Find ith permutation in javascript

Question

Given an array arr of size n, and and index 0<=i<n! I want to return the i'th permutation.

I was able to write a method that gets all permutations:

function permute (arr) {
  var permutations = [];
  if (arr.length === 1) {
    return [ arr ];
  }

  for (var i = 0; i <  arr.length; i++) { 
    var subPerms = permute(arr.slice(0, i).concat(arr.slice(i + 1)));
    for (var j = 0; j < subPerms.length; j++) {
      subPerms[j].unshift(arr[i]);
      permutations.push(subPerms[j]);
    }
  }
  return permutations;
}

How do I trim it to get only one branch of the recursion ?

Answer 1

You could use the factorial of the array length as helper for getting the target permutation. Basically, this algorithm calculates the array indices upon which reassembles the result.

function getN(n, array) {
    var f,
        l = array.length,
        indices = [];

    array = array.slice();
    while (l--) {
        f = factorial(l);
        indices.push(Math.floor(n / f));
        n %= f;
    }
    return indices.map(function (i) {
        return array.splice(i, 1)[0];
    });
}

function factorial(num) {
    var result = 1;
    while (num) {
        result *= num;
        num--;
    }
    return result;
}

var i, l,
    array = [1, 2, 3, 4];

for (i = 0, l = factorial(array.length); i < l; i++) {
    console.log(i, '>', getN(i, array).join(' '));
}

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