Algorithm for computing partitions of a set of n elements in

var count = 0;
var people = ["A","B","C","D","E","F"];
var combinations = [];
var partitions = [];

example();
generate(people.splice(0), []);
for (let i = 0; i < combinations.length; ++i)
pretty_print(partitions[i]);

function pretty_print(v) {
  var message = "combination no " + (++count) + ": [ ";
  for (let i = 0; i < v.length; ++i) { message += v[i] + " "; }
  message += "]";
  alert(message);
}

function go(combination, offset, k) {
  if (k == 0) {
    combinations.push(combination.slice(0));
    return;
  }
  for (let i = offset; i <= people.length - k; ++i) {
    combination.push(people[i]);
    go(combination, i+1, k-1);
    combination.pop();
  }
}

function example() {
  var k = 3;

  go([], 0, k);
}

function generate(people, partition)
{
    if (people.length == 0)
    {
        partitions.push(partition.splice(0));
        return;
    }

    for (let i = 0; i < combinations.length; ++i)
    {
        var combination = combinations[i];
        partition.push(combination);
        var peopleCopy = people.splice(0);
        for (let j = 0; j < combination.length; ++j)
        {
            peopleCopy.splice(peopleCopy.indexOf(combination[j]), 1);
        }
        generate(peopleCopy, partition);
        for (let j = 0; j < combination.length; ++j)
        {
            partition.splice(partition.indexOf(combination[j]), 1);
        }
    }
}