Tian Ji – The Horse Racing（田忌賽馬）

田忌賽馬的故事
（可以直接看題）
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

思路：
1、先從田忌的最差的馬和齊王的最差的馬比，如果田忌的馬速度大于齊王的馬贏一把。
2、如果田忌的最差的馬比齊王最差的馬還菜，讓田忌的最差馬拼掉齊王最好的馬。
3、如果田忌的最差的馬比齊王最差的馬一樣速度，則比較田忌最好的馬和齊王最好的馬：
① 如果田忌最好的馬比齊王最好的馬快，贏一把。
②如果田忌最差的馬比齊王最好的馬慢，讓田忌最差的馬和齊王最好的馬比，輸一把，一換一。
③如果田忌的最好的馬和齊王的最好的馬一樣快。讓田忌最差的馬把齊王的最好的馬比，輸一把，一換一。
AC代碼：

#include<stdio.h> #include<algorithm> using namespace std; int a[10050]; //田忌的馬 int b[10050]; //齊王的馬 int main() {int n;while(~scanf("%d",&n)) //多組輸入{int win=0,lost=0,s=n,e=0;int sum=0;if(n==0) //題目要求輸入0，退出程序{break;}for(int i=0;i<n;i++){scanf("%d",&a[i]);}for(int i=0;i<n;i++){scanf("%d",&b[i]);}//把馬的速度排序sort(a,a+n);sort(b,b+n);for(int i=0;i<n;i++){for(int j=e;j<s;j++){if(a[i]<b[j]) //田忌最慢的馬比齊王最慢的慢{lost++; //敗場加一s--;break; //跳出循環再次比較}else if(a[i]>b[j]) //田忌最慢的馬比齊王最慢的快{win++; //勝場加一e++;break; //跳出循環再次比較}else //田忌最慢的馬和齊王最慢的馬速度一樣{if(a[n-1]<b[s-1]) //田忌最好的馬速度小于齊王最好的馬{lost++; //敗場加一s--;break;}else if(a[n-1]==b[s-1]){if(a[i]<b[s-1]) //田忌最慢的馬和齊王最好的比{lost++; //敗場加一s--;break;}else //頂多可以相等大于是不可能了{s--;break;}}else //田忌最好的馬比齊王的快{win++; //勝場加一s--;n--;i--;break;}}}}sum=(win-lost)*200;printf("%d\n",sum);}return 0; }

總結

以上是生活随笔為你收集整理的Tian Ji -- The Horse Racing（田忌赛马）/贪心算法的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。