72. Edit Distance

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

Insert a character
Delete a character
Replace a character

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Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

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Example 2:

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: 
intention -> inention (remove 't')
inention -> enention (replace 'i' with 'e')
enention -> exention (replace 'n' with 'x')
exention -> exection (replace 'n' with 'c')
exection -> execution (insert 'u')

Constraints:

0 <= word1.length, word2.length <= 500
word1 and word2 consist of lowercase English letters.

Solution

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class Solution {
    public int minDistance(String word1, String word2) {
        int n = word1.length();
        int m = word2.length();
        
        int[][] d = new int[n + 1][m + 1];
        
        for (int i = 0; i < n + 1; i++) {
            d[i][0] = i;
        }
        
        for (int i = 0; i < m + 1; i++) {
            d[0][i] = i;
        }
        for (int i = 1; i < n + 1; i++) {
            for (int j = 1; j < m + 1; j++) {
                int editCost = Math.min(d[i - 1][j] + 1, d[i][j - 1] + 1);
                int diff = (word1.charAt(i - 1) == word2.charAt(j - 1)) ? 0: 1;
                d[i][j] = Math.min(editCost, d[i - 1][ j - 1] + diff);
            }
        }
        return d[n][m];
    }
}

Solution#

Solution