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How do I create groups of combinations that match specific conditions in C#?

I have a list of people List<Person> who I need to produce groups of combinations according to a couple of conditions. This may be easiest explained with an example. Let's say I have N = 19 people.
List<Person> people = new List<Person>(){A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S};
I am given as input a PreferredGroupSize. In this case, PreferredGroupSize = 5;.
I need as output combinations grouped by this PreferredGroupSize and +/-1 for remaining members lastGroupSizes.
For 19, I need all combinations of people with 3 groups of size 5 and a single group of size 4.
Using some modulus operations, I have already calculated the number of groups I need numGroups, as well as how many numNormalSizeGroups (i.e., number of PreferredGroupSize groups) and how many numOddSizeGroups.
This is calculated as follows:
//if(mod > (PreferredGroupSize)/2.0f)) make small groups.
//else make large groups.
float val1 = N % PreferredGroupSize;
float val2 = PreferredGroupSize / 2.0f;
if (N % PreferredGroupSize == 0)
{
lastGroupSizes = PreferredGroupSize;
numOddSizeGroups = 0;
numNormalSizeGroups = N / PreferredGroupSize;
}
else if (val1 > val2)
{
lastGroupSizes = PreferredGroupSize - 1;
numOddSizeGroups = PreferredGroupSize - N % PreferredGroupSize;
numGroups = (int)MathF.Ceiling(((float)N) / PreferredGroupSize);
numNormalSizeGroups = numGroups - numOddSizeGroups;
}
else
{
lastGroupSizes = PreferredGroupSize + 1;
numOddSizeGroups = N % PreferredGroupSize;
numGroups = (int)MathF.Floor(N / PreferredGroupSize);
numNormalSizeGroups = numGroups - numOddSizeGroups;
}
The issue I'm having is I do not know how to combine the groups to form valid combinations. Valid combinations should contain no duplicate members, the number of groups should be numGroups, and the total members should be N.
These will later be added to something like a Dictionary<List<Person>, float> Groups
So, for example, this would be a valid combination:
[A B C D E], 0.55
[F G H I J], 0.72
[K L M N O], 0.74
[P Q R S], 0.75
Each row is a List<Person>, followed by a float Score that represents the compatibility of the group. Higher is better. The floats aren't so important. What is important is that only valid combinations should be created.
This would be an invalid combination due to a repeated member:
[A B C D E], 0.55
[F B H I J], 0.77
[K L M N O], 0.74
[P Q R S], 0.75
This would be an invalid combination due to the wrong total number of people in the groups:
[A B C D], 0.63
[F G H I J], 0.72
[K L M N O], 0.74
[P Q R S], 0.75
If either condition is violated, it should be not be added to the list of valid groups.
Right now, I do the following:
Produce all combinations of people of size PreferredGroupSize. nCr = 19 choose 5
Produce all combinations of people of size lastGroupSizes. nCr = 19 choose 4
Calculate a group Score for all combinations produced by 1 and 2 and add the combinations and Score to the Groups Dictionary.
Produce all combinations of Groups of size numGroups.
This is where the major complexity comes into play, and why I want to avoid producing invalid groups:
nCr = ((19 choose 5) + (19 choose 4)) choose numGroups
Iterate over those using a foreach loop, looking for valid groups, adding only valid groups to a List<Person> ValidGroups.
Break out of the loop after a given M groups have been calculated. I have sorted Groups by the Score so that higher scoring groups are more likely to be found first.
Process the valid groups.
I skip Step 1 if numNormalSizeGroups is 0, and I skip Step 2 if numOddSizeGroups is 0.
There are a ton of invalid groups created this way, and the nCr is very large.
I believe there should be a better way to do this, but I have not yet found a way. Perhaps sharing how combinations are created may be helpful in assisting:
//make combinations of a certain length
public static IEnumerable<IEnumerable<T>> GetCombinations<T>(IEnumerable<T> items, int count)
{
int i = 0;
foreach (var item in items)
{
if (count == 1)
yield return new T[] { item };
else
{
foreach (var result in GetCombinations(items.Skip(i + 1), count - 1))
yield return new T[] { item }.Concat(result);
}
++i;
}
}
I attribute this code to here: Unique combinations of list
At the source, the code is listed as creating permutations instead of combinations. I have run this on many lists, and it produces combinations.
I'll also run through a somewhat minimal version of the current algorithm a bit with code:
//1. Produce all combinations of people of size PreferredGroupSize.
//2. Produce all combinations of people of size lastGroupSizes.
//Skip Step 1 if numNormalSizeGroups is 0
//Skip Step 2 if numOddSizeGroups is 0
bool calculatedNormal = false;
bool calculatedOdd = false;
while(!calculatedNormal || !calculatedOdd)
{
int gSize = 0;
if(!calculatedNormal)
{
calculatedNormal = true;
if(numNormalSizeGroups>0)
gSize = PreferredGroupSize;
else
continue;
}
else if(!calculatedOdd)
{
calculatedOdd = true;
if(numOddSizeGroups>0)
gSize = lastGroupSizes;
else
break;
}
//Calculate a group Score for all combinations produced by 1 and 2.
//Add the combinations and Score to the Groups Dictionary.
var combos = GetCombinations(people, gSize);
float groupScore = 0;
List<Person> curGroup;
//for purposes of this example, generate pseudorandom float:
Random rand = new Random();
foreach(var combo in combos)
{
//groupScore = CalculateGroupScore(combo);
groupScore = (float)rand.NextDouble();
curGroup = new List<Person>();
foreach(Person person in combo)
curGroup.Add(person);
Groups.Add(curGroup, groupScore);
}
}
//I have sorted Groups by the Score
//so that higher scoring groups are more
//likely to be found first.
Groups = Groups.OrderByDescending(x => x.Value).ToDictionary(x => x.Key, x => x.Value);
//4. Produce all combinations of Groups of size numGroups.
var AllGroupCombos = GetCombinations(Groups, numGroups);
int M = 10000;
List<Person> gList = new List<Person>();
List<Person> ValidGroups = new List<Person>();
int curPeopleInGroup = 0;
bool addGroup = true;
//5. Iterate over those using a foreach loop
foreach(var combo in AllGroupCombos)
{
curPeopleInGroup = 0;
addGroup = true;
gList.Clear();
//Look for valid groups
foreach(KeyValuePair<List<Person>, float> keyValuePair in combo)
{
foreach(Person person in keyValuePair.Key)
{
if(!gList.Contains(person)
{
gList.Add(person);
++curPeopleInGroup;
}
else
{
addGroup = false;
break;
}
}
if(!addGroup)
break;
}
//Add only valid groups to a List<Person> ValidGroups.
if(!addGroup || curPeopleInGroup != N)
continue;
var comboList = combo.ToList();
ValidGroups.Add(comboList);
//6. Break out of the loop after a given M
//groups have been calculated.
if(ValidGroups.Count() >= M)
break;
}
I hope this was helpful, and that someone will be able to assist. :)

How to distribute items evenly, without random numbers

I have a situation where I need to evenly distribute N items across M slots. Each item has its own distribution %. For discussion purposes say there are three items (a,b,c) with respective percentages of (50,25,25) to be distributed evenly across 20 slots. Hence 10 X a,5 X b & 5 X c need to be distributed. The outcome would be as follows:
1. a
2. a
3. c
4. b
5. a
6. a
7. c
8. b
9. a
10. a
11. c
12. b
13. a
14. a
15. c
16. b
17. a
18. a
19. c
20. b
The part that I am struggling with is that the number of slots, number of items and percentages can all vary, of course the percentage would always total up to 100%. The code that I wrote resulted in following output, which is always back weighted in favour of item with highest percentage. Any ideas would be great.
1. a
2. b
3. c
4. a
5. b
6. c
7. a
8. b
9. c
10. a
11. c
12. b
13. a
14. b
15. c
16. a
17. a
18. a
19. a
20. a
Edit
This is what my code currently looks like. Results in back weighted distribution as I mentioned earlier. For a little context, I am trying to evenly assign commercials across programs. Hence every run with same inputs has to result in exactly the same output. This is what rules out the use of random numbers.
foreach (ListRecord spl in lstRecords){
string key = spl.AdvertiserName + spl.ContractNumber + spl.AgencyAssignmentCode;
if (!dictCodesheets.ContainsKey(key)){
int maxAssignmentForCurrentContract = weeklyList.Count(c => (c.AdvertiserName == spl.AdvertiserName) && (c.AgencyAssignmentCode == spl.AgencyAssignmentCode)
&& (c.ContractNumber == spl.ContractNumber) && (c.WeekOf == spl.WeekOf));
int tmpAssignmentCount = 0;
for (int i = 0; i < tmpLstGridData.Count; i++)
{
GridData gData = tmpLstGridData[i];
RotationCalculation commIDRotationCalc = new RotationCalculation();
commIDRotationCalc.commercialID = gData.commercialID;
commIDRotationCalc.maxAllowed = (int)Math.Round(((double)(maxAssignmentForCurrentContract * gData.rotationPercentage) / 100), MidpointRounding.AwayFromZero);
tmpAssignmentCount += commIDRotationCalc.maxAllowed;
if (tmpAssignmentCount > maxAssignmentForCurrentContract)
{
commIDRotationCalc.maxAllowed -= 1;
}
if (i == 0)
{
commIDRotationCalc.maxAllowed -= 1;
gridData = gData;
}
commIDRotationCalc.frequency = (int)Math.Round((double)(100/gData.rotationPercentage));
if (i == 1)
{
commIDRotationCalc.isNextToBeAssigned = true;
}
lstCommIDRotCalc.Add(commIDRotationCalc);
}
dictCodesheets.Add(key, lstCommIDRotCalc);
}else{
List<RotationCalculation> lstRotCalc = dictCodesheets[key];
for (int i = 0; i < lstRotCalc.Count; i++)
{
if (lstRotCalc[i].isNextToBeAssigned)
{
gridData = tmpLstGridData.Where(c => c.commercialID == lstRotCalc[i].commercialID).FirstOrDefault();
lstRotCalc[i].maxAllowed -= 1;
if (lstRotCalc.Count != 1)
{
if (i == lstRotCalc.Count - 1 && lstRotCalc[0].maxAllowed > 0)
{
//Debug.Print("In IF");
lstRotCalc[0].isNextToBeAssigned = true;
lstRotCalc[i].isNextToBeAssigned = false;
if (lstRotCalc[i].maxAllowed == 0)
{
lstRotCalc.RemoveAt(i);
}
break;
}
else
{
if (lstRotCalc[i + 1].maxAllowed > 0)
{
//Debug.Print("In ELSE");
lstRotCalc[i + 1].isNextToBeAssigned = true;
lstRotCalc[i].isNextToBeAssigned = false;
if (lstRotCalc[i].maxAllowed == 0)
{
lstRotCalc.RemoveAt(i);
}
break;
}
}
}
}
}
}
}
Edit 2
Trying to clear up my requirement here. Currently, because item 'a' is to be assigned 10 times which is the highest among all three items, towards the end of distribution, items 16 - 20 all have been assigned only 'a'. As has been asked in comments, I am trying to achieve a distribution that "looks" more even.

One way to look at this problem is as a multi-dimensional line drawing problem. So I used Bresenham's line algorithm to create the distribution:
public static IEnumerable<T> GetDistribution<T>( IEnumerable<Tuple<T, int>> itemCounts )
{
var groupCounts = itemCounts.GroupBy( pair => pair.Item1 )
.Select( g => new { Item = g.Key, Count = g.Sum( pair => pair.Item2 ) } )
.OrderByDescending( g => g.Count )
.ToList();
int maxCount = groupCounts[0].Count;
var errorValues = new int[groupCounts.Count];
for( int i = 1; i < errorValues.Length; ++i )
{
var item = groupCounts[i];
errorValues[i] = 2 * groupCounts[i].Count - maxCount;
}
for( int i = 0; i < maxCount; ++i )
{
yield return groupCounts[0].Item;
for( int j = 1; j < errorValues.Length; ++j )
{
if( errorValues[j] > 0 )
{
yield return groupCounts[j].Item;
errorValues[j] -= 2 * maxCount;
}
errorValues[j] += 2 * groupCounts[j].Count;
}
}
}
The input is the actual number of each item you want. This has a couple advantages. First it can use integer arithmetic, which avoids any rounding issues. Also it gets rid of any ambiguity if you ask for 10 items and want 3 items evenly distributed (which is basically just the rounding issue again).

Here's one with no random number that gives the required output.
using System;
using System.Collections.Generic;
public class Program
{
public static void Main()
{
// name, percentage
Dictionary<string, double> distribution = new Dictionary<string,double>();
// name, amount if one more were to be distributed
Dictionary<string, int> dishedOut = new Dictionary<string, int>();
//Initialize
int numToGive = 20;
distribution.Add("a", 0.50);
distribution.Add("b", 0.25);
distribution.Add("c", 0.25);
foreach (string name in distribution.Keys)
dishedOut.Add(name, 1);
for (int i = 0; i < numToGive; i++)
{
//find the type with the lowest weighted distribution
string nextUp = null;
double lowestRatio = double.MaxValue;
foreach (string name in distribution.Keys)
if (dishedOut[name] / distribution[name] < lowestRatio)
{
lowestRatio = dishedOut[name] / distribution[name];
nextUp = name;
}
//distribute it
dishedOut[nextUp] += 1;
Console.WriteLine(nextUp);
}
Console.ReadLine();
}
}

Instead of a truly random number generator, use a fixed seed, so that the program has the same output every time you run it (for the same input). In the code below, the '0' is the seed, which means the 'random' numbers generated will always be the same each time the program is run.
Random r = new Random(0);

//AABC AABC…
int totalA = 10
int totalB = 5
int totalC = 5
int totalItems = 20 //A+B+C
double frequencyA = totalA / totalItems; //0.5
double frequencyB = totalB / totalItems; //0.25
double frequencyC = totalC / totalItems; //0.25
double filledA = frequencyA;
double filledB = frequencyB;
double filledC = frequencyC;
string output = String.Empty;
while(output.Length < totalItems)
{
filledA += frequencyA;
filledB += frequencyB;
filledC += frequencyC;
if(filledA >= 1)
{
filledA -= 1;
output += "A";
if(output.Length == totalItems){break;}
}
if(filledB >= 1)
{
filledB -= 1
output += "B";
if(output.Length == totalItems){break;}
}
if(filledC >= 1)
{
filledC -= 1
output += "C";
if(output.Length == totalItems){break;}
}
}

This answer was mostly stolen and lightly adapted for your use from here
My idea is that you distribute your items in the simplest way possible without care of order, then shuffle the list.
public static void ShuffleTheSameWay<T>(this IList<T> list)
{
Random rng = new Random(0);
int n = list.Count;
while (n > 1) {
n--;
int k = rng.Next(n + 1);
T value = list[k];
list[k] = list[n];
list[n] = value;
}
}
Fiddle here

Create a list of sequential numbers excluding one number

Requirements:
Create a list of n sequential numbers starting at a.
Exclude number x.
This is the best I have right now, the problem being that it creates n + 1 numbers if x is not within the range.
var numbers = Enumerable
.Range(a, numberOfDataRowsToAdd + 1)
.Where(i => i != TechnicalHeaderRowIndex);
Example 1 should produce 0,1,2,3,4,5,6,7,8,9.
var a = 0;
var n = 10;
var x = 11;
Example 2 should produce 0,1,2,3,4,5,7,8,9,10.
var a = 0;
var n = 10;
var x = 6;
Here is a Fiddle that demonstrates Mark's answer.

How about
Enumerable.Range(a, n + 1)
.Where(i => i != x)
.Take(n);

My example, how it can be done without LINQ and extra loop iterations:
public static IEnumerable<int> GenerateNumbers(int a, int n, int x)
{
for (var i = 0; i < n; i++)
{
if (a == x)
{
i--;
a++;
continue;
}
yield return a++;
}
}
But if you don't want create new method for this purpose, Mark Sowul or Jakub Lortz answers are better.

The problem can be described as
Get n + 1 sequential numbers starting from a
If x is in the range, remove x, otherwise remove the maximum number from the list
Translated to C#
int numberToExclude = Math.Min(n + a, x);
var numbers = Enumerable.Range(a, n + 1).Where(i => i != numberToExclude);

It makes sense to generate only necessary values instead of generating n + 1 values and then remove x:
Enumerable.Range(a, n).Select(i => i < x ? i : i + 1);
Example 1: 0,1,2,3,4,5,6,7,8,9.
Example 2: 0,1,2,3,4,5,7,8,9,10.

You can drop the last if your enumerable count is bigger than numberOfDataRowsToAdd
Extension method:
public static IEnumerable<T> DropLast<T>(this IEnumerable<T> enumerable)
{
return enumerable.Take(enumerable.Count()-1);
}
Usage:
var numbers = Enumerable
.Range(a, numberOfDataRowsToAdd + 1)
.Where(i => i != TechnicalHeaderRowIndex);
if(numbers.Count() > numberOfDataRowsToAdd)
numbers = numbers.DropLast();

I don't see what really is the challenge - Linq shortest or fastest or just working. How about the natural (which should also be the fastest Linq based)
var numbers = a <= x && x < a + n ?
Enumerable.Range(a, x - a).Concat(Enumerable.Range(x + 1, a - x + n)) :
Enumarble.Range(a, n);

List<int> separated into thirds

Assuming I have a list of numbers, which could be any amount, realistically over 15.
I want to separate that list of numbers into three groups depending on their size, small, medium, and large for instance.
What is the best way of achieving this?
I've written out the below, is it necessary to make my own function as per below, or is there anything existing that I can utilise in .NET?
public static List<int> OrderByThree (List<int> list)
{
list.Sort();
int n = list.Count();
int small = n / 3;
int medium = (2 * n) / 3;
int large = n;
// depending if the number is lower/higher than s/m/l,
// chuck into group via series of if statements
return list;
}
Example
Say I have a list of numbers, 1-15 for instance, I want 1-5 in small, 6-10 in medium and 11-15 in large. However I won't know the amount of numbers at the start, no dramas, using list.count I was hoping to divide for my own function.

Since you have the list sorted already, you can use some LINQ to get the results. I'm assuming a right-closed interval here.
list.Sort();
int n = list.Count();
var smallGroup = list.TakeWhile(x => (x <= n / 3)).ToList();
var middleGroup = list.Skip(smallGroup.Count).TakeWhile(x => (x <= (2 * n) / 3)).ToList();
var largeGroup = list.Skip(smallGroup.Count + middleGroup.Count).ToList();
EDIT
As Steve Padmore commented, you probably will want to return a list of lists (List<List<int>>) from your method, rather than just List<int>.
return new List<List<int>> { smallGroup, middleGroup, largeGroup };

This would be a simple way of doing it:
var result = list.GroupBy (x =>
{
if(x <= small) return 1;
if(x <= medium) return 2;
return 3;
});
Or:
var result = list.GroupBy (x => x <= small ? 1 : x <= medium ? 2 : 3);
(This does not require the list to be sorted)

LINQ get x amount of elements from a list

I have a query which I get as:
var query = Data.Items
.Where(x => criteria.IsMatch(x))
.ToList<Item>();
This works fine.
However now I want to break up this list into x number of lists, for example 3. Each list will therefore contain 1/3 the amount of elements from query.
Can it be done using LINQ?

You can use PLINQ partitioners to break the results into separate enumerables.
var partitioner = Partitioner.Create<Item>(query);
var partitions = partitioner.GetPartitions(3);
You'll need to reference the System.Collections.Concurrent namespace. partitions will be a list of IEnumerable<Item> where each enumerable returns a portion of the query.

I think something like this could work, splitting the list into IGroupings.
const int numberOfGroups = 3;
var groups = query
.Select((item, i) => new { item, i })
.GroupBy(e => e.i % numberOfGroups);

You can use Skip and Take in a simple for to accomplish what you want
var groupSize = (int)Math.Ceiling(query.Count() / 3d);
var result = new List<List<Item>>();
for (var j = 0; j < 3; j++)
result.Add(query.Skip(j * groupSize).Take(groupSize).ToList());

If the order of the elements doesn't matter using an IGrouping as suggested by Daniel Imms is probably the most elegant way (add .Select(gr => gr.Select(e => e.item)) to get an IEnumerable<IEnumerable<T>>).
If however you want to preserve the order you need to know the total number of elements. Otherwise you wouldn't know when to start the next group. You can do this with LINQ but it requires two enumerations: one for counting and another for returning the data (as suggested by Esteban Elverdin).
If enumerating the query is expensive you can avoid the second enumeration by turning the query into a list and then use the GetRange method:
public static IEnumerable<List<T>> SplitList<T>(List<T> list, int numberOfRanges)
{
int sizeOfRanges = list.Count / numberOfRanges;
int remainder = list.Count % numberOfRanges;
int startIndex = 0;
for (int i = 0; i < numberOfRanges; i++)
{
int size = sizeOfRanges + (remainder > 0 ? 1 : 0);
yield return list.GetRange(startIndex, size);
if (remainder > 0)
{
remainder--;
}
startIndex += size;
}
}
static void Main()
{
List<int> list = Enumerable.Range(0, 10).ToList();
IEnumerable<List<int>> result = SplitList(list, 3);
foreach (List<int> values in result)
{
string s = string.Join(", ", values);
Console.WriteLine("{{ {0} }}", s);
}
}
The output is:
{ 0, 1, 2, 3 }
{ 4, 5, 6 }
{ 7, 8, 9 }

You can create an extension method:
public static IList<List<T>> GetChunks<T>(this IList<T> items, int numOfChunks)
{
if (items.Count < numOfChunks)
throw new ArgumentException("The number of elements is lower than the number of chunks");
int div = items.Count / numOfChunks;
int rem = items.Count % numOfChunks;
var listOfLists = new List<T>[numOfChunks];
for (int i = 0; i < numOfChunks; i++)
listOfLists[i] = new List<T>();
int currentGrp = 0;
int currRemainder = rem;
foreach (var el in items)
{
int currentElementsInGrp = listOfLists[currentGrp].Count;
if (currentElementsInGrp == div && currRemainder > 0)
{
currRemainder--;
}
else if (currentElementsInGrp >= div)
{
currentGrp++;
}
listOfLists[currentGrp].Add(el);
}
return listOfLists;
}
then use it like this :
var chunks = query.GetChunks(3);
N.B.
in case of number of elements not divisible by the number of groups, the first groups will be bigger. e.g. [0,1,2,3,4] --> [0,1] - [2,3] - [4]