#include <conio.h>
#include <iostream>
#include <vector>
using namespace std;

class Permute
{
	vector<int> set;
	vector<vector<int> > all;

public:
	void Print()
	{
		unsigned size = all.size();
		for(unsigned i = 0; i < size; i++)
		{
			unsigned size_i = all[i].size();
			for(unsigned j = 0; j < size_i; j++)
				cout<< all[i][j] << "  ";
			cout<< "\n";
		}
	}
	//-------------------------------------------
	void Run()
	{
		unsigned size = set.size();
		if(size == 0)
			return;
		if(size == 1)
		{
			all.push_back(set);
			return;
		}

		unsigned i = 0; /* sweeper item can be any number between 0 & size - 1 */

		vector<int> subset;
		for(unsigned j = 0; j < size; j++)
		{
			if(i != j)
				subset.push_back(set[j]);
		}
		Permute P(subset);

		unsigned allsize = P.Size();

		for(unsigned k = 0; k < allsize; k++)
		{
			unsigned size_k = P[k].size();
			for(unsigned m = 0; m <= size_k; m++)
			{
				P[k].insert(P[k].begin() + m,set[i]);
				all.push_back(P[k]);
				P[k].erase(P[k].begin() + m);
			}
		}
	}
	//-------------------------------------------
	unsigned Size()
	{
		return all.size();
	}
	//-------------------------------------------
	vector<int>& operator [](unsigned i)
	{
		if(Size() <= i)
			i = Size() - 1;
		return all[i];
	}
public:
	Permute(vector<int> set)
		: set(set)
	{
		Run();
	}
};

int Sign(vector<int> v) // sign of the permutation
{
	unsigned returns = 0;
	unsigned size = v.size();
	for(unsigned i = 0; i < size; i++)
		for(unsigned j = i + 1; j < size; j++)
		{
			if(v[j] < v[i])
				returns++;
		}

	if(returns % 2 == 0)
		return 1;
	else
		return -1;
}

template<const int n> // n by n matrix
double Determinant(double a[n][n]) // determinant
{
	vector<int> v;
	for(unsigned i = 0; i < n; i++)
		v.push_back(i);
	Permute P(v);
	unsigned size = P.Size();

	double sum = 0;
	for(unsigned k = 0; k < size; k++)
	{
		double prod = Sign(P[k]);
		for(unsigned i = 0; i < n; i++)
			prod *= a[i][P[k][i]];
		sum += prod;
	}
	return sum;
}

int main()
{
	double a[3][3] =
	{
		{0, 0, 1},
		{5,-2, 6},
		{1, 1, 2}
	};	
	cout<< Determinant<3>(a);
	_getch();
}