Timus : 1052 (Rabbit Hunt)



// http://acm.timus.ru/problem.aspx?space=1&num=1052
// Runtime: 0.031s
// Memory: 112 KB
// Tag: Geometry
// Hints: if area of triangle ABC is zero, then points A, B, C are co-linear. 

// @BEGIN_OF_SOURCE_CODE

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cctype>
#include <stack>
#include <queue>
#include <list>
#include <vector>
#include <map>
#include <sstream>
#include <cmath>
#include <bitset>
#include <utility>
#include <set>
#include <numeric>

#define INF_MAX 2147483647
#define INF_MIN -2147483647
#define pi acos(-1.0)
#define N 1000000
#define LL long long

#define For(i, a, b) for( int i = (a); i < (b); i++ )
#define Fors(i, sz) for( size_t i = 0; i < sz.size (); i++ )
#define Fore(it, x) for(typeof (x.begin()) it = x.begin(); it != x.end (); it++)
#define Set(a, s) memset(a, s, sizeof (a))
#define Read(r) freopen(r, "r", stdin)
#define Write(w) freopen(w, "w", stdout)

int dr [] = {-1, -1, 0, 1, 1, 1, 0, -1};
int dc [] = {0, 1, 1, 1, 0, -1, -1, -1};

using namespace std;

int x [200 + 5];
int y [200 + 5];

int triangleArea (int a, int b, int c) {
    return x [a] * (y [b] - y [c]) + x [b] * (y [c] - y [a]) + x [c] * (y [a] - y [b]);
}

int main ()
{
    int n; scanf ("%d", &n);

    for ( int i = 0; i < n; i++ ) scanf ("%d %d", &x [i], &y [i]);

    int cnt;
    int maxi = INF_MIN;

    for ( int i = 0; i < n; i++ ) {
        for ( int j = i + 1; j < n; j++ ) {
            cnt = 2;
            for ( int k = j + 1; k < n; k++ ) {
                if ( triangleArea (i, j, k) == 0 ) cnt++;
            }
            if ( cnt > maxi ) maxi = cnt;
        }
    }

    printf ("%d\n", maxi);

	return 0;
}

// @END_OF_SOURCE_CODE
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