HDOJ 1052 Tian Ji -- The Horse Racing

Tian Ji -- The Horse Racing

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 26223    Accepted Submission(s): 7726

Problem Description

Here is a famous story in Chinese history.

"That was about 2300 years ago. General Tian Ji was a high official in the country Qi. He likes to play horse racing with the king and others."

"Both of Tian and the king have three horses in different classes, namely, regular, plus, and super. The rule is to have three rounds in a match; each of the horses must be used in one round. The winner of a single round takes two hundred silver dollars from the loser."

"Being the most powerful man in the country, the king has so nice horses that in each class his horse is better than Tian's. As a result, each time the king takes six hundred silver dollars from Tian."

"Tian Ji was not happy about that, until he met Sun Bin, one of the most famous generals in Chinese history. Using a little trick due to Sun, Tian Ji brought home two hundred silver dollars and such a grace in the next match."

"It was a rather simple trick. Using his regular class horse race against the super class from the king, they will certainly lose that round. But then his plus beat the king's regular, and his super beat the king's plus. What a simple trick. And how do you think of Tian Ji, the high ranked official in China?"



Were Tian Ji lives in nowadays, he will certainly laugh at himself. Even more, were he sitting in the ACM contest right now, he may discover that the horse racing problem can be simply viewed as finding the maximum matching in a bipartite graph. Draw Tian's horses on one side, and the king's horses on the other. Whenever one of Tian's horses can beat one from the king, we draw an edge between them, meaning we wish to establish this pair. Then, the problem of winning as many rounds as possible is just to find the maximum matching in this graph. If there are ties, the problem becomes more complicated, he needs to assign weights 0, 1, or -1 to all the possible edges, and find a maximum weighted perfect matching...

However, the horse racing problem is a very special case of bipartite matching. The graph is decided by the speed of the horses --- a vertex of higher speed always beat a vertex of lower speed. In this case, the weighted bipartite matching algorithm is a too advanced tool to deal with the problem.

In this problem, you are asked to write a program to solve this special case of matching problem.

 

Input

The input consists of up to 50 test cases. Each case starts with a positive integer n (n <= 1000) on the first line, which is the number of horses on each side. The next n integers on the second line are the speeds of Tian’s horses. Then the next n integers on the third line are the speeds of the king’s horses. The input ends with a line that has a single 0 after the last test case.

 

Output

For each input case, output a line containing a single number, which is the maximum money Tian Ji will get, in silver dollars.

 

Sample Input

3 92 83 71 95 87 74 2 20 20 20 20 2 20 19 22 18 0

 

Sample Output

200 0 0

 

Source

2004 Asia Regional Shanghai

 

题目是田忌赛马。大意是田忌赢一场得200，输一场输200，平局不变。问田忌最多能得多少钱。

本来我是想得很简单的= =，就是大于算赢，小于往下滚，等于平局。结果交上去之后发现根本不是那么回事！比我想象的要麻烦多了！（摔讲道理这么一比田忌好聪明

题解：

把田忌最快的和齐威王最快的比：

如果大于，钱+200

如果小于，把田忌最慢的马和齐威王最快的马比（并且钱 -200）

（重点）如果等于（重点）：

拿田忌最慢的马和齐威王最慢的马比：

如果大于，钱 +200

如果小于，等于，把田忌最慢的马和齐威王最快的马比（并且钱 -200）

关于直接对比的反例（转）：

1、如果选择全部打平，那么对于田忌 1 2 3 4，国王 1 2 3 4 ，这组数据，田忌什么黄金也得不到。但是如果选择 1->4, 4->3, 3->2, 2->1田忌可以得到400两黄金。 (大雄想的)

2、如果选择用最慢的马输掉比赛的话，对于田忌    3 4，国王 1    4 ，这组数据，田忌一胜一负，什么黄金也得不到，但是如果田忌选择 3->1 , 4->4 ,一胜一平，田忌可以得到200两黄金。

#include
#include
#include
#include
using namespace std;
int a[1111],b[1111];
bool cmp(int x,int y)
{
	return x>y;
}
int main()
{
	int i,n;
	int ai,aj,bi,bj;
	while(scanf("%d",&n),n)
	{
		for(i=0;ib[bi])
			{
				ans++;
				ai++;bi++;
			}
			else if(a[ai]==b[bi])
			{
				if(a[aj]>b[bj])
				{
					ans++;
					aj--;bj--;
				}
				else if(a[aj]