UVa 10589 - Area

题目：给你n个点和一个正方形，问落在以正方形四个顶点为圆心、边长为半径的圆相交的面积，面积公式：a*a*M/N，其中M是落在相交区域中点的个数。

分析：简单题、计算几何。利用已知点到矩形死歌顶点的距离判断位置关系，统计即可。

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef struct pnode
{
	double x,y;
	pnode( double a, double b ){x = a;y = b;}
	pnode(){}
}point;

double dist( point a, point b )
{
	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

int in( point p, double a )
{
	double d[4][2] = {0.0,0.0,1.0,0.0,0.0,1.0,1.0,1.0};
	for ( int i = 0 ; i < 4 ; ++ i ) {
		point q = point( a*d[i][0], a*d[i][1] );
		if ( dist( p, q ) > a ) 
			return 0;
	}
	return 1;
}

int main()
{
	int    n,a;
	point  p;
	while ( scanf("%d%d",&n,&a) && n ) {
		int count = 0;
		for ( int i = 0 ; i < n ; ++ i ) {
			scanf("%lf%lf",&p.x,&p.y);
			count += in( p, a+0.0 );
		}
		printf("%.5lf\n",1.0*count*a*a/n);
	}
	return 0;
}