uva 378Intersecting Lines

题意：判断两条直线之间的关系，相交，平行，或者同一条直线，相交的话给出交点
解题：数学问题，分情况讨论：先判断直线之间的关系，利用向量叉积不为0就相交，叉积为0可能是同一条直线，例如（p1,p2)(p3,p4) ,计算p1,p2）,(p1,p3)的叉积，等于0 ，就是同一条直线了，否则，就是平行。接着就是计算两条相交直线的交点，（肯定有交点了），然后看斜率是否存在，分步讨论k1 和 k2 是否存在
代码：

//uva 378 Intersecting Lines //AC By Warteac//2013-5-8//Runtime:0.009s#include<iostream>#include <iomanip>using namespace std;////////////////////////////////////////////////////////////////struct point{ int x,y; point(int x1 = 0, int y1 = 0){x = x1; y = y1;} void print(){cout  << x << y << endl;} };//定义点结构体 struct point2{     double x,y;     point2(double x1 = 0,double y1 = 0){x = x1; y = y1;}     void print(){         cout.precision(3);         cout.setf(ios_base::showpoint);//show point         cout << x << " " << y << endl;} }; int direction(point v1,point v2){ return (v1.x*v2.y-v1.y*v2.x); } bool isLine(point p1,point p2,point p3,point p4){     point p(p1.x - p2.x, p1.y - p2.y);     point q(p1.x - p3.x, p1.y - p3.y);     int d = direction(p,q);     if(d) return false;     else return true; }int isItersect(point p1,point p2,point p3,point p4){    point p (p1.x - p2.x, p1.y - p2.y);    point q (p3.x - p4.x, p3.y - p4.y);    int d1 = direction(p,q);    if(d1) return 1;//intersect    else if(isLine(p1,p2,p3,p4)) return -1;// a line    else return 0; // parallel}point2 intersectPoint(point p1,point p2,point p3,point p4){    if(p1.x == p2.x){//line1 has no slope       double k2 = (double)(p4.y - p3.y)/(p4.x - p3.x);       double b2 = p3.y - k2*p3.x;       int a = p1.x;       double y = k2*a + b2;       return point2(a,y);    }       if(p3.x == p4.x){//line2 has no slope         double k1 = (double)(p2.y - p1.y)/(p2.x - p1.x);         double b1 = p1.y - k1*p1.x;         int b = p3.x;         double y = k1*b + b1;         return point2(b,y);   }    double k1 = (double)(p2.y - p1.y)/(p2.x - p1.x);    double k2 = (double)(p4.y - p3.y)/(p4.x - p3.x);    double b1 = p1.y - k1*p1.x;    double b2 = p3.y - k2*p3.x;    double x3 = (b1 - b2)/(k2 - k1);    double y3 =(k1*b2 - k2*b1)/(k1 - k2);   // cout << k1 << "  "<<k2<<" "<<b1 <<" " << b2 <<endl;    return point2(x3,y3);}////////////////////////////////////////////////////////////////int main(){   int caseNum;   cin >> caseNum;   int x1,y1,x2,y2,x3,y3,x4,y4;    cout << "INTERSECTING LINES OUTPUT" << endl;   while(caseNum--){       cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> x4 >> y4;       point p1(x1,y1);       point p2(x2,y2);       point p3(x3,y3);       point p4(x4,y4);       int t = isItersect(p1,p2,p3,p4);            if(t == 1){           point2 r = intersectPoint(p1,p2,p3,p4);           cout << "POINT ";           r.print();       }else if(t == -1)           cout << "LINE" << endl;       else cout << "NONE" <<endl;      }    cout << "END OF OUTPUT" << endl;  return 0;}