Find Subarray With Bitwise OR Closest to K

Find Subarray With Bitwise OR Closest to K

What is this problem about?

The Find Subarray With Bitwise OR Closest to K interview question is a challenging optimization problem. You are given an array of integers and a target value k. Your goal is to find a contiguous subarray such that the bitwise OR of all its elements is as close to k as possible. You need to return the minimum absolute difference $| ext{OR\_sum} - k |$.

Why is this asked in interviews?

Salesforce and other top-tier companies ask the Find Subarray With Bitwise OR Closest to K coding problem to test a candidate's deep understanding of bitwise operations and efficient range queries. Bitwise OR is monotonic (adding elements to a subarray never decreases the OR sum), which opens the door for optimization. This problem evaluations your ability to use Bit Manipulation interview patterns and efficient search techniques.

Algorithmic pattern used

This problem relies on the Monotonicity of Bitwise OR and can be solved using a Sliding Window or a Logarithmic Set approach.

1. Sliding Window: Because the OR sum only increases as the window expands, you can use two pointers to maintain a window whose OR sum is close to k.
2. State Management: To "shrink" the window (remove an element from the OR sum), you need to keep track of the count of set bits at each of the 32 bit positions.
3. Optimization: Another approach is to maintain a set of all possible OR sums ending at the current index. Because OR sums only change at most 30 times (for a 32-bit integer), this set stays small ($O(\log (\max A))$).

Example explanation

Array: [1, 2, 4], $k=3$.

• Subarray [1]: OR = 1. $|1-3|=2$.
• Subarray [1, 2]: OR = 3. $|3-3|=0$.
• Subarray [2, 4]: OR = 6. $|6-3|=3$. The minimum difference is 0.

Common mistakes candidates make

• Brute Force: Checking all $O(N^2)$ subarrays, which is too slow for large inputs ($N = 10^5$).
• Removing OR: Trying to "undo" an OR operation using XOR or subtraction. Bitwise OR is not reversible; you must track bit counts to remove an element from a range OR.
• Ignoring 0: Forgetting that the bitwise OR can be exactly k.

Interview preparation tip

Master the "Logarithmic Property of Bitwise Operations." In any array, there are only $O(N \log (\max A))$ unique bitwise OR results across all subarrays. This insight is the key to solving many "Hard" level Bit Manipulation interview pattern questions.