uva-10112-计算几何

题意:给你一些点,求这些点组成的三角形面积最大,而且三角形内不能包含其他点

 

#include <iostream>
#include <math.h>
#include<stdio.h>
using namespace std;

struct Node
{
	char c;
	int x;
	int y;
};
void sort(Node nodes[3], int length)
{
	for (int i = 0; i < length; i++)
	{
		for (int j = 1; j < length - i; j++)
		{
			if (nodes[j - 1].c > nodes[j].c)
			{
				Node temp = nodes[j];
				nodes[j] = nodes[j - 1];
				nodes[j - 1] = temp;
			}
		}
	}
}
double area(double x1, double y1, double x2, double y2, double x3, double y3)
{
	double i = (y3 - y1) * (x2 - x1) - (y2 - y1) * (x3 - x1);
	return fabs(i) * 0.5;
}

int main()
{
	while (true)
	{
		int n;
		cin >> n;
		if (!n)
			return 0;
		Node* nodes = new Node[n];
		Node res[3];
		for (int i = 0; i < n; i++)
		{
			Node node;
			cin >> node.c >> node.x >> node.y;
			nodes[i] = node;
		}
		double maxa = -1;
		for (int i = 0; i < n; i++)
		{
			for (int j = i + 1; j < n; j++)
			{
				for (int k = j + 1; k < n; k++)
				{
					double a = area(nodes[i].x, nodes[i].y, nodes[j].x,
							nodes[j].y, nodes[k].x, nodes[k].y);
					if (a <= maxa)
						continue;
					int contain = false;
					for (int t = 0; t < n; t++)
					{
						if(t == i || t == j || t == k)
							continue;
						double s1, s2, s3;
						s1 = area(nodes[t].x, nodes[t].y, nodes[j].x,
								nodes[j].y, nodes[k].x, nodes[k].y);

						s2 = area(nodes[i].x, nodes[i].y, nodes[t].x,
								nodes[t].y, nodes[k].x, nodes[k].y);

						s3 = area(nodes[i].x, nodes[i].y, nodes[j].x,
								nodes[j].y, nodes[t].x, nodes[t].y);
						if ((s1 + s2 + s3) == a)
						{
							contain = true;
							break;
						}
					}
					if (!contain)
					{
						res[0] = nodes[i];
						res[1] = nodes[j];
						res[2] = nodes[k];
						maxa = a;
					}
				}
			}
		}
		sort(res, 3);
		cout << res[0].c << res[1].c << res[2].c << endl;
	}
	return 0;
}