【LeetCode 72】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

思路：

　　典型的动态规划题，递归要超时哦。状态转移方程：

a[i][j] = min(

1. a[i-1][j] + 1,

2. a[i][j-1] + 1,

3. word1[i] == word2[j] ? a[i-1][j-1] : a[i-1][j-1] + 1

);

C++:

 1 class Solution {
 2 public:
 3     int minDistance(string word1, string word2) {
 4
 5         const int row = word1.size() + 1;
 6         const int col = word2.size() + 1;
 7
 8         int a[row][col];
 9
10         for(int i = 0; i < row; i++)
11             a[i][0] = i;
12         for(int i = 0; i < col; i++)
13             a[0][i] = i;
14
15         for(int i = 1; i < row; i++)
16             for(int j = 1; j < col; j++)
17                 a[i][j] = min((word1[i-1] == word2[j-1] ? a[i-1][j-1] : (a[i-1][j-1] + 1)), min(a[i-1][j] + 1, a[i][j-1] + 1));
18
19         return a[row-1][col-1];
20     }
21 };