POJ 1410 Intersection(线段非规范相交)

题目链接：POJ 1410 Intersection

判断一条线段是否与一个矩形有交点，如果线段在矩形内部，也算有交点。

这题挺多细节需要考虑，要不是discuss上给的68组数据，我还得用更多时间去改bug。

有两个点在矩形内部比较容易处理，面积法搞定，难点在于相交的处理。刘汝佳的模版是线段规范相交的，而这道题是非规范的，就是说可能一条线段的端点恰好与另一条线段相交。但是仅仅加上OnSegment也是不行的，因为这个函数不能处理两个线段恰好端点相交这种情况。

#include <iostream>#include <cstdio>#include <cmath>using namespace std;const double eps = 1e-10;struct Point{int x, y;Point(int x=0, int y=0):x(x),y(y) { }};struct Line{    Point a, b;};typedef Point Vector;Vector operator + (const Vector& A, const Vector& B){    return Vector(A.x+B.x, A.y+B.y);}Vector operator - (const Point& A, const Point& B){    return Vector(A.x-B.x, A.y-B.y);}Vector operator * (const Vector& A, double p){    return Vector(A.x*p, A.y*p);}bool operator < (const Point& a, const Point& b){return a.x < b.x || (a.x == b.x && a.y < b.y);}bool operator == (const Point& a, const Point &b){return (a.x-b.x) == 0 && (a.y-b.y) == 0;}double Cross(const Vector& A, const Vector& B){    return A.x*B.y - A.y*B.x;}bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2){int c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1),c3 = Cross(b2-b1,a1-b1), c4=Cross(b2-b1,a2-b1);return c1*c2<0 && c3*c4<0;}int Dot(const Vector& A, const Vector& B){    return A.x*B.x + A.y*B.y;}bool OnSegment(const Point& p, const Point& a1, const Point& a2){return Cross(a1-p, a2-p) == 0 && Dot(a1-p, a2-p) < 0;}Point p[4];int get_area(Point a, Point b, Point c){    return abs(a.x * b.y + c.x * a.y + b.x * c.y - c.x * b.y - a.x * c.y - b.x * a.y);}bool is_in(int sum, Point k1, Point k2){    double area1, area2, area3, area4;    area1 = get_area(p[0], p[1], k1);    area2 = get_area(p[1], p[2], k1);    area3 = get_area(p[2], p[3], k1);    area4 = get_area(p[3], p[0], k1);    if(2 * sum == area1 + area2 + area3 + area4)        return true;    area1 = get_area(p[0], p[1], k2);    area2 = get_area(p[1], p[2], k2);    area3 = get_area(p[2], p[3], k2);    area4 = get_area(p[3], p[0], k2);    if(2 * sum == area1 + area2 + area3 + area4)        return true;    return false;}bool is_intersect(Point k1, Point k2){    if(SegmentProperIntersection(k1, k2, p[0], p[1]))        return true;    if(SegmentProperIntersection(k1, k2, p[1], p[2]))        return true;    if(SegmentProperIntersection(k1, k2, p[2], p[3]))        return true;    if(SegmentProperIntersection(k1, k2, p[3], p[0]))        return true;    if(OnSegment(k1, p[0], p[1]) || OnSegment(k1, p[1], p[2]) || OnSegment(k1, p[2], p[3]) || OnSegment(k1, p[3], p[0]))        return true;    if(OnSegment(k2, p[0], p[1]) || OnSegment(k2, p[1], p[2]) || OnSegment(k2, p[2], p[3]) || OnSegment(k2, p[3], p[0]))        return true;    if(OnSegment(p[0], k1, k2) || OnSegment(p[1], k1, k2) || OnSegment(p[2], k1, k2) || OnSegment(p[3], k1, k2))        return true;    if(k1 == p[0] || k1 == p[1] || k1 == p[2] || k1 == p[3])        return true;    if(k2 == p[0] || k2 == p[1] || k2 == p[2] || k2 == p[3])        return true;    return false;}int main(){    //freopen("in.txt", "r", stdin);    //freopen("out.txt", "w", stdout);    int T;    scanf("%d", &T);    Line line;    while(T--)    {        scanf("%d%d%d%d", &line.a.x, &line.a.y, &line.b.x, &line.b.y);        int lx, rx, by, ty, temp;        scanf("%d%d%d%d", &lx, &ty, &rx, &by);        if(lx > rx)            temp = lx, lx = rx, rx = temp;        if(by > ty)            temp = by, by = ty, ty = temp;        p[0] = Point(lx, ty), p[1] = Point(rx, ty), p[2] = Point(rx, by), p[3] = Point(lx, by);        int area = (ty - by) * (rx - lx);        if(is_in(area, line.a, line.b) || is_intersect(line.a, line.b))            printf("T\n");        else            printf("F\n");    }    return 0;}