72. Edit Distance

• Difficulty: Hard

• Topics: String, Dynamic Programming

• Similar Questions:

  • One Edit Distance

  • Delete Operation for Two Strings

  • Minimum ASCII Delete Sum for Two Strings

  • Uncrossed Lines

Problem:

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 operations permitted on a word:

1. Insert a character
2. Delete a character
3. 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')

Solutions:

class Solution {
public:
    int minDistance(string word1, string word2) {
        int len1 = word1.length();
        int len2 = word2.length();

        vector<vector<int>> dp(1 + len1, vector<int> (1 + len2, 0));
        for (int i = 0 ; i <= len1; ++i) {
            dp[i][0] = i;
        }

        for (int j = 0; j <= len2; ++j) {
            dp[0][j] = j;
        }

        for (int i = 1; i <= len1; ++i) {
            for (int j = 1; j <= len2; ++j) {
                if (word1[i-1] == word2[j-1]) {
                    dp[i][j] = dp[i-1][j-1];
                } else {
                    dp[i][j] = 1 + min(dp[i-1][j], min(dp[i][j-1],dp[i-1][j-1])); 
                }
            }
        }

        return dp[len1][len2];
    }
};