LeetCode OJ - 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

分析：典型動態規劃，使用二維記錄表，dp[i][j]表示從word1字符串1到i、word2字符串從1到j位置的最小編輯次數。

dp[i][j] = min{dp[i-1][j] + 1, dp[i][j-1] + 1, dp[i-1][j-1] + word1[i-1] == word2[j-1] ? 0 : 1}

class Solution {
public:
    int minDistance(string word1, string word2) {
        int row = word1.size() + 1;
        int col = word2.size() + 1;
        
        vector<vector<int> > f(row, vector<int>(col));

        for (int i = 0; i < row; i++)
            f[i][0] = i;

        for (int i = 0; i < col; i++)
            f[0][i] = i;

        for (int i = 1; i < row; i++)
            for (int j = 1; j < col; j++){
                f[i][j] = min(f[i-1][j-1] + (word1[i-1] == word2[j-1] ? 0 : 1), min(f[i-1][j]+1, f[i][j-1]+1));
            }

        return f[row-1][col-1];
    }
};