UVa : 11579 (Triangle Trouble)



// http://uva.onlinejudge.org/external/115/11579.html
// Runtime: 0.164s
// Tag: triangle, geometry 

/* 
 * File:   main.cpp
 * Author: shahab
 * Created on March 23, 2011, 12:26 PM
 */

// @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 Set(a, s) memset (a, s, sizeof (a))

using namespace std;

double area (double x, double y, double z)
{
    if ( x + y < z || x + z < y || y + z < x ) return 0;
    double area = x + y + z;
    area /= 2;

    return sqrt (area * (area - x) * (area - y) * (area - z));
}

int main(int argc, char** argv) {
    int testCase;
    scanf ("%d", &testCase);

    while ( testCase-- ) {
        int n; scanf ("%d", &n);
        double s [10000 + 10];

        For (i, 0, n) scanf ("%lf", &s [i]);

        sort (s, s + n);

        double ret = 0;

        for ( int i = n - 1; i >= 2; i-- ) {
            ret = max (ret, area (s [i], s [i - 1], s [i - 2]));
        }

        printf ("%.2lf\n", ret);

    }

    return 0;
}

// @END_OF_SOURCE_CODE

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