No — it’s not a queue pattern at all, and it’s not really a single pattern either. Let me clarify what’s actually going on, because “generate numbers from given digits” is a problem family, not a data-structure-driven pattern like the others in your notes.
Why it’s not queue
Queue/BFS patterns apply when you’re exploring a graph or grid level-by-level and order-of-discovery matters (shortest path, spreading, dependency order). “Generate numbers with given digits” problems are combinatorial generation — you’re building sequences digit-by-digit, and the real technique underneath is almost always backtracking/DFS, sometimes BFS if you specifically want them level-by-level (e.g., in increasing digit-count order), and occasionally math/counting (combinatorics) if you only need a count, not the actual numbers.
So the structure depends entirely on what the question actually asks:
| Variant | LC example | Real technique |
|---|---|---|
| Generate all valid combinations | Letter Combinations of a Phone Number (17) | Backtracking/DFS |
| Generate all numbers ≤ N with given digit set | Numbers At Most N Given Digit Set (902) | Digit DP / combinatorics |
| Count numbers with a property (no counting-out) | Count Numbers with Unique Digits (357) | Combinatorics/DP |
| Generate in increasing order (e.g. k-th smallest) | Ugly Number II (264), K-th Smallest in Lexicographical Order (440) | Heap or BFS-like level generation, or trie-DFS |
| Smallest/largest number after removals | Remove K Digits (402) | This is your monotonic stack, not this family at all |
Where the queue confusion probably comes from
There’s one genuine queue-based sub-case: generating numbers in strictly increasing order using a BFS-like multi-queue approach — e.g., Ugly Number II (264), where you maintain pointers/queues per prime factor and always emit the next-smallest candidate. That’s a real (if niche) pattern: “BFS-style incremental generation using multiplier queues.” It’s legitimate but low-frequency — I’d call it a minor sub-pattern under BFS, not deserving its own top-level category in your Queue note.
Recommendation for your PKM
Don’t add “generate numbers” as a queue pattern. Instead:
- If you’re prepping combinatorics/generation problems, that’s a separate note — “Backtracking / Combinatorial Generation” — sibling to Stack and Queue, not a subcategory of either.
- Add one line under your Queue note’s BFS section for the niche Ugly-Number-style case, since it does use queues legitimately:
### Minor sub-case: Multi-pointer/queue incremental generation
Generate values in sorted order by maintaining per-factor queues/pointers and always emitting the smallest next candidate.
- Ugly Number II (264), Super Ugly Number (313)Want me to draft the Backtracking/Generation note as its own topic, similar structure to Stack and Queue?