UASCO Wormholes 解析 and C 语言实现

题目大意：

农场有N个洞（2<=N<=12,N为偶数），且组成N/2个连接对。每一个洞的给出平面坐标（x,y）。

假设A和B相连，则进入A会从B出来，进入B会从A出来。有仅仅会沿着x轴正方向前进的牛，非常可能就会陷入一个循环中。比如，A（1,1）。B（3,1），这头牛从（2,1）出发，首先会进入B，然后从A出来，由于牛仅仅沿着x方向前进，牛又进入了B，就这样无限循环下去了。

给定N个洞的坐标，牛能够从不论什么点出发，求全部可能出现牛陷入循环的可能情况数（及N个洞的配对情况）

分析：

这个题目有个关键点，就是牛的走向。及牛仅仅能沿着x轴的正方向行走，要想形成无限循环，及每当牛每次经过一个pair后，总能在其x正方向处存在下一个点。

所以题目的关键变为寻找平行的右邻接点

N的数目较小。对全部的情况进行列举就可以。

另外，无限循环的检測。发现一个周期就可以，或者。走过的次数大于各个周期最大行走次数后。这个点还有平行的右邻接点。由于一共就N个点。周期最大行走次数肯定不会大于N （是否不会大于N/2 还有待思考）

/*

ID: abc18711

LANG: C

TASK: wormhole

*/

#include <stdio.h>

#include <string.h>

#define MAXN 12+1

int X[MAXN];

int Y[MAXN];

int pair[MAXN];

int right_hole[MAXN];

int N;

int exist_cycle()

{

	int start_hole;

	int flag;

	int i;

	for (start_hole=1; start_hole<=N; start_hole++)

	{

		for (i=1,flag=start_hole; i<=N; i++)

		{

			flag = right_hole[ pair[flag] ];

			if(flag == 0) break;

		}

		if (flag > 0) return 1;

	}

	return 0;

}

// the pair combination

int solutions()

{

	int i;

	int j;

	int total = 0;

	//find first unpaired hole

	for (i=1; i<=N; i++)

		if(pair[i] == 0) break;

	//no unpaired hole,test the cycle

	if (i > N){

		return exist_cycle();

	}

        //pairing i and j

	for (j=i+1; j<=N; j++)

		if (pair[j] == 0)

		{

			pair[i] = j;

			pair[j] = i;

			total += solutions();

			pair[i] = pair[j] = 0;

		}

	return total;

}

int main()

{

	int i;

	int j;

        FILE *fin = fopen("wormhole.in", "r");

	FILE *fout = fopen("wormhole.out", "w");

	// get the input

	fscanf(fin, "%d", &N);

	for (i=1; i<=N; i++)

		fscanf(fin, "%d %d", &X[i], &Y[i]);

	memset(pair, 0, MAXN*sizeof(int));

	memset(right_hole, 0, MAXN*sizeof(int));

	// find the right hole

	for( i=1; i<=N; i++)

		for (j=1; j<=N; j++)

			if (Y[i] == Y[j] && X[j] > X[i])

				if (right_hole[i] == 0 || (X[j]-X[i]) < (X[ right_hole[i] ]-X[i]))

					right_hole[i] = j;

	fprintf(fout, "%d\n", solutions());

	return 0;

}

附录：

Wormholes

Farmer John's hobby of conducting high-energy physics experiments on weekends has backfired, causing N wormholes (2 <= N <= 12, N even) to materialize on his farm, each located at a distinct point

on the 2D map of his farm (the x,y coordinates are both integers).

According to his calculations, Farmer John knows that his wormholes will form N/2 connected pairs. For example, if wormholes A and B are connected as a pair, then

any object entering wormhole A will exit wormhole B moving in the same direction, and any object entering wormhole B will similarly exit from wormhole A moving in

the same direction. This can have rather unpleasant consequences.

For example, suppose there are two paired wormholes A at (1,1) and B at (3,1), and that Bessie the cow starts from position (2,1) moving in the +x direction. Bessie will

enter wormhole B [at (3,1)], exit from A [at (1,1)], then enter B again, and so on, getting trapped in an infinite cycle!

| . . . . | A > B . Bessie will travel to B then + . . . . A then across to B again

Farmer John knows the exact location of each wormhole on his farm. He knows that Bessie the cow always walks in the +x direction, although he does not remember

where Bessie is currently located.

Please help Farmer John count the number of distinct pairings of the wormholes such that Bessie could possibly get trapped in an infinite cycle if she starts from an

unlucky position. FJ doesn't know which wormhole pairs with any other wormhole, so find all the possibilities.

PROGRAM NAME: wormhole

INPUT FORMAT:

Line 1:

The number of wormholes, N.

Lines 2..1+N:

Each line contains two space-separated integers describing the (x,y) coordinates of a single wormhole.

Each coordinate is in the range 0..1,000,000,000.

SAMPLE INPUT (file wormhole.in):

0 0

1 0

1 1

0 1

INPUT DETAILS:

There are 4 wormholes, forming the corners of a square.

OUTPUT FORMAT:

Line 1:

The number of distinct pairings of wormholes such that Bessie could conceivably get stuck in

a cycle walking from some starting point in the +x direction.

SAMPLE OUTPUT (file wormhole.out):

OUTPUT DETAILS:

If we number the wormholes 1..4 as we read them from the input, then if wormhole 1 pairs with wormhole 2 and wormhole 3 pairs with wormhole 4,

Bessie can get stuck if she starts anywhere between (0,0) and (1,0) or between (0,1) and (1,1).

| . . . . 4 3 . . . Bessie will travel to B then 1-2-.-.-. A then across to B again

Similarly, with the same starting points, Bessie can get stuck in a cycle if the pairings are 1-3 and 2-4 (if Bessie enters WH#3 and comes out at WH#1, she then walks to WH#2 which transports here to WH#4 which directs her towards WH#3

again for a cycle).

Only the pairings 1-4 and 2-3 allow Bessie to walk in the +x direction from any point in the 2D plane with no danger of cycling.