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

reference: https://www.youtube.com/watch?v=Uv9dNpHlSY4

Solution：DP

思路：

Screen Shot 2017-11-23 at 17.23.58.png

Time Complexity: O(mn) Space Complexity: O(mn)

Solution Code：

class Solution {
    public int minDistance(String word1, String word2) {
        int m = word1.length();
        int n = word2.length();
        
        int[][] dist = new int[m + 1][n + 1];
        // init
        for(int i = 0; i <= m; i++) dist[i][0] = i;
        for(int j = 0; j <= n; j++) dist[0][j] = j;
        for(int i = 1; i <= m; i++) {
            for(int j = 1; j <= n; j++) {
                dist[i][j] = Integer.MAX_VALUE;
            }
        }
        
        // start dp
        for(int i = 1; i <= m; i++) {
            for(int j = 1; j <= n; j++) {
                // (1) and (2)
                dist[i][j] = Math.min(dist[i][j - 1], dist[i - 1][j]) + 1; 
                // (3)
                if(word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    dist[i][j] = Math.min(dist[i][j], dist[i - 1][j - 1]);
                }
                else {
                    dist[i][j] = Math.min(dist[i][j], dist[i - 1][j - 1] + 1);
                }
            }
        }
        
        return dist[m][n];
            
    }
}