2013-08-23 17:47:39Morris

[UVA] 11800 - Determine the Shape


 

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 integers xi yi (-10000≤xi, yi≤ 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 and s 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

 

 

Note: If you have forgotten elementary geometry, here is the definitions to remind you:

Square: All sides are of equal size all angles are 90o
Rectangle: Opposite sides are of equal size and all angles are 90o
Rhombus: All sides are of equal size but no angle is 90o
Parallelogram: Opposite sides are of equal size but no angle is 90o
Trapezium: Any two opposite sides are parallel but the other two is not.
Simple Polygon: Polygon having no self intersecting edge.



正方形:Square

矩形:Rectangle

菱形:Rhombus

平行四边形:Parallelogram

梯形:Trapezium

普通四边形:Ordinary Quadrilateral

考慮先做一次凸包,以免拉到對角線進行判斷。

接著判斷邊與邊之間的關係。


#include <stdio.h>
#include <math.h>
#include <algorithm>
using namespace std;
struct Pt {
    long long x, y;
    bool operator<(const Pt &a) const {
        if(x != a.x)
            return x < a.x;
        return y < a.y;
    }
    Pt operator-(const Pt &a) {
        Pt r;
        r.x = x-a.x, r.y = y-a.y;
        return r;
    }
};
long long cross(Pt o, Pt a, Pt b) {
    return (a.x-o.x)*(b.y-o.y)-(a.y-o.y)*(b.x-o.x);
}
int monotone(int n, Pt p[], Pt ch[]) {
    sort(p, p+4);
    int i, m = 0, t;
    for(i = 0; i < n; i++) {
        while(m >= 2 && cross(ch[m-2], ch[m-1], p[i]) <= 0)
            m--;
        ch[m++] = p[i];
    }
    for(i = n-1, t = m+1; i >= 0; i--) {
        while(m >= t && cross(ch[m-2], ch[m-1], p[i]) <= 0)
            m--;
        ch[m++] = p[i];
    }
    return m-1;
}
long long dot(Pt a, Pt b) {
    return a.x*b.x + a.y*b.y;
}
long long len(Pt a) {
    return a.x*a.x + a.y*a.y;
}
int main() {
    int testcase, cases = 0;
    int i, j, k;
    Pt D[50], CH[50];
    scanf("%d", &testcase);
    while(testcase--) {
        for(i = 0; i < 4; i++)
            scanf("%lld %lld", &D[i].x, &D[i].y);
        int flag = monotone(4, D, CH);
        Pt a, b, c, d;
        Pt o;
        o.x = o.y = 0;
        a = CH[0], b = CH[1], c = CH[2], d = CH[3];
        printf("Case %d: ", ++cases);
        if(flag != 4) {
            puts("Ordinary Quadrilateral");
            continue;
        }
        if(dot(b-a, d-a) == 0 && dot(c-b, a-b) == 0 && dot(d-c, b-c) == 0) {
            if(len(b-a) == len(c-b))
                puts("Square");
            else
                puts("Rectangle");
        } else if(len(b-a) == len(c-b) && len(b-a) == len(d-c) && len(b-a) == len(a-d))
            puts("Rhombus");
        else if(cross(o, b-a, c-d) == 0 && cross(o, c-b, d-a) == 0)
            puts("Parallelogram");
        else if(cross(o, b-a, c-d) == 0 || cross(o, c-b, d-a) == 0)
            puts("Trapezium");
        else
            puts("Ordinary Quadrilateral");
    }
    return 0;
}