Algorithm or expression to put n elements in k sets

[xeon123]

I have 17 elements, and I want to put them in 3 sets. This makes 2 sets with 6 elements, and 1 set with 5 elements. Now I want to find an algorithm to partition n elements in k sets.

Can anyone give me an algorithm, or a math expression for me to implement in a algorithm?

Thanks

 

[mfb]

There are many ways to put n elements in k sets. Do you want the set sizes to be similar to each other?
A naive approach would be n/k elements per set. This is not always an integer, but you can fix this by rounding in an appropriate way.

 

[rcgldr]

You could add 1 element at a time to each set, cycling through all the sets as you add elements. If the number of elements isn't an multiple of the number of sets, you just run out of elements before cycling through all the sets on the last cycle.

 

[dodo]

Is there a 'distance' function, a way to quantify how close or how similar two items are (so that you place similar items in the same set)? (Examples would be assigning customers to their closest service center, or grouping objects of similar colors.)

If this sounds like the case, it may be a clustering problem; one possible algorithm, not difficult to implement, could be this one. (Or, for a clearer explanation that Wikipedia, see here.)

 

[CellCoree]

for your question! There are several different algorithms that could be used to partition n elements into k sets. One possible approach is to use a greedy algorithm, where you start by placing the first element in the first set, the second element in the second set, and so on until you have placed k elements. Then, you go back to the first set and continue placing elements until all n elements have been distributed among the k sets. This approach will result in sets with roughly equal numbers of elements, but it may not always be the most efficient or optimal solution.

Another approach is to use a recursive algorithm, where you divide the n elements into smaller groups and then assign those groups to the k sets. This approach may be more efficient, but it may also require more computational resources.

A mathematical expression for this problem could be written as:

n / k = x

Where n is the total number of elements, k is the number of sets, and x is the number of elements in each set. This expression would give you the number of elements to place in each set, but it does not take into account the need for equal distribution or any other constraints.

Ultimately, the best algorithm for this problem will depend on the specific constraints and objectives of your project. I suggest researching different partitioning algorithms and selecting one that best fits your needs. Good luck!