leetcode 19: 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

class Solution {
public:
    int minDistance(string word1, string word2) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int n = word1.size();
        int m = word2.size();
        
        int d[n+1][m+1];
        
        for( int i=0; i<=n; i++) {
            d[i][0] = i;
        }
        
        for( int i=0; i<=m; i++) {
            d[0][i] = i;
        }
        
        for( int i=1; i<=n; i++) {
            for(int j=1; j<=m; j++) {

			//attention: index of d array and word array are different.
                d[i][j] = minimum( d[i-1][j] + 1 , d[i][j-1] + 1, d[i-1][j-1] + (word1[i-1] == word2[j-1] ? 0 : 1)   );  
            }
        }
        
        return d[n][m];
    }
    
    int minimum( int x, int y, int z) {
        
        return x>y ? ( y>z ? z : y  ) : ( x>z ? z : x  );
        
    }
    
};