Solution: Binary Watch

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:

• $0 \leq$ enabled $\leq 10$

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 $10$ possible LED positions ($4$ for hours and $6$ for minutes), we recursively try each position, updating the values for hours and minutes based on which LED is turned on. We check whether the time is valid once the required LEDs are turned on. If it is valid, the time is stored. After each recursive step, we backtracked by undoing the previous changes, allowing us to explore other possible combinations of LEDs turned on.

Using the above intuition, we create a recursive function, BinaryWatchRec, to try all possible configurations of LEDs being turned on. We implement the recursive function as follows:

1. The parameters that BinaryWatchRec takes are as follows:

   1. position: Tracks the current LED position (from $0$ to $9$ ...