UVA11800--Determine the Shape（计算几何）

G

Determine the Shape

Input

Standard Input

Output

Standard Output

A toy company recently found that toys like revolver, machine guns, fighting planes are making children violent and destroying the peace of the world. The parents also began to avoid these toys and inclined to educational toys. So they decided to manufacture educational toys. One of these is a electric touch pad on which children can put four points and the program will automatically join the points to form a closed shape. Children will try to guess the shape and when they press a button then it will automatically announce the shape. But they are struggling to determine the shape and seek your help.

Your task is simple. You are given four points, no three of them are collinear, you have to output the simple polygonal shape formed by these points in the following order:

Square
Rectangle
Rhombus
 Parallelogram
Trapezium
Ordinary Quadrilateral

For example if it is possible to form a square with the four points you must output ‘Square’,  if it is not possible to form a square but possible to form a rectangle you must output ‘Rectangle’ and so on.

Input

Input starts with an integer T, the number of test cases (T≤50000). Each test case contains 4 lines. Each of the lines contains two space separated integersx_i y_i (-10000≤x_i, y_i≤ 10000) which are the coordinate values of a point.

 

Output

For each set of input output one line in the format “Case k: s”. Here k is the case number starting from 1 ands is the shape as described above. See sample input output for more details.

Sample Input

Sample Output

6

0 0

2 0

2 2

0 2

0 0

3 0

3 2

0 2

0 0

8 4

5 0

3 4

0 0

2 0

3 2

1 2

0 0

5 0

4 3

1 3

0 0

5 0

4 3

1 4

 

Case 1: Square

Case 2: Rectangle

Case 3: Rhombus

Case 4: Parallelogram

Case 5: Trapezium

Case 6: Ordinary Quadrilateral

 

                                                                     

给出四个点，求出四点连线的四边形是什么类型的~

T^T 因为长方形的单词复制错了WA了N多遍，555555~~~~~~~~~

CODE：

#include <iostream>#include <cstdio>#include <algorithm>#include <cmath>#include <string>#include <cstring>#include <queue>#include <stack>#include <vector>#include <set>#include <map>const int inf=0xfffffff;typedef long long ll;using namespace std;//const ll pai=acos(-1.0);char s[][25]={"","Square","Rectangle","Rhombus","Parallelogram","Trapezium","Ordinary Quadrilateral"};struct node{    ll x,y;    bool operator<(const node &a)const{        if(x==a.x) return y<a.y;        return x<a.x;    }}fan[4];bool cmp(node a,node b){    if(a.x == b.x) return a.y<b.y;    return a.x<b.x;}ll len(node a,node b){    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);}int angle_90(node a,node b,node c,node d){    ll x1=a.x-b.x, y1=a.y-b.y,       x2=c.x-d.x, y2=c.y-d.y;    if((x1*x2+y1*y2)==0) return 1;    return 0;}int angle_0(node a,node b,node c,node d){    ll x1=a.x-b.x, y1=a.y-b.y,       x2=c.x-d.x, y2=c.y-d.y;    if(x1*y2==x2*y1) return 1;    return 0;}int work(){    ll a=len(fan[0],fan[1]), b=len(fan[1],fan[2]), c=len(fan[2],fan[3]), d=len(fan[3],fan[0]);    int ang1=angle_90(fan[0],fan[1],fan[2],fan[1]), ang2=angle_90(fan[1],fan[2],fan[3],fan[2]),        ang3=angle_90(fan[2],fan[3],fan[0],fan[3]), ang4=angle_90(fan[3],fan[0],fan[1],fan[0]),        op=angle_90(fan[0],fan[2],fan[1],fan[3]),        par1=angle_0(fan[0],fan[1],fan[3],fan[2]), par2=angle_0(fan[1],fan[2],fan[0],fan[3]);            if(a==b && b==c && c==d && d==a && (ang1+ang2+ang3+ang4)==4) return 1; //正方形    if(a==c && b==d && a!=b && ang1 && ang2 && ang3 && ang4) return 2; //长方形    if(a==b && b==c && c==d && d==a && op && par1 && par2 && (ang1+ang2+ang3+ang4)==0) return 3; //菱形    if(a==c && b==d && par1 && par2) return 4; //平行四边形    if(a!=c && par1 && par2==0) return 5; // 梯形    return 0;}int main(){    //freopen("in.in","r",stdin);    int N;    scanf("%d",&N);    for(int nn=1;nn<=N;nn++){        for(int i=0;i<4;i++){            scanf("%lld%lld",&fan[i].x,&fan[i].y);        }        int ok=1;        do{            if(work()!=0){                printf("Case %d: %s\n",nn,s[work()]);                ok=0;                break;            }        }while(next_permutation(fan,fan+4,cmp));        if(ok) printf("Case %d: %s\n",nn,s[6]);    }    return 0;}