Unfold

Title Description

A secret organization is holding a military exercise in the desert. The goal of this exercise is to dismantle a bomb hidden in the desert.

The first part of the exercise was airborne operations. Each soldier jumped off the helicopter hovering over the desert in a certain order. When landing, every soldier will stop at his landing point.

Every airborne has a survival radius. If the distance between the bomb and him is less than or equal to this survival radius, the airborne soldiers will sacrifice themselves to detonate the bomb. The commander wants to send as few soldiers as possible, but he wants at least one soldier to survive in the worst case.

The whole desert can be abstracted as a plane, and the landing point of each soldier can be represented by a coordinate (x,y)(x,y). We set his survival radius as rr. All soldiers' information is given in the order in which they parachute, that is, when the − ii soldier parachutes, the first − i-1i − 1 soldier has landed.

Your task is to read the information of all soldiers from the standard input and output the minimum number of soldiers to be sent.

Input format

The first line is an integer {nn.

Next, line # nn # and line # ii # contain three integers # x_i,y_i,r_ixi, yi, ri, representing the landing coordinates of the ， ii ， soldier is (x_i,y_i)(xi, yi), and the survival radius is ， r_iri​.

Output format

If at least one soldier cannot survive, output NIE.

Otherwise, an integer representing at least the number of soldiers to be sent is output.

Input and output samples

Enter #1 copy

5
2 2 4
7 2 3
4 3 1
5 7 1
8 7 1

Output #1 copy

4

Description / tips

In the worst case, the bomb is located at (5,3) (5,3), the first three soldiers will be killed, and the fourth soldier will survive.

Upper Code:
 

#include<bits/stdc++.h>
using namespace std;
#define reg register
typedef long long ll;

const double eps=1e-6;

inline int sgn(reg double x){
	if(fabs(x)<eps)
		return 0;
	else
		return x<0?-1:1;
}

inline double sqr(reg double x){
	return x*x;
}

const int MAXN=2e3+5;

struct Vector{
	double x,y;
	inline Vector(reg double x=0,reg double y=0):x(x),y(y){
		return;
	}
	inline Vector operator+(const Vector& a)const{
		return Vector(x+a.x,y+a.y);
	}
	inline Vector operator-(const Vector& a)const{
		return Vector(x-a.x,y-a.y);
	}
	inline Vector operator*(const double a)const{
		return Vector(x*a,y*a);
	}
};

inline double dot(const Vector& a,const Vector& b){
	return a.x*b.x+a.y*b.y;
}

inline double cross(const Vector& a,const Vector& b){
	return a.x*b.y-a.y*b.x;
}

typedef Vector Point;

inline double getDis2(const Point& a,const Point& b){
	return dot(a-b,a-b);
}

inline double getDis(const Point& a,const Point& b){
	return sqrt(getDis2(a,b));
}

inline bool isEmpty(const Point& a){
	return a.x!=a.x||a.y!=a.y;
}

struct Circle{
	Point o;
	double r;
	inline bool contain(const Point& x)const{
		return sgn(sqr(r)-getDis2(x,o))>=0;
	}
	inline Point getRig(void)const{
		return o+Vector(r,0);
	}
};

inline bool isCon(const Circle& a,const Circle& b){
	return sgn(sqr(a.r-b.r)-getDis2(a.o,b.o))>=0;
}

inline bool isSep(const Circle& a,const Circle& b){
	return sgn(getDis2(a.o,b.o)-sqr(a.r+b.r))>0;
}

inline Point getPot(const Circle &a,const Circle &b){
	if(isCon(a,b))
		if(sgn(b.getRig().x-a.getRig().x)>0)
			return a.getRig();
		else
			return b.getRig();
	else if(isSep(a,b))
		return Point(nan(""),nan(""));
	else{
		if(a.contain(b.getRig()))
			return b.getRig();
		else if(b.contain(a.getRig()))
			return a.getRig();
		else{
			reg double d=getDis(a.o,b.o);
			reg double ang=acos(((sqr(a.r)+sqr(d))-sqr(b.r))/(2*a.r*d));
			reg double delta=atan2(b.o.y-a.o.y,b.o.x-a.o.x);
			reg double ang1=delta+ang,ang2=delta-ang;
			Point p1=a.o+Vector(cos(ang1)*a.r,sin(ang1)*a.r);
			Point p2=a.o+Vector(cos(ang2)*a.r,sin(ang2)*a.r);
			Point res;
			if(sgn(p2.x-p1.x)>0)
				res=p2;
			else
				res=p1;
			return res;
		}
	}
}

int n;
Circle a[MAXN];

int main(void){
	scanf("%d",&n);
	Point lef(0,0);
	for(reg int i=1;i<=n;++i){
		static int x,y,r;
		scanf("%d%d%d",&x,&y,&r);
		a[i].o=Point(x,y),a[i].r=r;
		if(i==2)
			lef=getPot(a[1],a[2]);
		else if(i>2){
			for(reg int j=1;j<i&&!isEmpty(lef);++j){
				Point tmp=getPot(a[i],a[j]);
				if(isEmpty(tmp)||tmp.x<=lef.x)
					lef=tmp;
			}
			for(reg int j=1;j<=i&&!isEmpty(lef);++j)
				if(!a[j].contain(lef))
					lef=Point(nan(""),nan(""));
		}
		if(isEmpty(lef)){
			printf("%d\n",i);
			return 0;
		}
	}
	puts("NIE");
	return 0;
}