POJ 2653 Pick-up sticks(线段相交)

最新推荐文章于 2021-07-14 11:20:25 发布

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本文详细介绍了POJ2653 Pick-upsticks问题的解决思路，通过判断线段是否相交来计算未被覆盖的木棍数量。包括算法原理、代码实现与实例演示。

题目链接：POJ 2653 Pick-up sticks

计算没有被盖住的木棍有多少个，判断线段是否相交就行了。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>

using namespace std;

const double eps = 1e-10;

struct Point
{
	double x, y;
	Point(double x=0, double y=0):x(x),y(y){ }
};
struct Line
{
    Point a, b;
    int i;
};
typedef Point Vector;

Vector operator + (const Vector& A, const Vector& B)
{
    return Vector(A.x+B.x, A.y+B.y);
}

Vector operator - (const Point& A, const Point& B)
{
    return Vector(A.x-B.x, A.y-B.y);
}

Vector operator * (const Vector& A, double p)
{
    return Vector(A.x*p, A.y*p);
}

bool operator < (const Point& a, const Point& b)
{
	return a.x < b.x || (a.x == b.x && a.y < b.y);
}

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

bool operator == (const Point& a, const Point &b)
{
	return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;
}

double Dot(const Vector& A, const Vector& B)
{
    return A.x*B.x + A.y*B.y;
}

double Length(const Vector& A)
{
    return sqrt(Dot(A, A));
}

double Angle(const Vector& A, const Vector& B)
{
    return acos(Dot(A, B) / Length(A) / Length(B));
}

double Cross(const Vector& A, const Vector& B)
{
    return A.x*B.y - A.y*B.x;
}

double Area2(Point A, Point B, Point C)
{
    return Cross(B - A, C - A);
}

bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2)
{
	double c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1),
		c3 = Cross(b2-b1,a1-b1), c4=Cross(b2-b1,a2-b1);
	return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
}

bool OnSegment(const Point& p, const Point& a1, const Point& a2)
{
	return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;
}

//求两直线交点，先确保两直线有唯一交点，当且仅当Cross(v, w)非0
Point GetLineIntersection(const Point& P, const Point& v, const Point& Q, const Point& w)
{
	Vector u = P-Q;
	double t = Cross(w, u) / Cross(v, w);
	return P+v*t;
}

Vector Rotate(const Vector& A, double rad)
{
	return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}

vector <Line> v1, v2;

int main()
{
    int n;
    while(scanf("%d", &n), n)
    {
        Line line;
        double x1, y1, x2, y2;
        for(int i = 0; i < n; i++)
        {
            v1.clear();
            scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
            line.a.x = x1, line.a.y = y1, line.b.x = x2, line.b.y = y2;
            line.i = i + 1;
            int _size = v2.size();
            for(int j = 0; j < _size; j++)
                if(!SegmentProperIntersection(line.a, line.b, v2[j].a, v2[j].b))
                    v1.push_back(v2[j]);
            v1.push_back(line);
            v2 = v1;
        }
        printf("Top sticks: ");
        int _size = v2.size();
        for(int j = 0; j < _size - 1; j++)
            printf("%d, ", v2[j].i);
        printf("%d.\n", v2[_size - 1].i);
        v2.clear();
        v1.clear();
    }
    return 0;
}