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;
}