Edit Distance

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:

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')

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