51nod 1451 合法三角形（暴力，思维）

先枚举了下相同x坐标和相同y坐标的情况，总情况减去后发现不对，少了个相同斜率的情况。那就枚举斜率，正好还包含了坐标相等的情况，反正数据范围小，暴力搞呗。用pair保存分数的最简形式。

#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;
}