[UVA] 378 - Intersecting Lines

題目連結

題意：

由兩點組成一個線段，

現在給你兩條線段，要你求出這兩條線段是
平行(NONE)
重疊(LINE)
還是交於一點(POINT)
若是焦於一點則輸出該點並輸出到小數第二位。

--------------------------------------------------

我的作法：

有兩點就可以求出向量(i,j)，
有向量帶入一點就可以求出方程式(jx - iy = c)，
有方程式就可以求出delta, deltax, deltay;
if(delta == 0)
{
     if(deltax == 0 and deltay == 0) then 重疊
     else then 無解
}
else
{
     x = deltax / delta;
     y = deltay / delta;
}
--------------------------------------------------

程式碼：

/* 題目: UVa 378 - Intersecting Lines

 * Language: C++

 * Created on: 2015年12月16日

 *   Author: hanting

 */

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;

struct Point

{

    int x, y;

};

struct Line

{

    Point s, e;

};

struct equation // ax + by = c

{

    int a, b, c;

    equation(int i, int j, int k)

    {

        a = i;

        b = j;

        c = k;

    }

};

istream& operator>>(istream& in, Point &a)

{

    in >> a.x >> a.y;

    return in;

}

istream& operator>>(istream& in, Line &a)

{

    in >> a.s >> a.e;

    return in;

}

int Determinant(int i, int j, int k, int l)

{

    return i*l - j*k;

}

Point operator - (Point &a, Point &b)

{

    Point result;

    result.x = a.x - b.x;

    result.y = a.y - b.y;

    return result;

}

int main()

{

    int testCase;

    cin >> testCase;

    cout << "INTERSECTING LINES OUTPUT" << endl;

    while(testCase--)

    {

        Line a, b;

        cin >> a >> b;

        Point v1, v2;

        v1 = a.e - a.s;

        v2 = b.e - b.s;

        equation e1(v1.y, -v1.x, v1.y*a.s.x-v1.x*a.s.y), e2(v2.y, -v2.x, v2.y*b.s.x-v2.x*b.s.y);

        double delta, deltax, deltay;

        delta = Determinant(e1.a, e1.b, e2.a, e2.b);

        deltax = Determinant(e1.c, e1.b, e2.c, e2.b);

        deltay = Determinant(e1.a, e1.c, e2.a, e2.c);

        if(delta == 0)

        {

            if(deltax == 0 and deltay == 0)

            {

                cout << "LINE" << endl;

            }

            else

            {

                cout << "NONE" << endl;

            }

        }

        else

        {

            cout << "POINT ";

            double x, y;

            x = deltax / delta;

            y = deltay / delta;

            if(fabs(x) < 1e-6) x = 0;

            if(fabs(y) < 1e-6) y = 0;

            cout << fixed << setprecision(2) << x << " " << y << endl;

        }

    }

    cout << "END OF OUTPUT" << endl;

    return 0;

}