三角形适合另一个三角形

Question

给定2个三角形边长.确定第二个三角形是否适合第一个三角形？

有关更详细的信息,请阅读以下完整的问题陈述:

http://acm.timus.ru/problem.aspx?space=1&num=1566&locale=en

我在下面的实现尝试了对齐三角形底边的所有(3!)^ 2种可能的组合.然后它尝试在第一个三角形内移动第二个三角形,同时检查第二个三角形的底边是否不超过第一个三角形的底边.

但我一直得到错误答案(WA)#16.

我给出的案例是第二张图片.很明显,如果旋转PQR以对齐长度为2.77和3.0的边,则第三个顶点将不在三角形ABC内.长度4.2的边只能沿len 5的边对齐.因此,这种情况仅在第二张图像中的配置中得到满足.

你能帮我找到这个bug,建议一些我的算法崩溃的测试用例.也欢迎替代算法.

#include <cmath>
#include <iostream>
using namespace std;

const double PI = atan(1.0)* 4;

// Traingle ABC (Envelope)
double xa, ya, xb, yb, xc, yc;

// Traingle PQR (Postcard)
double xp, yp, xq, yq, xr, yr;

// Angle between sides AB and AC
double theta;

double signWrtLine(double x1, double y1, double x2, double y2, double x, double y)
{
    double A = y2 - y1;
    double B = x1 - x2;
    double C = -(A * x1 + B * y1);

    return (A * x + B * y + C);
}

bool fit()
{ 
    if ((xr > xc) || (yq > yb)) return false;

    if (signWrtLine(xa, ya, xb, yb, xq, yq) < 0) {
        double d = (yq / tan(theta)) - xq;
        return (xr + d <= xc);
    }

    return (signWrtLine(xa, ya, xb, yb, xq, yq) >= 0 && 
            signWrtLine(xb, yb, xc, yc, xq, yq) >= 0 && 
            signWrtLine(xc, yc, xa, ya, xq, yq) >= 0);
}

bool fit(double a[], double b[])
{
    // generate the 3! permutations of the envelope
    // loops i,k
    for (int i = 0; i < 3; i++) {

        double angle;
        double u = a[i], v = a[(i + 1) % 3], w = a[(i + 2) % 3];

        for (int k = 0; k < 2; k++) {
            switch (k) {
            case 0:
                xa = 0, ya = 0;
                angle = theta = acos((u * u + v * v - w * w) / (2 * u * v));
                xb = v * cos(angle), yb = v * sin(angle);
                xc = u, yc = 0;     
                break;
            case 1:
                // reflect envelope
                swap(v, w);
                angle = theta = acos((u * u + v * v - w * w) / (2 * u * v));
                xb = v * cos(angle), yb = v * sin(angle);       
                break;
            }

            // generate the 3! permutations of the postcard
            // loops j,k
            for (int j = 0; j < 3; j++) {

                double angle;
                double u = b[j], v = b[(j + 1) % 3], w = b[(j + 2) % 3];

                for (int k = 0; k < 2; k++) {
                    switch (k) {
                    case 0:
                        xp = 0, yp = 0;
                        angle = acos((u * u + v * v - w * w) / (2 * u * v));
                        xq = v * cos(angle), yq = v * sin(angle);
                        xr = u, yr = 0;
                        break;
                    case 1:
                        // reflect postcard
                        swap(v, w);
                        angle = acos((u * u + v * v - w * w) / (2 * u * v));
                        xq = v * cos(angle), yq = v * sin(angle);
                        break;
                    }

                    if (fit()) return true;
                }
            }
        }
    }
    return false;
}


int main()
{
    double a[3], b[3];

    for (int i = 0; i < 3; i++) cin >> a[i];
    for (int i = 0; i < 3; i++) cin >> b[i];

    if(fit(a, b)) cout << "YES" << endl;
    else cout << "NO" << endl;

    return 0;
}

Answer 1

比较双精度数时使用 epsilon (1e-10)！