1. Full length
A complete permutation uses every element exactly once.
if (path.length === nums.length)Typorithm · medium
Permutations
▷ Interactive algorithm labpermutationsbacktrackingorderingsused-arraychoose-explore-undo
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn Permutations
Backtracking
Build every ordering by trying each unused element at each position, marking and unmarking as you go.
Unlike subsets, order matters and every permutation uses all n elements.
A used array tracks which elements are already in the current path so none repeats.
Mark before recursing and unmark after — the choose/explore/undo shape extended with a used set.
Preparing algorithm lab…
01
Base case: path is full length.
02
Skip elements already used.
03
Mark, recurse, then unmark.
function permute(nums) {
const result = [];
function backtrack(path, used) {
if (path.length === nums.length) {
result.push([...path]);
return;
}
for (let i = 0; i < nums.length; i += 1) {
if (used[i]) continue;
used[i] = true;
path.push(nums[i]);
backtrack(path, used);
path.pop();
used[i] = false;
}
}
backtrack([], []);
return result;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Try every index
Order matters, so each position may use any unused element.
for (let i = 0; i < nums.length; i += 1)3. Skip used
A used element cannot appear twice in one permutation.
if (used[i]) continue4. Mark + choose
Mark the element used before recursing.
used[i] = true5. Unmark (undo)
Free the element again for sibling branches.
used[i] = falseA complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.