LeetCode Problem : Edit Distance

Problem

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

Code

int minDistance(string word1, string word2) {
    // IMPORTANT: Please reset any member data you declared, as
    // the same Solution instance will be reused for each test case.
    int m = word1.size();
    int n = word2.size();
    vector<vector<int> > M(m+1,vector<int>(n+1));
    M[0][0] = 0;
    for(int j = 0;j < n;++j)
        M[0][j + 1] = j + 1;
    for(int i = 0;i < m;++i)
        M[i + 1][0] = i + 1;
    for(int i = 1;i <= m;++i){
        for(int j = 1;j <= n;++j){
            int a = min(M[i-1][j],M[i][j - 1]) + 1;
            if(word1[i - 1] == word2[j - 1])
                M[i][j] = M[i - 1][j - 1];
            else{
                int a = min(M[i-1][j],M[i][j - 1]);
                a = min(a,M[i - 1][j - 1]);
                M[i][j] = a + 1;
            }
        }
    }
    return M[m][n];
}