72_edit_distance.md

72 - Edit Distance

leetcode link

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')

Solution

// 31/05/2020
int minDistance(string word1, string word2) {
    auto size1 = word1.size();
    auto size2 = word2.size();
    vector<vector<int>> mindist(size2+1, vector<int>(size1+1, 0));
    for(int i = 1; i < size1 + 1; ++i)
        mindist[0][i] = i;
    for(int j = 1; j < size2 + 1; ++j)
        mindist[j][0] = j;
    for(int j = 1; j < size2 +1; ++j){
        for(int i = 1; i < size1 + 1; ++i){
            mindist[j][i] = (word1[i-1] == word2[j-1])?
                mindist[j-1][i-1]
                :1 + min({mindist[j-1][i], 
                          mindist[j][i-1], 
                          mindist[j-1][i-1]});
        }
    }
    return mindist[size2][size1];
}