/*
 @Time:20181112
 @Title:判斷多邊形是否在圓內
 @Desc:圓是一個凸集，判斷多邊形的每一個頂點是否在圓內即可
 */
#include<stdio.h>
#include<stdlib.h>

#define EXP 1e-8 //精度

typedef struct point{
	double x;
	double y;
	struct point *next;
}Point, *Polygon;
typedef struct circle{
	Point centre;
	double r;
}Circle;

int InitPolygon
 
(Polygon *p); //初始化多邊形
int InitCircle(Circle *c);	//初始化圓
int PolygonInCircle(Polygon p, Circle C); //多邊形是否在圓內
int PointInCircle(Point A, Circle C); //點是否在圓內

/*測試資料
// 第一組
11
0 0 
1 2
2 1
3 2
4 2
5 3
6 0
3 1
2 0
1 1.5
0 0
1 1
6
// 第二組
11
0 0 
1 2
2 1
3 2
4 2
5 3
6 0
3 1
2 0
1 1.5
0 0
1 1
2
 */
int main() {
	Polygon P;
	Circle C;
 


	InitPolygon(&P);
	printf("Polygon init success\n");
	InitCircle(&C);
	printf("circle init success\n");

	printf("多邊形是否在圓內：%d", PolygonInCircle(P, C) );

	return 0;
}

// 返回1：建立成功
// 返回0：建立不成功，點沒有閉合
int InitPolygon(Polygon *pHead) {
	int n;
	int i;
	Point *p,*q;
	double a,b;
	double suba, subb;
	
	scanf
 
("%d", &n);
	p = NULL;
	for (i=0; i<n; i++) {
		scanf("%lf%lf", &a, &b);
		q = (Point *)malloc(sizeof(Point)); if (!q) exit(0);
		q->x = a; q->y = b;
		// 連線
		if (p==NULL) { //第一個點
			q->next = q; //迴圈佇列
			p = q;
			*pHead = q;
		} else {
			suba = (*pHead)->x - a;
			subb = (*pHead)->y - b;
			if ( suba>=-EXP && suba<=EXP && subb>=-EXP && subb<=EXP) {//閉合 構造完成
				free(q);
				return 1;
			}
			p->next = q;
			q->next = *pHead;
			// 下一個
			p = q;
		}
	}
	return 0;
}

// 返回1：建立成功
// 返回0：建立失敗
int InitCircle(Circle *c) {
	scanf("%lf%lf", &c->centre.x, &c->centre.y);
	scanf("%lf", &c->r);
	return 1;
}

// 多邊形是否在圓內
int PolygonInCircle(Polygon head, Circle c) {
	Point *p;
	
	p = head;
	do {
		if ( PointInCircle(*p, c)==0 ) return 0;
		p = p->next;
	} while (p!=head);

	return 1;
}

// 點是否在圓內
int PointInCircle(Point A, Circle C) {
	double d2;
	d2 = (A.x - C.centre.x) * (A.x - C.centre.x) + (A.y - C.centre.y) * (A.y - C.centre.y);
	if (d2 > C.r*C.r) {
		return 0;
	} else {
		return 1;
	}
}