HDU 4597 Play Game(DFS,区間DP)
Play Game
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others) Total Submission(s): 1274 Accepted Submission(s): 737
Problem Description Alice and Bob are playing a game. There are two piles of cards. There are N cards in each pile, and each card has a score. They take turns to pick up the top or bottom card from either pile, and the score of the card will be added to his total score. Alice and Bob are both clever enough, and will pick up cards to get as many scores as possible. Do you know how many scores can Alice get if he picks up first?
Input The first line contains an integer T (T≤100), indicating the number of cases. Each case contains 3 lines. The first line is the N (N≤20). The second line contains N integer ai (1≤ai≤10000). The third line contains N integer bi (1≤bi≤10000).
Output For each case, output an integer, indicating the most score Alice can get.
Sample Input 2
1 23 53
3 10 100 20 2 4 3
Sample Output 53 105
dp[x 1][y 1][x 2][y 2]は、現在の先手のこの人がx 1~y 1,x 2~y 2の2つの区間で最大値を得ることができることを示し、dp[x 1][y 1][x 2][y 2]の値は現在の和sum-(次の状態、すなわち相手の先手が得ることができる最大値)に等しい.
区間DPについては、このブログを参照http://blog.csdn.net/dacc123/article/details/50885903
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others) Total Submission(s): 1274 Accepted Submission(s): 737
Problem Description Alice and Bob are playing a game. There are two piles of cards. There are N cards in each pile, and each card has a score. They take turns to pick up the top or bottom card from either pile, and the score of the card will be added to his total score. Alice and Bob are both clever enough, and will pick up cards to get as many scores as possible. Do you know how many scores can Alice get if he picks up first?
Input The first line contains an integer T (T≤100), indicating the number of cases. Each case contains 3 lines. The first line is the N (N≤20). The second line contains N integer ai (1≤ai≤10000). The third line contains N integer bi (1≤bi≤10000).
Output For each case, output an integer, indicating the most score Alice can get.
Sample Input 2
1 23 53
3 10 100 20 2 4 3
Sample Output 53 105
dp[x 1][y 1][x 2][y 2]は、現在の先手のこの人がx 1~y 1,x 2~y 2の2つの区間で最大値を得ることができることを示し、dp[x 1][y 1][x 2][y 2]の値は現在の和sum-(次の状態、すなわち相手の先手が得ることができる最大値)に等しい.
区間DPについては、このブログを参照http://blog.csdn.net/dacc123/article/details/50885903
#include <iostream>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
#include <math.h>
#include <stdio.h>
using namespace std;
int dp[30][30][30][30];
int a[30];
int b[30];
int n;
int sum;
int dfs(int x1,int y1,int x2,int y2,int sum)
{
if(dp[x1][y1][x2][y2])
return dp[x1][y1][x2][y2];
if((x1>y1)&&(x2>y2))
return 0;
int num=0;
if(x1<=y1)
{
num=max(num,sum-dfs(x1+1,y1,x2,y2,sum-a[x1]));
num=max(num,sum-dfs(x1,y1-1,x2,y2,sum-a[y1]));
}
if(x2<=y2)
{
num=max(num,sum-dfs(x1,y1,x2+1,y2,sum-b[x2]));
num=max(num,sum-dfs(x1,y1,x2,y2-1,sum-b[y2]));
}
dp[x1][y1][x2][y2]=num;
return dp[x1][y1][x2][y2];
}
int main()
{
int t;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
sum=0;
for(int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
sum+=a[i];
}
for(int i=1;i<=n;i++)
{
scanf("%d",&b[i]);
sum+=b[i];
}
memset(dp,0,sizeof(dp));
printf("%d
",dfs(1,n,1,n,sum));
}
return 0;
}