51nod 1451 合法三角形（暴力，思维）

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MAXN = 2010;
struct Point
{
int x,y;
}ps[MAXN];

LL calc(LL num)
{
if(num < 3) return 0;
return num*(num-1)*(num-2)/6;
}

int main()
{
int n;
scanf("%d",&n);
for(int i = 0; i < n; ++i)
scanf("%d %d",&ps[i].x,&ps[i].y);
if(n < 3)
{
puts("0");
return 0;
}
LL all = calc(n);
int x,y,gd;
map<pair<int,int>,int> mp;
for(int i = 0; i < n; ++i)
{
mp.clear();
for(int j = i+1; j < n; ++j)
{
x = ps[i].x - ps[j].x;
y = ps[i].y - ps[j].y;
gd = __gcd(x,y);
mp[make_pair(x/gd,y/gd)]++;
}

for(map<pair<int,int>, int>::iterator it = mp.begin(); it != mp.end(); ++it)
{
if(it->second > 1)
all -= it->second*(it->second-1)/2;
}
}
printf("%I64d\n",all);
return 0;
}