Permutation of array and its subsets with repetition

repeated-permutations-with-subsets.js

// Note: this uses generators exclusively to avoid blowing up your RAM - 10-item
// arrays will produce about 11 billion entries. You can use
// `repeatedPermutationWithSubsetsCount` with the length to see how many items
// will be produced.
function *permRep(array, data, index) {
    if (index === data.length) {
        yield data.slice()
    } else {
        for (let i = 0; i < array.length; i++) {
            data[index] = array[i]
            yield* permRep(array, data, index + 1)
        }
    }
}

function *repeatedPermutationWithSubsets(array) {
    const data = []

    for (let i = 0; i < array.length; i++) {
        yield* permRep(array, data, 0)
        data.push(undefined)
    }

    yield* permRep(array, data, 0)
}

// Note: 
//            l+1
//  l   k    l    - 1
//  ∑  l  = ---------- , where l = `length`
// k=0        l - 1
function repeatedPermutationWithSubsetsCount(length) {
    return (Math.pow(length, length + 1) - 1) / (length - 1)
}