*Edit Distance

题目：

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:

Insert a character

Delete a character

Replace a character

Example

Given word1 =

"mart"

and word2 =

"karma"

, return

3

.

/**
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*/

public class Solution {
public int minDistance(String word1, String word2) {
int n = word1.length();
int m = word2.length();

int[][] dp = new int[n+1][m+1];
for(int i=0; i< m+1; i++){
dp[0][i] = i;
}
for(int i=0; i<n+1; i++){
dp[i][0] = i;
}

for(int i = 1; i<n+1; i++){
for(int j=1; j<m+1; j++){
if(word1.charAt(i-1) == word2.charAt(j-1)){
dp[i][j] = dp[i-1][j-1];
}else{
dp[i][j] = 1 + Math.min(dp[i-1][j-1],Math.min(dp[i-1][j],dp[i][j-1]));
}
}
}
return dp
[m];
}
}