sicily 1176 Two Ends

Description

In the two-player game "Two Ends", an even number of cards is laid out in a row. On each card, face up, is written a positive integer. Players take turns removing a card from either end of the row and placing the card in their pile. The player whose cards add up to the highest number wins the game. Now one strategy is to simply pick the card at the end that is the largest -- we'll call this the greedy strategy. However, this is not always optimal, as the following example shows: (The first player would win if she would first pick the 3 instead of the 4.) 
3 2 10 4 
You are to determine exactly how bad the greedy strategy is for different games when the second player uses it but the first player is free to use any strategy she wishes.

Input

There will be multiple test cases. Each test case will be contained on one line. Each line will start with an even integer n followed by n positive integers. A value of n = 0 indicates end of input. You may assume that n is no more than 1000. Furthermore, you may assume that the sum of the numbers in the list does not exceed 1,000,000.

Output

For each test case you should print one line of output of the form: 
In game m, the greedy strategy might lose by as many as p points. 
where m is the number of the game (starting at game 1) and p is the maximum possible difference between the first player's score and second player's score when the second player uses the greedy strategy. When employing the greedy strategy, always take the larger end. If there is a tie, remove the left end.

Sample Input

4 3 2 10 4
8 1 2 3 4 5 6 7 8
8 2 2 1 5 3 8 7 3
0

Sample Output

 

In game 1, the greedy strategy might lose by as many as 7 points.
In game 2, the greedy strategy might lose by as many as 4 points.
In game 3, the greedy strategy might lose by as many as 5 points.

分析：

如果只是为了正确，深搜是种可行的办法，但是显然数据规模不小，深搜要超时。用空间换时间，用DP的办法做，也算是中记忆化搜索。每次抽牌方法需要比较的是抽出两端任意一张后的取法最大所得，而另一人取法是贪心，递归可求。

代码：

// Problem#: 1176
// Submission#: 1914687
// The source code is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
// URI: http://creativecommons.org/licenses/by-nc-sa/3.0/
// All Copyright reserved by Informatic Lab of Sun Yat-sen University
#include <iostream>
#include <cstring>
using namespace std;

#define MAX 1000

int num[MAX];
int buf[MAX][MAX];

inline int max(int a, int b) { return a > b ? a : b; }

int dp(int a, int b) {
    if (a == b-1) return buf[a][b] = max(num[a], num[b]);
    if (buf[a][b]) return buf[a][b];
    int t1, t2;
    t1 = num[a];
    t1 += (num[a + 1] >= num[b]) ? dp(a + 2, b) : dp(a + 1, b - 1);
    t2 = num[b];
    t2 += (num[a] >= num[b - 1]) ? dp(a + 1, b - 1) : dp(a, b - 2);
    return buf[a][b] = max(t1, t2);
}

int main(void) {
    int n, s, cnt = 1;
    while (cin >> n && n) {
        s = 0;
        for (int i = 0; i < n; ++i) {
            cin >> num[i];
            s += num[i];
        }
        memset(buf, 0, sizeof(buf));
        cout << "In game " << cnt++ << ", the greedy strategy might lose by as many as " << 2 * dp(0, n - 1) - s << " points." << endl;
    }
    return 0;
}