码迷,mamicode.com
首页 > 其他好文 > 详细

动态规划——Edit Distance

时间:2018-11-01 20:31:41      阅读:153      评论:0      收藏:0      [点我收藏+]

标签:[]   class   动态   replace   状态转移方程   nat   执行   ring   size   

大意:给定两个字符串word1和word2,为了使word1变为word2,可以进行增加、删除、替换字符三种操作,请输出操作的最少次数
 

Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace ‘h‘ with ‘r‘)
rorse -> rose (remove ‘r‘)
rose -> ros (remove ‘e‘)

Example 2:

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: 
intention -> inention (remove ‘t‘)
inention -> enention (replace ‘i‘ with ‘e‘)
enention -> exention (replace ‘n‘ with ‘x‘)
exention -> exection (replace ‘n‘ with ‘c‘)
exection -> execution (insert ‘u‘)
 
状态:dp[i][j]把word1[0..i-1]转换到word2[0..j-1]的最少操作次数
状态转移方程:
  (1)如果word1[i-1] == word2[j-1],则令dp[i][j] = dp[i-1][j-1]
  (2)如果word1[i-1] != word2[j-1],由于没有一个特别有规律的方法来断定执行何种操作,在增加、删除、替换三种操作中选一种操作次数少的赋值给dp[i][j];
    增加操作:dp[i][j] = dp[i][j-1] + 1
    删除操作:dp[i][j] = dp[i-1][j] + 1
       替换操作:dp[i][j] = dp[i-1][j-1] + 1
 
 1 int minDistance(string word1,string word2){
 2     int wlen1 = word1.size();
 3     int wlen2 = word2.size();
 4     
 5     int**dp = new int*[wlen1 + 1];
 6     for (int i = 0; i <= wlen1; i++)
 7         dp[i] = new int[wlen2 + 1];
 8     
 9     //int dp[maxn][maxn] = { 0 };
10     for (int i = 0; i <= wlen1; i++)
11         dp[i][0] = i;
12     for (int j = 0; j <= wlen2; j++)
13         dp[0][j] = j;
14     int temp = 0;
15     for (int i = 1; i <= wlen1; i++){
16         for (int j = 1; j <= wlen2; j++){
17             if (word1[i - 1] == word2[j - 1])dp[i][j] = dp[i - 1][j-1];
18             else{
19                 temp = dp[i - 1][j - 1]<dp[i - 1][j] ? dp[i - 1][j - 1] : dp[i - 1][j];
20                 temp = temp < dp[i][j - 1] ? temp : dp[i][j - 1];
21                 dp[i][j] = temp + 1;
22             }
23         }
24     }
25 
26     /*
27     for (int i = 0; i <= wlen1; i++)
28         delete[]dp[i];
29     delete[]dp;
30     */
31 
32     return dp[wlen1][wlen2];
33 }

 

 
 

动态规划——Edit Distance

标签:[]   class   动态   replace   状态转移方程   nat   执行   ring   size   

原文地址:https://www.cnblogs.com/messi2017/p/9892109.html

(0)
(0)
   
举报
评论 一句话评论(0
登录后才能评论!
© 2014 mamicode.com 版权所有  联系我们:gaon5@hotmail.com
迷上了代码!