LeetCode #3370 — EASY

Smallest Number With All Set Bits

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

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The Problem

Problem Statement

You are given a positive number n.

Return the smallest number x greater than or equal to n, such that the binary representation of x contains only set bits

Example 1:

Input: n = 5

Output: 7

Explanation:

The binary representation of 7 is "111".

Example 2:

Input: n = 10

Output: 15

Explanation:

The binary representation of 15 is "1111".

Example 3:

Input: n = 3

Output: 3

Explanation:

The binary representation of 3 is "11".

Constraints:

  • 1 <= n <= 1000
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: You are given a positive number n. Return the smallest number x greater than or equal to n, such that the binary representation of x contains only set bits

Baseline thinking

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

Pattern signal: Math · Bit Manipulation

Example 1

5

Example 2

10

Example 3

3

Related Problems

  • Minimum Number of K Consecutive Bit Flips (minimum-number-of-k-consecutive-bit-flips)
  • Minimum Bit Flips to Convert Number (minimum-bit-flips-to-convert-number)
  • Find Sum of Array Product of Magical Sequences (find-sum-of-array-product-of-magical-sequences)
Step 02

Core Insight

What unlocks the optimal approach

  • Find the strictly greater power of 2, and subtract 1 from it.
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 #3370: Smallest Number With All Set Bits
class Solution {
    public int smallestNumber(int n) {
        int x = 1;
        while (x - 1 < n) {
            x <<= 1;
        }
        return x - 1;
    }
}
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(log n)
Space
O(1)

Approach Breakdown

SORT + SCAN
O(n log n) time
O(n) space

Sort the array in O(n log n), then scan for the missing or unique element by comparing adjacent pairs. Sorting requires O(n) auxiliary space (or O(1) with in-place sort but O(n log n) time remains). The sort step dominates.

BIT MANIPULATION
O(n) time
O(1) space

Bitwise operations (AND, OR, XOR, shifts) are O(1) per operation on fixed-width integers. A single pass through the input with bit operations gives O(n) time. The key insight: XOR of a number with itself is 0, which eliminates duplicates without extra space.

Shortcut: Bit operations are O(1). XOR cancels duplicates. Single pass → O(n) time, O(1) space.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.