File: binary-watch/solution.py

Date: 2026-06-06

Time: 15:27

binary-watch/solution.py

Purpose

This file solves LeetCode 401 — Binary Watch. A binary watch has 4 LEDs for hours (0–11) and 6 LEDs for minutes (0–59). Given a number of lit LEDs, return all valid times the watch could display. It's the single source of the readBinaryWatch function for this problem directory.

Key Components

readBinaryWatch(turnedOn: int) -> list[str] — The only public function. Takes the count of lit LEDs and returns all valid time strings in "h:mm" format (no leading zero on hours, zero-padded minutes).

Patterns

Brute-force enumeration with bit-counting filter. Rather than generating combinations of LED positions across hour/minute partitions, the solution iterates every possible (h, m) pair and keeps only those whose total popcount matches turnedOn. This is the canonical "count bits" approach for this problem — simple, correct, and fast enough given the tiny search space (12 × 60 = 720 candidates).

The entire function is a single list comprehension — no intermediate state, no mutation.

Dependencies

Imports: None. Uses only builtins (bin, range, f-strings).

Imported by: binary-watch/testsolution.py directly. The "Imported By" list in the prompt is misleading — those are all test files for *other* problems; they don't actually import this module. Only binary-watch/testsolution.py exercises this code.

Flow

1. Outer loop: h iterates 0–11 (valid hours).

2. Inner loop: m iterates 0–59 (valid minutes).

3. Filter: bin(h).count("1") + bin(m).count("1") == turnedOn — counts set bits in both values, keeps the pair only if the total equals the input.

4. Format: f"{h}:{m:02d}" — hour with no padding, minute zero-padded to 2 digits.

The result order is deterministic: hours ascending, minutes ascending within each hour (Python's range guarantees this).

Invariants

• Hours are always in [0, 11], minutes in [0, 59] — enforced by the range bounds, not by explicit validation.
• Output format is always "h:mm" — the f-string's :02d ensures two-digit minutes; hours are naturally unpadded.
• The function never raises for any turnedOn value — if turnedOn exceeds the maximum possible set bits (10), the comprehension simply yields an empty list.

Error Handling

None. Invalid inputs (negative values, values > 10) silently return an empty list because no (h, m) pair can satisfy the bit-count condition. This matches LeetCode's constraint that 0 <= turnedOn <= 10.