UVA_191_Intersection_WA

</pre><pre name="code" class="cpp">#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<list>
#include<set>
#include<map>
#include<stack>
#include<queue>
#include<algorithm>
#include<numeric>
#include<cmath>
#pragma warning(disable:4996)
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::string;
using std::vector;
using std::list;
using std::pair;
using std::set;
using std::multiset;
using std::map;
using std::multimap;
using std::stack;
using std::queue;
using std::priority_queue;
class Point
{
public:
	long double x, y;
	Point() {}
	Point(const long double &X, const long double &Y)
	{
		x = X;
		y = Y;
	}
};
class Line
{
public:
	long double a, b, c;//ax+by=c
	long double x_min, x_max, y_min, y_max;//直线的值域
	Line() {}
	Line(const Point &first, const Point &second)
	{
		x_min = std::min(first.x, second.x);
		x_max = std::max(first.x, second.x);
		y_min = std::min(first.y, second.y);
		y_max = std::max(first.y, second.y);
		if (first.x != second.x)//斜率式可行
		{
			b = 1;
			a = -(first.y - second.y) / (first.x - second.x);
			c = first.y + a*first.x;
		}
		else//k->无穷
		{
			b = 0;
			a = 1;
			c = first.x;
		}
	}
	bool lineIntersected(const Line &line)//直线相交的判定
	{
		auto D = a*line.b - line.a*b;
		if (D)
		{
			return true;
		}
		return false;
	}
	bool lineParallel(const Line&line)//判断两直线是否平行
	{
		auto D = a*line.b - line.a*b;
		if (!D)
		{
			return true;
		}
		return false;
	}
	bool lineOverlapped(const Line&line)//判断两直线是否重合（平行的特例）
	{
		auto D = a*line.b - line.a*b;
		auto Dx = c*line.b - line.c*b;
		auto Dy = a*line.c - line.a*c;
		if (!D&&!Dx&&!Dy)
		{
			return true;
		}
		return false;
	}
	long double fixed(long double value)
	{
		value *= (long double)1000000000000.0;
		value += 0.5;
		value = floor(value);
		value /= (long double)1000000000000.0;
		return value;
	}
	Point getIntersection(const Line&line)//行列式求两直线交点,要修正误差
	{
		auto D = a*line.b - line.a*b;
		auto Dx = c*line.b - line.c*b;
		auto Dy = a*line.c - line.a*c;
		return{ fixed(Dx / D),fixed(Dy / D) };
	}
	bool segmentIntersected(const Line &line)
	{
		if (lineIntersected(line))
		{
			auto point = getIntersection(line);
			if (point.x >= x_min&&point.x <= x_max
				&&point.y >= y_min&&point.y <= y_max
				&&point.x >= line.x_min&&point.x <= line.x_max
				&&point.y >= line.y_min&&point.y <= line.y_max
				)//交点在两线段的值域内
			{
				return true;
			}
		}
		return false;
	}
	bool segmentOverlapped(const Line &line)
	{
		if (lineOverlapped(line))
		{
			if ((x_min <= line.x_max&&x_min >= line.x_min) || (x_max <= line.x_max&&x_max >= line.x_min))
			{
				return true;
			}
		}
		return false;
	}
};
class Rectangle
{
public:
	long double left, right, top, bottom;
	bool inRectangle(const Point &point)
	{
		if (point.x >= left&&point.x <= right&&point.y >= bottom&&point.y <= top)
		{
			return true;
		}
		return false;
	}
};
int main()
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int n;
	while (cin >> n)
	{
		for (int i = 0; i < n; i++)
		{
			long double x1, y1, x2, y2;
			cin >> x1 >> y1 >> x2 >> y2;
			Rectangle rectangle;
			cin >> rectangle.left >> rectangle.top >> rectangle.right >> rectangle.bottom;
			if (rectangle.left > rectangle.right)
			{
				std::swap(rectangle.left, rectangle.right);
			}
			if (rectangle.bottom > rectangle.top)
			{
				std::swap(rectangle.bottom, rectangle.top);
			}
			if (rectangle.inRectangle({ x1,y1 }) || rectangle.inRectangle({ x2,y2 }))
			{
				//只要一个端点在矩形内，就有交点  
				cout << 'T' << endl;
			}
			else
			{
				Line line({ x1,y1 }, { x2,y2 });
				vector<long double>segment(4);
				segment[0] = rectangle.top;
				segment[1] = rectangle.right;
				segment[2] = rectangle.bottom;
				segment[3] = rectangle.left;
				bool flag = false;
				for (int i = 0; i < 4; i++)
				{
					Line another({ segment[i],segment[(i + 1) % 4] }, { segment[(i + 1) % 4],segment[(i + 2) % 4] });
					if (line.segmentIntersected(another)||line.lineOverlapped(another))
					{
						flag = true;
						break;
					}
				}
				if (flag)
				{
					cout << 'T' << endl;
				}
				else
				{
					cout << 'F' << endl;
				}
			}
		}
	}
	return 0;
}