[状压dp] hdu 4628 Pieces

深度解析代码优化与算法应用

最新推荐文章于 2021-11-18 20:39:39 发布

原创最新推荐文章于 2021-11-18 20:39:39 发布 · 1.3k 阅读

1 ·

CC 4.0 BY-SA版权

动态规划专栏收录该内容

91 篇文章

订阅专栏

本文深入探讨了代码优化的策略与算法在实际开发中的应用，从性能提升角度出发，详细介绍了如何通过优化代码结构、选择高效算法来提高程序运行效率。包括排序算法、动态规划、贪心算法等经典算法的实战案例分析，以及如何利用现代工具和技术实现自动化代码优化。

题目链接：

http://acm.hdu.edu.cn/showproblem.php?pid=4628

Pieces

Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1665 Accepted Submission(s): 862

Problem Description

You heart broke into pieces.My string broke into pieces.But you will recover one day,and my string will never go back.
Given a string s.We can erase a subsequence of it if this subsequence is palindrome in one step. We should take as few steps as possible to erase the whole sequence.How many steps do we need?
For example, we can erase abcba from axbyczbea and get xyze in one step.

Input

The first line contains integer T,denote the number of the test cases. Then T lines follows,each line contains the string s (1<= length of s <= 16).
T<=10.

Output

For each test cases,print the answer in a line.

Sample Input

  
   2
aa
abb

Sample Output

1
2

Source

2013 Multi-University Training Contest 3

Recommend

zhuyuanchen520 | We have carefully selected several similar problems for you: 5061 5060 5059 5058 5057

Statistic | Submit | Discuss | Note 题目意思：

给一字符串，每次可以移除一个回文串，求最少要多少步，可以把该串移空。

解题思路：

状态压缩dp

dp[i]表示i状态表示的字符串是否是回文的。

对每个状态，枚举除掉是回文串的子状态进行更新。

ps:对于状态i，枚举i的子状态可以这样写 for(int j=i;j;j=(i&(j-1))

代码：

//#include<CSpreadSheet.h>

#include<iostream>
#include<cmath>
#include<cstdio>
#include<sstream>
#include<cstdlib>
#include<string>
#include<string.h>
#include<cstring>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<ctime>
#include<bitset>
#include<cmath>
#define eps 1e-6
#define INF 0x3f3f3f3f
#define PI acos(-1.0)
#define ll __int64
#define LL long long
#define lson l,m,(rt<<1)
#define rson m+1,r,(rt<<1)|1
#define M 1000000007
//#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;

int dp[1<<16],ans[1<<16];
char sa[22];
int n;

int main()
{
    //freopen("in.txt","r",stdin);
   //freopen("out.txt","w",stdout);
   int t;

   scanf("%d",&t);
   while(t--)
   {
       scanf("%s",sa);
       n=strlen(sa);

       dp[0]=false;
       for(int i=1;i<(1<<n);i++)
       {
           int l=0,r=n-1;
           bool flag=true;

           while(l<=r)
           {
               while(l<n&&(i&(1<<l))==0)
                    l++;
               while(r>=0&&(i&(1<<r))==0)
                    r--;
               if(l>r)
                    break;

               if(sa[l]!=sa[r])
               {
                   flag=false;
                   break;
               }

               l++;
               r--;
           }
           dp[i]=flag;
           //printf("i:%d %d\n",i,dp[i]);
           ans[i]=n;
       }
       ans[0]=0;
       for(int i=1;i<(1<<n);i++)
       {
           for(int j=i;j;j=(i&(j-1)))
           {
               if(dp[j])
                    ans[i]=min(ans[i],ans[i-j]+1);
           }
       }
       printf("%d\n",ans[(1<<n)-1]);



   }
    return 0;
}