72. Edit Distance

https://leetcode.com/problems/edit-distance/

Problem

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.

Solution

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

• #dp