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Grokking the Coding Interview Patterns in Python

Solution: Binary Watch

Explore how backtracking algorithms solve the binary watch problem by recursively turning on LEDs to represent hours and minutes. Understand the validation of time formats, recursive exploration of LED combinations, and the tradeoffs in time and space complexity to deepen your problem-solving skills in coding interviews.

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Statement

A binary watch has 4 LEDs for displaying hours (ranging from 0 to 11) and 6 for displaying minutes (ranging from 0 to 59). Each LED can be on (1) or off (0), with the least significant bit on the right. For example, the binary watch below reads “9:22.”

Given an integer enabled, which represents the number of LEDs currently turned on, return all possible times that the watch could display. You may return the answer in any order.

Note: Remember the following regarding leading zeros:

  • The hour cannot have a leading zero (e.g., “01:00” is invalid, it should be “1:00”).

  • The minute must be two digits and may include a leading zero (e.g., “10:2” is invalid, it should be “10:02”).

Constraints:

  • 0≤0 \leq enabled ≤10\leq 10

Solution

The core intuition behind solving this problem is to use backtracking to explore all possible configurations of the LEDs that can be turned on. Because there are ...