uva 11800 Determine the Shape

　　vjudge上题目链接：Determine the Shape

　　第二道独自 A 出的计算几何水题，题意就是给你四个点，让你判断它是哪种四边形：正方形、矩形、菱形、平行四边形、梯形 or 普通四边形。

　　按照各个四边形的特征层层判断就行，只是这题四个点的相对位置不确定（点与点之间是相邻还是相对并不确定），所以需要枚举各种情况，幸好 4 个点一共只有 3 种不同的情况：abcd、abdc、acbd 画个图就能一目了然，接下来就是编码了，无奈因为一些细节问题我还是调试了还一会 o(╯□╰)o

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;

struct Vector {
    double x,y;
    Vector(double x = 0, double y = 0): x(x), y(y) {}
    void readint() {
        int x,y;
        scanf("%d %d",&x,&y);
        this->x = x;
        this->y = y;
    }
    Vector operator + (const Vector &b) const {
        return Vector(x + b.x, y + b.y);
    }
    Vector operator - (const Vector &b) const {
        return Vector(x - b.x, y - b.y);
    }
    Vector operator * (double p) const {
        return Vector(x * p, y * p);
    }
    Vector operator / (double p) const {
        return Vector(x / p, y / p);
    }
};

typedef Vector point;
typedef const point& cpoint;
typedef const Vector& cvector;

Vector operator * (double p, const Vector &a) {
    return a * p;
}

double dot(cvector a, cvector b) {
    return a.x * b.x + a.y * b.y;
}

double length(cvector a) {
    return sqrt(dot(a,a));
}

double cross(cvector a, cvector b) {
    return a.x * b.y - a.y *b.x;
}

const double eps = 1e-10;
int dcmp(double x) {
    return fabs(x) < eps ? 0: (x < 0 ? -1 : 1);
}

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

const char s[8][30] = {"Ordinary Quadrilateral", "Trapezium", "Parallelogram",
                "Rhombus", "Rectangle", "Square" };

int judge(cpoint a, cpoint b, cpoint c, cpoint d) {
    if(dcmp(cross(a - b, c - d)) == 0) {
        if(dcmp(cross(b - c, a - d)) == 0) {
            if(dcmp(length(b - a) - length(d - a)) == 0) {
                if(dcmp(dot(b - a, d - a)) == 0)    return 5;
                else    return 3;
            }
            else if(dcmp(dot(b - a, d - a)) == 0)   return 4;
            else    return 2;
        }
        else   return 1;
    }
    else if(dcmp(cross(b - c, a - d)) == 0)    return 1;
    else    return 0;
}

int main() {
    int t,Case = 0;
    point a,b,c,d;
    scanf("%d",&t);
    while(t--) {
        a.readint();
        b.readint();
        c.readint();
        d.readint();
        printf("Case %d: ",++Case);
        int ans = 0;
        ans = max(ans, judge(a,b,c,d));
        ans = max(ans, judge(a,b,d,c));
        ans = max(ans, judge(a,c,b,d));
        printf("%s
",s[ans]);
    }
    return 0;
}

　　计算几何，还是很有趣的。。。