LeetCode #401 — EASY

Binary Watch

Build confidence with an intuition-first walkthrough focused on backtracking fundamentals.

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The Problem

Problem Statement

A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right.

  • For example, the below binary watch reads "4:51".

Given an integer turnedOn which represents the number of LEDs that are currently on (ignoring the PM), return all possible times the watch could represent. You may return the answer in any order.

The hour must not contain a leading zero.

  • For example, "01:00" is not valid. It should be "1:00".

The minute must consist of two digits and may contain a leading zero.

  • For example, "10:2" is not valid. It should be "10:02".

Example 1:

Input: turnedOn = 1
Output: ["0:01","0:02","0:04","0:08","0:16","0:32","1:00","2:00","4:00","8:00"]

Example 2:

Input: turnedOn = 9
Output: []

Constraints:

  • 0 <= turnedOn <= 10
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right. For example, the below binary watch reads "4:51". Given an integer turnedOn which represents the number of LEDs that are currently on (ignoring the PM), return all possible times the watch could represent. You may return the answer in any order. The hour must not contain a leading zero. For example, "01:00" is not valid. It should be "1:00". The minute must consist of two digits and may contain a leading zero. For example, "10:2" is not valid. It should be "10:02".

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Backtracking · Bit Manipulation

Example 1

1

Example 2

9

Related Problems

  • Letter Combinations of a Phone Number (letter-combinations-of-a-phone-number)
  • Number of 1 Bits (number-of-1-bits)
Step 02

Core Insight

What unlocks the optimal approach

  • Simplify by seeking for solutions that involve comparing bit counts.
  • Consider calculating all possible times for comparison purposes.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #401: Binary Watch
class Solution {
    public List<String> readBinaryWatch(int turnedOn) {
        List<String> ans = new ArrayList<>();
        for (int i = 0; i < 12; ++i) {
            for (int j = 0; j < 60; ++j) {
                if (Integer.bitCount(i) + Integer.bitCount(j) == turnedOn) {
                    ans.add(String.format("%d:%02d", i, j));
                }
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(1)
Space
O(1)

Approach Breakdown

EXHAUSTIVE
O(nⁿ) time
O(n) space

Generate every possible combination without any filtering. At each of n positions we choose from up to n options, giving nⁿ total candidates. Each candidate takes O(n) to validate. No pruning means we waste time on clearly invalid partial solutions.

BACKTRACKING + PRUNING
O(n!) time
O(n) space

Backtracking explores a decision tree, but prunes branches that violate constraints early. Worst case is still factorial or exponential, but pruning dramatically reduces the constant factor in practice. Space is the recursion depth (usually O(n) for n-level decisions).

Shortcut: Backtracking time = size of the pruned search tree. Focus on proving your pruning eliminates most branches.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Missing undo step on backtrack

Wrong move: Mutable state leaks between branches.

Usually fails on: Later branches inherit selections from earlier branches.

Fix: Always revert state changes immediately after recursive call.