2) Choose integers so that average is close to given real nu

#include <iostream>

using namespace std;
#include <cmath>
#include <set>

set<long> bestAverage(double target, long first, long range)
{
    set<long> ret;

    double bestError = range;
    long bestDivider = 0;
    long bestIncrement;
    long divider;

    if (target < first)
    {
        ret.insert(first);
        return ret;
    }
    if (target > first + range - 1)
    {
        ret.insert(first + range - 1);
        return ret;
    }

    for(divider = 1; divider < range; divider++)
    {
        // find the franctions with given divider we can reach by averaging in the [first, first+range[ range
        double lowerBound = (first + (first + divider - 1)) / 2.0;
        double higherBound = ((first + range - 1) + (first + range - divider)) / 2.0;
        // there exists a set with average in the range [lowerBound, higherBound] of the form n/divider

        double c1 = floor(target * divider) / divider;
        double c2 = ceil(target * divider) / divider;
        double error = min(target - c1, c2 - target);

        if ((lowerBound <= target) && (target <= higherBound) && (error < bestError))
        {
            bestError = error;
            bestDivider = divider;
            if (target - c1 < c2 - target)
            {
                bestIncrement = (long)floor((target - lowerBound) * divider);
            }
            else
            {
                bestIncrement = (long)ceil((target - lowerBound) * divider);
            }
        }
    }

    if (bestDivider == 0)
    {
        return ret;
    }

    long incrementLarge = range - bestDivider; // how many increment (from the least possible average) of 1/divider we make my moving an integer all the way from one side of the range to the other
    long numberLarge = bestIncrement / incrementLarge; // how many integers we move all the way (integer division: rounds down)
    long numberSmall = bestDivider - numberLarge;
    long remainder = bestIncrement - numberLarge * incrementLarge;

    if (remainder > 0)
    {
        numberSmall--;
    }

    for(long index = 0; index < numberSmall; index++)
    {
        ret.insert(first + index);
    }

    if (remainder)
    {
        ret.insert(first + numberSmall + remainder);
    }

    for(long index = 0; index < numberLarge; index++)
    {
        ret.insert(first + range - numberLarge + index);
    }

    return ret;
}

int main()
{
    set<long> answer;
    set<long>::iterator it;

    double target = 3.1415926536;
    double sum = 0;

    cout << "target is " << target << endl;

    answer = bestAverage(target, -100, 200);

    cout << "Average of " << endl;
    for(it = answer.begin(); it != answer.end(); it++)
    {
        cout << *it << ", ";
        sum += *it;
    }
    cout << endl << " is " << sum / answer.size() << endl;

    return 0;
}