Construct the Minimum Bitwise Array I

Construct the Minimum Bitwise Array I

What is this problem about?

In the Construct the Minimum Bitwise Array I interview question, you are given an array of prime numbers nums. For each number nums[i], you need to find the smallest non-negative integer x such that x OR (x + 1) = nums[i]. If no such x exists, return -1. This version of the problem typically has small constraints, allowing for more straightforward searching.

Why is this asked in interviews?

This Construct the Minimum Bitwise Array I coding problem is a test of Bit Manipulation logic. It evaluates whether a candidate understands the properties of the OR operator and how incrementing a number (x + 1) affects its bit representation. It’s a great problem for testing mathematical curiosity and edge-case handling.

Algorithmic pattern used

This utilizes the Array, Bit Manipulation interview pattern.

• The operation x OR (x + 1) has a specific property: it effectively sets the rightmost zero bit of x to 1.
• For example, if x = 101 (binary 5), x+1 = 110 (binary 6). 101 OR 110 = 111 (binary 7).
• For the "Easy" version, you can simply iterate x from 0 up to nums[i] and check the condition.

Example explanation

Suppose nums[i] = 11.

1. Try x=0: 0 OR 1 = 1 != 11.
2. Try x=1: 1 OR 2 = 3 != 11.
3. ...
4. Try x=9: 1001 OR 1010 = 1011 (binary 11).
5. Success! Smallest x is 9. If nums[i] = 2, no such x exists (since 0 OR 1 = 1 and 1 OR 2 = 3).

Common mistakes candidates make

• Linear search on large numbers: While acceptable for small constraints, it's good to realize the bitwise pattern for later versions.
• Ignoring x=0: Forgetting that x can be 0.
• Incorrect OR logic: Misunderstanding how the carry-over in addition interacts with the OR bitmask.

Interview preparation tip

Always look for patterns in bitwise operations. x OR (x + 1) always results in a number that has all the bits of x plus the lowest unset bit.