hdu4745（区间dp，求最大回文串的长度）

Two Rabbits

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 1346    Accepted Submission(s): 669

Problem Description

Long long ago, there lived two rabbits Tom and Jerry in the forest. On a sunny afternoon, they planned to play a game with some stones. There were n stones on the ground and they were arranged as a clockwise ring. That is to say, the first stone was adjacent to the second stone and the n-th stone, and the second stone is adjacent to the first stone and the third stone, and so on. The weight of the i-th stone is ai.

The rabbits jumped from one stone to another. Tom always jumped clockwise, and Jerry always jumped anticlockwise.

At the beginning, the rabbits both choose a stone and stand on it. Then at each turn, Tom should choose a stone which have not been stepped by itself and then jumped to it, and Jerry should do the same thing as Tom, but the jumping direction is anti-clockwise.

For some unknown reason, at any time , the weight of the two stones on which the two rabbits stood should be equal. Besides, any rabbit couldn't jump over a stone which have been stepped by itself. In other words, if the Tom had stood on the second stone, it cannot jump from the first stone to the third stone or from the n-the stone to the 4-th stone.

Please note that during the whole process, it was OK for the two rabbits to stand on a same stone at the same time. 

Now they want to find out the maximum turns they can play if they follow the optimal strategy.

 

Input

The input contains at most 20 test cases.
For each test cases, the first line contains a integer n denoting the number of stones.
The next line contains n integers separated by space, and the i-th integer ai denotes the weight of the i-th stone.(1 <= n <= 1000, 1 <= ai <= 1000)
The input ends with n = 0.

 

Output

For each test case, print a integer denoting the maximum turns.

 

Sample Input

   
   
   
   

    
    
    
    1
1
4
1 1 2 1
6
2 1 1 2 1 3
0
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    1
4
5

    
    
    
    
 
     
 
      Hint 
     
 For the second case, the path of the Tom is 1, 2, 3, 4, and the path of Jerry is 1, 4, 3, 2. For the third case, the path of Tom is 1,2,3,4,5 and the path of Jerry is 4,3,2,1,5. 
    
   
   
   
   

题意：两只兔子，在n块围成一个环形的石头上跳跃，每块石头有一个权值ai，一只从左往右跳，一只从右往左跳，每跳一次，两只兔子所在的石头的权值都要相等，在一圈内（各自不能超过各自的起点，也不能再次回到起点）问它们最多能经过多少个石头。

思路：其实仔细观察后可以发现其实就是求回文串的最大长度，只是最后处理的时候要注意的是因为是一个环，所以可能出现回文串+1的情况，所以得出答案的时候要进行一下判断。

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<queue>
#include<stack>
using namespace std;
typedef long long ll;
int dp[2010][2010];
int x[2010];
int fdp(int a,int b)
{
    if(dp[a][b]!=-1)
        return dp[a][b];
    if(a==b)
        return dp[a][b]=1;
    if(a>b)
        return dp[a][b]=0;
    int max0=0;
    max0=max(fdp(a+1,b),fdp(a,b-1));
    if(x[a]==x[b])
        max0=max(max0,fdp(a+1,b-1)+2);
    return dp[a][b]=max0;
}
int main()
{
    int n;
    while(~scanf("%d",&n)&&n)
    {
        memset(dp,-1,sizeof(dp));
        for(int i=0; i<n; i++)
            scanf("%d",&x[i]),x[i+n]=x[i];
        fdp(0,n*2-1);
        int ans=0;
        for(int i=0; i<n; i++)
            ans=max(ans,dp[i][i+n-1]),
            ans=max(ans,dp[i][i+n-2]+1);///判断是否为回文串+1的情况
        printf("%d\n",ans);
    }
    return 0;
}