HDU 4745 Two Rabbits 区间dp

I - Two Rabbits

Time Limit:5000MS    Memory Limit:65535KB    64bit IO Format:%I64d & %I64u

Submit Status Practice HDU 4745

Appoint description:

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
  
  
  
  

因为是个环要求这环的最长不连续回文环可以把数组扩2倍求回文链

也可以不扩 对于数据 2 1 1 2 1 3可以看成 回文环 2 1 1 2 和 回文环 1or3 组成的

所以状态转移方程为 dp【i，j】=max（dp【i，j】，dp【i+1，j】，dp【i，j-1】）

如何s【i】=s【j】 dp【i，j】=max（dp【i，j】，dp【i+1，j-1】+2）

最后答案为两个区间的回文长度和

ACcode：

#include <map>
#include <queue>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
#define maxn 1010
using namespace std;
int dp[maxn][maxn];
int a[maxn];
int main(){
    int n,ans;
    while(scanf("%d",&n),n){
        memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;++i){
            scanf("%d",&a[i]);
            dp[i][i]=1;
        }
        for(int l=2;l<=n;++l)
            for(int i=1;i+l-1<=n;++i){
                int j=i+l-1;
                dp[i][j]=max(dp[i][j],max(dp[i+1][j],dp[i][j-1]));
                if(a[i]==a[j])dp[i][j]=max(dp[i][j],dp[i+1][j-1]+2);
            }
        ans=0;
        for(int i=1;i<=n;++i)ans=max(ans,dp[1][i]+dp[i+1][n]);
        printf("%d\n",ans);
    }
}