计算几何判断多边形顶点是否是顺时针

计算面积，用面积的正负判断方向，如果面积是正，则是逆时针，面积是负则是顺时针

计算几何中计算三角形面积

在计算几何里，我们知道，△ABC的面积就是“向量AB”和“向量AC”两个向量叉积的绝对值的一半。其正负表示三角形顶点是在右手系还是左手系(面积是有向面积（有正负）), 负则是左手系，反之，右手系。

http://codeforces.com/gym/101116/attachments

问题 H: Hunter’s Apprentice

题目描述

When you were five years old, you watched in horror as a spiked devil murdered your parents. You would have died too, except you were saved by Rose, a passing demon hunter. She ended up adopting you and training you as her apprentice.
Rose’s current quarry is a clock devil which has been wreaking havoc on the otherwise quiet and unassuming town of Innsmouth. It comes out each night to damage goods, deface signs, and kill anyone foolish enough to wander around too late. The clock devil has offed the last demon hunter after it; due to its time-warping powers, it is incredibly agile and fares well in straight-up fights.
The two of you have spent weeks searching through dusty tomes for a way to defeat this evil. Eventually, you stumbled upon a relevant passage. It detailed how a priest managed to ensnare a clock devil by constructing a trap from silver, lavender, pewter, and clockwork. The finished trap contained several pieces, which must be placed one-by-one in the shape of a particular polygon, in counter-clockwise order. The book stated that the counter-clockwise order was important to counter the clock devil’s ability to speed its own time up, and that a clockwise order would only serve to enhance its speed.
It was your responsibility to build and deploy the trap, while Rose prepared for the ensuing fight. You carefully reconstruct each piece as well as you can from the book. Unfortunately, things did not go as planned that night. Before you can finish preparing the trap, the clock devil finds the two of you. Rose tries to fight the devil, but is losing quickly. However, she is buying you the time to finish the trap. You quickly walk around them in the shape of the polygon, placing each piece in the correct position. You hurriedly activate the trap as Rose is knocked out. Just then, you remember the book’s warning. What should you do next?

输入

The first line of input contains a single integer T (1 ≤ T ≤ 100), the number of test cases. The first line of each test case contains a single integer n (3 ≤ n ≤ 20), the number of pieces in the trap. Each of the next n lines contains two integers xi and yi (|xi |, |yi | ≤ 100), denoting the x and y coordinates of where the ith piece was placed. It is guaranteed that the polygon is simple; edges only intersect at vertices, exactly two edges meet at each vertex, and all vertices are distinct.

输出

For each test case, output a single line containing either fight if the trap was made correctly or run if the trap was made incorrectly.

样例输入

复制样例数据

样例输出

fight
run

#include<bits/stdc++.h>
using namespace std;
const int maxn=1e5+5;
struct node
{
    int x,y;
}p[maxn];

double S(int start,int n)//计算多边形的面积
{
    if(n<3)
        return 0.00;
    double s=p[0].y*(p[n-1].x-p[1].x);
    p[n]=p[0];
    for(int i=1;i<n;i++)
        s+=p[i].y*(p[i-1].x-p[i+1].x);

    return s*0.5;
}

int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        int n;
        scanf("%d",&n);
        for(int i=0;i<n;i++)
            scanf("%d%d",&p[i].x,&p[i].y);
        if(S(0,n)>0)
            printf("fight\n");
        else
            printf("run\n");
    }
}