UVA 11800 Determine the Shape --凸包第一题

时间：2025-05-09 20:05:44

题意： 给四个点，判断四边形的形状。可能是正方形，矩形，菱形，平行四边形，梯形或普通四边形。

解法： 开始还在纠结怎么将四个点按序排好，如果直接处理的话，有点麻烦，原来凸包就可搞，直接求个凸包，然后点就自动按逆时针排好了，然后就判断就可以了，判断依据题目下面有，主要是用到点积和叉积，判断垂直用点积，判断平行用叉积。

代码：

#include <iostream>

#include <cstdio>

#include <cstring>

#include <cstdlib>

#include <cmath>

#include <algorithm>

#define eps 1e-8

using namespace std;

struct Point{

    double x,y;

    Point(double x=, double y=):x(x),y(y) {}

    void input() { scanf("%lf%lf",&x,&y); }

};

typedef Point Vector;

struct Circle{

    Point c;

    double r;

    Circle(){}

    Circle(Point c,double r):c(c),r(r) {}

    Point point(double a) { return Point(c.x + cos(a)*r, c.y + sin(a)*r); }

    void input() { scanf("%lf%lf%lf",&c.x,&c.y,&r); }

};

struct Line{

    Point p;

    Vector v;

    double ang;

    Line(){}

    Line(Point p, Vector v):p(p),v(v) { ang = atan2(v.y,v.x); }

    Point point(double t) { return Point(p.x + t*v.x, p.y + t*v.y); }

    bool operator < (const Line &L)const { return ang < L.ang; }

};

int dcmp(double x) {

    if(x < -eps) return -;

    if(x > eps) return ;

    return ;

}

template <class T> T sqr(T x) { return x * x;}

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

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

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

Vector operator / (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); }

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

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

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

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

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

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

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

Vector VectorUnit(Vector x){ return x / Length(x);}

Vector Normal(Vector x) { return Point(-x.y, x.x) / Length(x);}

double angle(Vector v) { return atan2(v.y, v.x); }

int ConvexHull(Point* p, int n, Point* ch)

{

    sort(p,p+n);

    int m = ;

    for(int i=;i<n;i++) {

        while(m >  && Cross(ch[m-]-ch[m-], p[i]-ch[m-]) <= ) m--;

        ch[m++] = p[i];

    }

    int k = m;

    for(int i=n-;i>=;i--) {

        while(m > k && Cross(ch[m-]-ch[m-], p[i]-ch[m-]) <= ) m--;

        ch[m++] = p[i];

    }

    if(n > ) m--;

    return m;

}

//data segment

Point p[],ch[];

Point A,B,C,D;

//data ends

int main()

{

    int t,n,i,cs = ;

    scanf("%d",&t);

    while(t--)

    {

        for(i=;i<;i++) p[i].input();

        printf("Case %d: ",cs++);

        int m = ConvexHull(p,,ch);

        if(m < ) { puts("Ordinary Quadrilateral"); continue; }

        A = ch[], B = ch[], C = ch[], D = ch[];

        if(dcmp(Dot(B-A,D-A)) ==  && dcmp(Dot(B-A,C-B)) ==  && dcmp(Dot(C-B,C-D)) ==  && dcmp(Dot(D-C,D-A)) ==

        && dcmp(Length(B-A)-Length(C-B)) ==  && dcmp(Length(C-B)-Length(D-C)) ==  && dcmp(Length(C-D)-Length(A-D)) == )

            puts("Square");

        else if(dcmp(Dot(B-A,D-A)) ==  && dcmp(Dot(B-A,C-B)) ==  && dcmp(Dot(C-B,C-D)) ==  && dcmp(Dot(D-C,D-A)) ==

             && dcmp(Length(A-D)-Length(C-B)) ==  && dcmp(Length(A-B)-Length(C-D)) == )

            puts("Rectangle");

        else if(dcmp(Length(B-A)-Length(C-B)) ==  && dcmp(Length(C-B)-Length(D-C)) ==  && dcmp(Length(C-D)-Length(A-D)) == )

            puts("Rhombus");

        else if(dcmp(Length(A-D)-Length(B-C)) ==  && dcmp(Length(A-B)-Length(C-D)) == )

            puts("Parallelogram");

        else if(dcmp(Cross(B-C,D-A)) ==  || dcmp(Cross(B-A,D-C)) == )

            puts("Trapezium");

        else

            puts("Ordinary Quadrilateral");

    }

    return ;

}

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