// Created by Alex Kontorovich & John F. Nash Jr. 6/11/2002

void reverse_sort(double **vect)
// sorts elements in vect of size coalitions from biggest to smallest
{
	double temp;
	int i,j,found,low,mid,high;

	for (i=1;i<coalitions;i++)
	{
//		determine location for i'th vector element
		temp=(*vect)[i];

		if (temp>=(*vect)[0])
			mid=0;
		else if (temp<=(*vect)[i-1])
			mid=i;
		else
		{
			low=0;
			high=i-1;
			mid=(low+high)/2;
			found=0;

			while (!found)
			{
				if (temp==(*vect)[mid]) // if we're equal, done, found it
					found=1;
				else if (temp>(*vect)[mid]) // if location is bigger
				{
					if (temp<(*vect)[mid-1]) // found right place
						found=1;
					else // close in bars
					{
						high=mid;
						mid=(low+high)/2;
					}
				}
				else // temp < location, bump up low
				{
					low=mid;
					mid=(low+high)/2;
					if (high-low<2)
						mid+=found=1; // tricky way of setting found=1 and mid++ in one line
				}
				

				if (high==low)
					found=1;
			}
		}

		// mid now contains correct place

		for (j=i-1;j>=mid;j--)
			(*vect)[j+1]=(*vect)[j];
		(*vect)[mid]=temp;
	}
	return;
}

int less_than(double *v1, double *v2)
// returns true if v1 != v2, and v1 is lexicographically smaller than v2. Vectors of size coalitions
{
	int i=0;

	while ((i<coalitions)&&(v1[i]==v2[i]))
		i++;

	if (i==coalitions)
		return 0; // v1=v2

	if (v1[i]>v2[i])
		return 0; // v1 not smaller than v2

	return 1; // v1 < v2
}