Problem Statement

The set of combinations with repetitions is computed from a set,

S

{\displaystyle S}

(of cardinality

n

{\displaystyle n}

), and a size of resulting selection,

k

{\displaystyle k}

, by reporting the sets of cardinality

k

{\displaystyle k}

where each member of those sets is chosen from

S

{\displaystyle S}

. In the real world, it is about choosing sets where there is a “large” supply of each type of element and where the order of choice does not matter. For example: Note that both the order of items within a pair, and the order of the pairs given in the answer is not significant; the pairs represent multisets. Also note that doughnut can also be spelled donut.

Let's start with the solution:

combos = (arr, k) ->
  return [ [] ] if k == 0
  return [] if arr.length == 0
    
  combos_with_head = ([arr[0]].concat combo for combo in combos arr, k-1)
  combos_sans_head = combos arr[1...], k
  combos_with_head.concat combos_sans_head
  
arr = ['iced', 'jam', 'plain']
console.log "valid pairs from #{arr.join ','}:"
console.log combos arr, 2
console.log "#{combos([1..10], 3).length} ways to order 3 donuts given 10 types"