hdoj 5563 Clarke and five-pointed star 【判断五角星】-优快云博客

本文链接：https://blog.youkuaiyun.com/chenzhenyu123456/article/details/50165727

本文介绍了一种通过比较五个点之间的距离来判断这些点是否能构成一个五角星的算法。该算法首先获取五个点的坐标，然后计算并排序每个点与其他点之间的距离。最后通过比较所有点间的距离，判断是否满足五角星的特性。

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Clarke and five-pointed star

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 590 Accepted Submission(s): 312

Problem Description

Clarke is a patient with multiple personality disorder. One day, Clarke turned into a learner of geometric.
When he did a research with polygons, he found he has to judge if the polygon is a five-pointed star at many times. There are 5 points on a plane, he wants to know if a five-pointed star existed with 5 points given.

Input

The first line contains an integer

T(1≤T≤10), the number of the test cases.
For each test case, 5 lines follow. Each line contains 2 real numbers

xi,yi(−109≤xi,yi≤109), denoting the coordinate of this point.

Output

Two numbers are equal if and only if the difference between them is less than

10−4.
For each test case, print

Yes if they can compose a five-pointed star. Otherwise, print

No. (If 5 points are the same, print

Yes. )

Sample Input

2
3.0000000 0.0000000
0.9270509 2.8531695
0.9270509 -2.8531695
-2.4270509 1.7633557
-2.4270509 -1.7633557
3.0000000 1.0000000
0.9270509 2.8531695
0.9270509 -2.8531695
-2.4270509 1.7633557
-2.4270509 -1.7633557

Sample Output

Yes
No

Hint

题意：给定五个点，判断它们能否组成五角星。

直接暴力枚举即可。

AC代码：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <vector>
#define INF 0x3f3f3f
#define eps 1e-4
#define MAXN (100+10)
#define MAXM (100000)
#define Ri(a) scanf("%d", &a)
#define Rl(a) scanf("%lld", &a)
#define Rf(a) scanf("%lf", &a)
#define Rs(a) scanf("%s", a)
#define Pi(a) printf("%d\n", (a))
#define Pf(a) printf("%.2lf\n", (a))
#define Pl(a) printf("%lld\n", (a))
#define Ps(a) printf("%s\n", (a))
#define W(a) while(a--)
#define CLR(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define LL long long
#define lson o<<1, l, mid
#define rson o<<1|1, mid+1, r
#define ll o<<1
#define rr o<<1|1
using namespace std;
struct Point{
    double x, y;
    Point(){}
    Point(double X, double Y){
        x = X; y = Y;
    }
};
Point P[5];
double d0[5], d1[5], d2[5], d3[5], d4[5];
int dcmp(double x)
{
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1 : 1;
}
double dis(Point A, Point B){
    return (A.x-B.x) * (A.x-B.x) + (A.y-B.y) * (A.y-B.y);
}
int main()
{
    int t; Ri(t);
    W(t)
    {
        for(int i = 0; i < 5; i++)
            Rf(P[i].x), Rf(P[i].y);
        for(int i = 0; i < 5; i++)
            d0[i] = dis(P[0], P[i]);
        for(int i = 0; i < 5; i++)
            d1[i] = dis(P[1], P[i]);
        for(int i = 0; i < 5; i++)
            d2[i] = dis(P[2], P[i]);
        for(int i = 0; i < 5; i++)
            d3[i] = dis(P[3], P[i]);
        for(int i = 0; i < 5; i++)
            d4[i] = dis(P[4], P[i]);
        sort(d0, d0+5);
        sort(d1, d1+5);
        sort(d2, d2+5);
        sort(d3, d3+5);
        sort(d4, d4+5);
        bool flag = true;
        for(int i = 0; i < 5; i++)
        {
            if(dcmp(d0[i]-d1[i]) || dcmp(d0[i]-d2[i]) || dcmp(d0[i]-d3[i]) || dcmp(d0[i]-d4[i]))
            {
                flag = false;
                break;
            }
        }
        printf(flag ? "Yes\n" : "No\n");
    }
    return 0;
}