Backtracking & Subsets

Every backtracking problem is choose → explore → un-choose. The only thing that varies is the loop's start index and the pruning condition.

Build every ordering of distinct elements by fixing one position at a time and exploring choices, then undo (backtrack).

Choose exactly k distinct numbers from 1..n without caring about order — build increasing sequences and prune when too few numbers remain.

Build sums with unlimited reuse of each candidate; after including candidates[i], recurse with i (not i+1) so the same value can be picked again.

Only extend strings that can still become valid: add '(' while open < n, add ')' while close < open.