Possibilities and nested foreach loops C#

Question

I am writing a program that can calculate all possible places for people sitting at a random amount of tables (can go up to 1000+):

As you see on the image, the black dots represent people (but in the computer, there are different types of people.) There are two types of tables : blue and pink ones. The blue ones can contain 3 people and the pink 2 people.

To get all possible places for any person to sit I could use foreach loops (8of them) and then I can run some extra code...

But what happens if I add 200 tables? Then do I need to use 200 foreach loops? Is there any way that this can be coded faster and less-space-consuming-coded?

What I tried? =>

  switch(listoftables.Count)
  {
      case 1:foreach(Table table in listoftables){ //code to add people to this table}break;
      case 2: foreach(Table table1 in listoftables)
      {foreach(Table table1 in       listoftables){//code to add people to this table
   }}break;
   }

INPUT : array with editable Table class objects (its a class created by myself) PROCESS : the above List is edited and is added to another List object, where after the whole foreach process has ended, the OUTPUT will write all possible configurations (who are in the other List object) to the screen.

Example part of output :

  // List<Table> listofalltables was processed
  List<listofalltables> output 

=> contains as [0] in array : List first => contains as [0] in array : Table.attachedpeople (is list)

Answer 1

Try a recursive method. A small example :

public List<Table> assignToTable(List<Person> invited, List<Table> tables)
{
    if(!tables.HasRoom)
         return tables;
     else
     {
         assign(tables,invited) //code to add a person to a table
         assignToTable(invited, tables);
     }
}

If I were you I'll create a object taht represent you tables with a propertie to know if there is still some room avaiblable. This will assign to every people a table without any foreach. Then in you main you could have a method that will rearrange the tables in all the way possible : Table 1 Table 2 Table 3

Then

Table 1 Table 3 Table 2 ...

Table 3 Table 2 Table 1

and call the recursive method on those lists and you will have all the possibility where poeple can sit...

Answer 2

Taken @Guigui's answer and changed it to how I interpret the question. This will try to seat everyone everywhere (except when there are more people than chairs, is that a case? I assumed more chairs than people) by recursion and loops, as you see the complexity will be of the form O(Math.Power(nrPeople, nrSeats)) which is a lot (if I'm not mistaken).

Person[] peopleInvited = ....; // Avoid copying this, we are not modifying it
public void AssignToTable(int invited, SeatingArrangements tables)
{
  if(!tables.HasRoom || invited == peopleInvited.Length)
    // Do what? Print the seating?
  else
  {
    var personToSeat = peopleInvited[invited];
    foreach (var possibleSeating in tables.GetEmptyChairs()) 
    {
      // Add one person to a table somewhere, but don't modify tables
      var newArrangments = Assign(possibleSeating, personToSeat, tables) 
      AssignToTable(invited + 1, newArrangements);
    }
  }
}

Answer 3

Well, it more a question about math than programming. What you are trying to do is creating permutations of people. Basically you have N tables and 2N+2 seats. You can assign a number to each seat. Then the result will be the set of K-permutations of 2N+2, where K is the number of people invited, and N is the number of tables.

You can do this using loops, but you can also do it recursively. There are algorithms ready to use out there. For example:

Algorithm to generate all possible permutations of a list?