Permutations

Problem

Given an array nums of distinct integers, return every possible ordering of its elements. The orderings may be returned in any sequence, but each must appear exactly once.

• Up to 8 elements.
• Each value is between -20 and 20.
• All values are distinct.

Examples

• nums = [4, 5, 6] → [[4,5,6], [4,6,5], [5,4,6], [5,6,4], [6,4,5], [6,5,4]] in any order; 3! = 6 results.
• nums = [0, 8] → [[0,8], [8,0]].
• nums = [7] → [[7]].

Hints

1. Fix the element that goes first. How many ways are there to arrange the rest, and does that sub-problem look like the original?
2. Keep track of which elements are already placed so you never reuse one within the same ordering.
3. Backtracking with a used array (or in-place swapping); record the path when its length reaches n.