2014软专高级程序语言T4（三角形面积）

平面有100个点，任意三个点可以构成一个三角形。编一个程序，输入100个点的坐标，输出在构成的所有三角形中，最大的三角形的面积。

代码如下：

#include<stdio.h>

double area(int x1,int y1,int x2,int y2,int x3,int y3)
{
	return (x1*y2-y1*x2+x2*y3-y2*x3+x3*y1-y3*x1)/2;
}

int main()
{
	int x[100]={
		1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,
		1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,
		1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,
		1,2,3,4,5,6,7,8,9,10
	};
	int y[100]={
		2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,
		2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,
		2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,2,3,4,5,2,5,6,7,11,88,
		2,3,4,5,2,5,6,7,11,88
	};
	double maxx=0.0;
	for(int i=0;i<98;i++)//选第一个节点
	{
		for(int j=i+1;j<99;j++)//选第二个节点
		{
			for(int k=j+1;k<100;k++)//选第三个节点
			{
				double S=area(x[i],y[i],x[j],y[j],x[k],y[k]);
				if(S>maxx) maxx=S;
			}
		}
	}
	printf("%lf\n",maxx);
	return 0;
}

https://www.cnblogs.com/Running-Time/p/4753089.html

三点坐标求三角形的面积

方法1：行列式

设三角形的面积为S， 则S = (1/2)*(下面行列式)

|x1 y1 1| 
|x2 y2 1| 
|x3 y3 1|

即 S=(1/2)*(x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2) = (1 / 2) * ((x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1));

代码：

方法2：海伦公式

　　S = sqrt (p * (p - a)(p - b)(p - c))  其中p = (a + b + c) / 2, abc为三角形三边长

　　代码：