How do you solve Smallest Number With All Set Bits on LeetCode?

Smallest Number With All Set Bits (LeetCode #3370) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: The smallest number with all set bits is always of the form (2^k - 1).

What is the time complexity of Smallest Number With All Set Bits?

The optimal solution for Smallest Number With All Set Bits runs in O(log n) time and uses O(1) space. The time complexity is O(log n) because we are doubling the power of 2 until we reach or exceed n, which is logarithmic in nature.

What is the brute force solution for Smallest Number With All Set Bits?

The brute force approach for Smallest Number With All Set Bits is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks each number starting from n and finds the first number that has all bits set. This is simple but inefficient for larger values. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Smallest Number With All Set Bits?

Smallest Number With All Set Bits uses the following concepts: Math, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Mathematical Properties.

What are the interview tips for Smallest Number With All Set Bits?

Always start with a brute-force approach to understand the problem better before optimizing. Think about how binary representations work and how they relate to powers of 2. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Smallest Number With All Set Bits?

Students often forget that the binary representation of numbers with all set bits is a series of 1s, which can be derived from powers of 2. Some may not realize that they can use bit manipulation to find the next power of 2 efficiently.

#3370

Smallest Number With All Set Bits

Easy

MathBit ManipulationBit ManipulationMathematical Properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log n)
Space	O(1)	O(1)

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Intuition

Time O(log n)Space O(1)

The optimal approach leverages the fact that the smallest number with all set bits is always of the form (2^k - 1). We find the next power of 2 greater than or equal to n and subtract 1.

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Algorithm

2 steps

1Step 1: Find the smallest power of 2 that is greater than or equal to n.
2Step 2: Subtract 1 from that power of 2 to get the result.

solution.py7 lines

1# Full working Python code
2
3def smallest_number_with_all_set_bits(n):
4    power = 1
5    while power < n:
6        power <<= 1
7    return power - 1

ℹ

Complexity note: The time complexity is O(log n) because we are doubling the power of 2 until we reach or exceed n, which is logarithmic in nature.

1The smallest number with all set bits is always of the form (2^k - 1).
2Finding the next power of 2 can be done efficiently using bit manipulation.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.