Is Smallest Number With All Set Bits easy or hard?

Smallest Number With All Set Bits is classified as an Easy problem. The key insight is recognizing that valid answers follow the binary pattern 2^k - 1, which makes the optimal solution a short O(1) bit manipulation calculation.

Smallest Number With All Set Bits Python/Java solution

In Python or Java, compute k based on the bit length of n and return (1 << k) - 1. Python provides n.bit_length() for this calculation, while Java can use Integer.SIZE - Integer.numberOfLeadingZeros(n) to determine the required shift.

How to solve Smallest Number With All Set Bits in O(1)?

Use the property that numbers with all set bits equal 2^k - 1. Find the smallest k such that 2^k - 1 is greater than or equal to n, which can be derived from the bit length of n or using ceil(log2(n + 1)). Then return (1 << k) - 1.

What is the best approach for Smallest Number With All Set Bits?

The most efficient approach uses bit manipulation and the observation that numbers with all bits set follow the pattern 2^k - 1. Compute k = ceil(log2(n + 1)) and return (1 << k) - 1. This runs in O(1) time and O(1) space because it directly constructs the result without iteration.

Is Smallest Number With All Set Bits asked at Google/Amazon/Meta?

This problem reflects common interview patterns around bit manipulation and binary number properties. Variations involving powers of two, bit masks, or numbers of the form 2^k - 1 appear in interviews at companies like Amazon, Google, and Meta.

What data structure is used in Smallest Number With All Set Bits?

No complex data structures are required. The solution relies on mathematical reasoning and bit manipulation operations such as bit shifts and bitwise AND checks.

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

The optimal bit manipulation solution runs in O(1) time and O(1) space because it calculates the answer using a simple formula. A brute-force incremental approach may take O(ans - n) time in the worst case since it checks numbers sequentially until it finds one with all bits set.

Description Hints 1 Solution Video 9:20

3370. Smallest Number With All Set Bits

Q: How to solve Smallest Number With All Set Bits in O(1)?

Use the property that numbers with all set bits equal 2^k - 1. Find the smallest k such that 2^k - 1 is greater than or equal to n, which can be derived from the bit length of n or using ceil(log2(n + 1)). Then return (1 << k) - 1.

Q: What is the best approach for Smallest Number With All Set Bits?

The most efficient approach uses bit manipulation and the observation that numbers with all bits set follow the pattern 2^k - 1. Compute k = ceil(log2(n + 1)) and return (1 << k) - 1. This runs in O(1) time and O(1) space because it directly constructs the result without iteration.

Q: Is Smallest Number With All Set Bits asked at Google/Amazon/Meta?

This problem reflects common interview patterns around bit manipulation and binary number properties. Variations involving powers of two, bit masks, or numbers of the form 2^k - 1 appear in interviews at companies like Amazon, Google, and Meta.

Q: What data structure is used in Smallest Number With All Set Bits?

No complex data structures are required. The solution relies on mathematical reasoning and bit manipulation operations such as bit shifts and bitwise AND checks.

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

The optimal bit manipulation solution runs in O(1) time and O(1) space because it calculates the answer using a simple formula. A brute-force incremental approach may take O(ans - n) time in the worst case since it checks numbers sequentially until it finds one with all bits set.

Easy80.4% acceptance3 companies

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

Asked at 3 companies

Google Amazon Microsoft

Topics

Bit Manipulation Math

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Hint 1

Find the strictly greater power of 2, and subtract 1 from it.

9:20

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3370. Smallest Number With All Set Bits

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