LeetCode Edit Distance

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

Solution:

classical edit distance

pay attention to the initialization circumstances, we can get dp[i][0] = i and dp[0][j] = j

<span style="font-size:18px;">import java.util.*;

public class Solution {
public int minDistance(String word1, String word2) {
if (word1 == null)
return 0;
if (word2 == null)
return 0;

int n = word1.length();
int m = word2.length();
if (n == 0)
return m;
if (m == 0)
return n;

int dp[][] = new int[n + 1][m + 1];

for (int i = 0; i <= n; i++)
dp[i][0] = i;
for (int j = 0; j <= m; j++)
dp[0][j] = j;

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

return dp
[m];
}
}</span>