LeetCode: 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

   typedef vector< vector<int> > vvi;  
   typedef vector<int> vi;  

   int minDistance(string word1, string word2) {  
     int n1 = word1.length();  
     int n2 = word2.length();  
     if(n1 == 0)return n2;  
     if(n2 == 0)return n1;  
     vvi dp(n1+1, vi(n2+1,0));  
     for(int i = 1; i<=n1; i++)dp[i][0] = i;  
     for(int i = 1; i<=n2; i++)dp[0][i] = i;  
     for (int i = 1; i <=n1; i++)  
     {  
       for (int j = 1; j <=n2; j++)  
       {  
         if(word1[i-1] == word2[j-1])  
         {  
           dp[i][j] = dp[i-1][j-1];  
         }  
         else  
         {  
           dp[i][j] = min(min(dp[i-1][j],dp[i][j-1]),dp[i-1][j-1]) + 1;  
         }  
       }  
     }  
     return dp[n1][n2];  
   }