return s1.length;

3、if  s1.charat(i)==s2.charat(j),res[i][j]=res[i-1][j-1]

　　else  res[i][j]=min(res[i-1][j],res[i][j-1],res[i-1][i-1]+1)

具体看代码：

public class Solution {
    public int minDistance(String word1, String word2) {
int len1 = word1.length();
    int len2 = word2.length();
 
    // len1+1, len2+1, because finally return dp[len1][len2]
    int[][] dp = new int[len1 + 1][len2 + 1];
 
    for (int i = 0; i <= len1; i++) 
        dp[i][0] = i;
    
    for (int j = 0; j <= len2; j++) 
        dp[0][j] = j;
    
 
    //iterate though, and check last char
    for (int i = 1; i <= len1; i++) {
        char c1 = word1.charAt(i-1);
        for (int j = 1; j <= len2; j++) {
            char c2 = word2.charAt(j-1);
 
            //if last two chars equal
            if (c1 == c2) {
                //update dp value for +1 length
                dp[i][j] = dp[i-1][j-1];
            } else {
                int replace = dp[i-1][j-1] + 1;
                int insert = dp[i-1][j] + 1;
                int delete = dp[i][j-1] + 1;
 
                int min = Math.min(replace, insert);
                min = Math.min(min,delete);
                dp[i][j] = min;
            }
        }
    }
 
    return dp[len1][len2];
    }
}