Robot Race UVALive - 7020（几何数学 判断钝角）

题目链接：https://vjudge.net/problem/UVALive-7020

题意：按顺序给定n个点的坐标，问有没有一个点到第三个点的距离小于第二个点到那第三个点的距离，切第二个点在第一个点之后，有存在输出Unfair，反之输出Fair。

思路：判断相邻点与他们后面其他点之间会不会组成钝角，若会则Unfair，反之Fair。

代码如下：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<cstdlib>
#include<sstream>
#include<deque>
#include<stack>
#include<set>
#include<map>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const double eps = 1e-9;
const int maxn = 10000 + 20;
const int maxt = 300 + 10;
const int mod = 10;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, -1, 1};
const int Dis[] = {-1, 1, -5, 5};
const double inf = 0x3f3f3f3f;
const int MOD = 1000;
const double PI = acos(-1.0);
struct node{
ll x, y;
}num[maxn];
bool judge(node a, node b, node c){
return (b.x - a.x) * (c.x - b.x) + (b.y - a.y) * (c.y - b.y) >= 0;
}
int main(){
int n;
while(~scanf("%d", &n) && n){
memset(num, 0, sizeof num);
for(int i = 0; i < n; ++i){
scanf("%lld%lld", &num[i].x, &num[i].y);
}
bool ok = true;
for(int i = 0; i < n - 2; ++i){
for(int j = i + 2; j < n; ++j){
if(!judge(num[i], num[i + 1], num[j])){
ok = false;
break;
}
}
if(!ok) break;
}
printf("%s\n", ok ? "Fair" : "Unfair");
}
return 0;
}