| name | recursion-backtracking |
| description | Generate all valid arrangements using backtracking with pruning. Use when solving permutations, combinations, subsets, N-queens, sudoku, or constraint satisfaction problems. |
| topic | Backtracking |
| token_cost | 100 |
| related | ["dynamic-programming","dfs-vs-bfs"] |
| keywords | ["permutation","combination","subset","backtrack","constraint","generate","valid","recursive","pruning","n-queens","sudoku","exhaustive","all","solutions","choose","pick","arrangement","password","sequence"] |
When to use
Use backtracking for constraint satisfaction and combinatorial generation: permutations, combinations, subsets, N-queens, sudoku, valid arrangements.
Rules
- Pattern: make a choice, recurse, undo the choice (backtrack)
- Prune early — skip branches that already violate constraints to avoid exploring dead ends
- For subsets: at each element, choose to include or exclude it (2^n total)
- For permutations: choose each unused element at each position (n! total)
- ALWAYS pass state by reference and undo mutations rather than copying
- NEVER copy state — it's wasteful and slow
- If the problem says "generate all" or "find all valid," backtracking is usually the right approach
Complexity
Subsets: 2^n. Permutations: n!.
Example
Subsets of [1,2,3]: at each element, branch include/exclude. def solve(i): if i==n: yield list(path); return; path.append(nums[i]); solve(i+1); path.pop(); solve(i+1).
