Distributing Items Evenly Across a Number of Days

Question

I need to distribute a remainder of items over a fixed number of days. e.g. say I have 197 items and 75 days to distribute them over. If I display 2 items for 75 days then I have 47 items not displayed. How do I distribute the remaining 47 items over the 75 days evenly so that I will get a sequence like 2,3,3,2,3,3,2,2,3.... i.e. the 3's are evenly distributed over the whole display. This is what I have so far

const double num = (double)197/75;
double temp = num;
var list = new List<int>();
for (var t = 1; t <= days; t++)
{
    var intPart = int.Parse(Math.Truncate(temp).ToString());

    list.Add(intPart);

    var remainder = num - intPart;

    temp = num + remainder;
}

but I only end up with 187 items displayed. I'm missing 10.

Answer 1

The original answer that turned out to give suboptimal results in some cases, as noted by AlexD:

int numItems = 197;
int numDays = 75;
var list = new List<int>();
for (int t = 0; t < numDays; t++)
{
    int numItemsInDay = ((t+1)*numItems+numDays/2)/numDays - (t*numItems+numDays/2)/numDays;
    list.Add(numItemsInDay);
}

The idea is that every item goes into the day defined by the rounded value of itemIndex*numDays/numItems, and you can calculate the number of items in a day directly, without keeping track of previous items.

---

Another approach.

To spread numItems items among numDays days as evenly as possible, you need to group the days into spans of days with floor(numItems/numDays) items and spans of days with ceil(numItems/numDays) items, spreading the spans as evenly as possible. So the problem can be solved by recursively reducing the number of days to the number of spans.

static List<int> Spread(int numDays, int numItems)
{
    List<int> result = new List<int>();
    if (numDays <= 1)
    {
        if (numDays == 1)
            result.Add(numItems);
        return result;
    }
    int numItemsInDayLower = numItems/numDays;
    int numItemsInDayHigher = numItemsInDayLower+1;
    int numDaysHigher = numItems - numItemsInDayLower * numDays;
    int numDaysLower = numDays-numDaysHigher;
    int numSpansLower = numDaysLower > numDaysHigher ? numDaysHigher + 1 : numDaysLower;
    int numSpansHigher = numDaysHigher > numDaysLower ? numDaysLower + 1 : numDaysHigher;
    bool isStartingFromSpanLower = numDaysLower > numDaysHigher;
    List<int> spanLehgthsLower = Spread(numSpansLower, numDaysLower);
    List<int> spanLehgthsHigher = Spread(numSpansHigher, numDaysHigher);
    for (int iSpan = 0; iSpan < spanLehgthsLower.Count + spanLehgthsHigher.Count; iSpan++)
    {
        if ((iSpan % 2 == 0) == isStartingFromSpanLower)
        {
            for (int i = 0; i < spanLehgthsLower[iSpan/2]; i++)
                result.Add(numItemsInDayLower);
        }
        else
        {
            for (int i = 0; i < spanLehgthsHigher[iSpan/2]; i++)
                result.Add(numItemsInDayHigher);
        }
    }
    return result;
}