Edit_Distance.cpp

// Given two words word1 and word2, find the minimum number of steps required 
// to convert word1 to word2. (each operation is counted as 1 step.)

// You have the following 3 operations permitted on a word:
// a) Insert a character
// b) Delete a character
// c) Replace a character

class Solution {
public:
    int minDistance(string word1, string word2) {
        // dp[i, j] = dp[i-1, j-1],  if (w1[i] == w2[j])
        // dp[i, j] = 1 + min(dp[i-1, j], dp[i, j-1], dp[i-1, j-1])
        int len1 = word1.size(), len2 = word2.size();
        int dp[len1+1][len2+1];
        for (int i = 0; i <= len1; i++) {
            dp[i][0] = i;
        }
        for (int j = 1; 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][j-1], min(dp[i-1][j], dp[i-1][j-1]));
                }
            }
        }
        return dp[len1][len2];
    }
};