72. Edit Distance

Problem Statement

Hard

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

Example 1:

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

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.

C++

Source file

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.size(), n = word2.size(), pre;
        vector<int> cur(n + 1, 0);
        for (int j = 1; j <= n; j++) {
            cur[j] = j;
        }
        for (int i = 1; i <= m; i++) {
            pre = cur[0];
            cur[0] = i;
            for (int j = 1; j <= n; j++) {
                int temp = cur[j];
                if (word1[i - 1] == word2[j - 1]) {
                    cur[j] = pre;
                } else {
                    cur[j] = min(pre, min(cur[j - 1], cur[j])) + 1;
                }
                pre = temp;
            }
        }
        return cur[n];
    }
};