# [LeetCode 72] Edit Distance

### Question

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

### Stats

 Frequency 3 Difficulty 4 Adjusted Difficulty 3 Time to use --------

Ratings/Color = 1(white) 2(lime) 3(yellow) 4/5(red)

### Analysis

This is a difficult DP problem. A lot of people said in their blog that they spent tons of time on this question.

### Solution

I posted below a very standard solution. The unconventional part of this solution is instead of declaring DP array of m*n size, I must declare it (m+1)*(n+1) size, where dp[i][j] denotes the distance of 2 strings that ends with (i)th and (j)th char respectively.

The rest of the code is easy to understand.

### Code

my code

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

int[][] dp = new int[m+1][n+1];
for (int i = 0; i <= m; i++) {
dp[i][0] = i;
}
for (int i = 0; i <= n; i++) {
dp[0][i] = i;
}
for (int a = 1; a <= m; a++) {
char aa = word1.charAt(a-1);
for (int b = 1; b <= n; b++) {
char bb = word2.charAt(b-1);
if (aa == bb)
dp[a][b] = dp[a-1][b-1];
else {
int t1 = dp[a-1][b-1] + 1;
int t2 = dp[a][b-1] + 1;
int t3 = dp[a-1][b] + 1;
dp[a][b] = Math.min(Math.min(t1, t2), t3);
}
}
}
return dp[m][n];
}
``````