Edit Distance

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

Solution: Dynamic Programming.
1. Time: O(mn) Space: O(mn)
2. Time: O(mn) Space: O(n);

class Solution {
public:
    int minDistance(string word1, string word2) {
        int M = word1.size(), N = word2.size();
        int dp[M+1][N+1];
        for(int i = 0; i < M + 1; i++) {
            dp[i][0] = i;
        }
        for(int j = 0; j < N + 1; j++) {
            dp[0][j] = j;
        }
        for(int i = 1; i < M + 1; i++) {
            for(int j = 1; j < N + 1; 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][j-1], dp[i-1][j])) + 1;
                }
            }
        }
        return dp[M][N];
    }
};