Find the Maximum Sequence Value of Array - Video Solutions

Problem Overview: You receive an integer array and must construct a sequence that maximizes a specific value derived from bitwise operations across selected elements. The challenge is choosing elements in the right order or partition so the resulting bitwise combination produces the largest possible value.

Approach 1: Sorting and Partitioning (Time: O(n log n), Space: O(1) or O(n))

This strategy sorts the array to prioritize numbers with higher bit contribution. After sorting, you partition the array into candidate segments and evaluate the sequence value produced by combining elements from each partition. Sorting helps cluster numbers with strong high‑bit influence, which tends to increase the resulting bitwise expression. The algorithm iterates through valid split points and calculates the resulting sequence value using efficient bitwise OR or XOR operations. This method works well when the optimal sequence is dominated by elements containing larger high bits.

The core idea relies on understanding how bit patterns interact. Numbers with overlapping high bits amplify the result when combined, so grouping them strategically increases the sequence value. While sorting adds an O(n log n) cost, the subsequent evaluation step is linear.

Approach 2: Greedy Selection with Sliding Window (Time: O(n), Space: O(1))

A more efficient method scans the array while dynamically maintaining a candidate sequence. Using a sliding window, you track the current set of elements contributing to the sequence value and update the running bitwise state as elements enter or leave the window. The greedy insight is that if a new element improves the bitwise outcome, it should be included while less useful elements can be discarded.

The window maintains the best possible sequence under the current constraints, updating the computed value using constant‑time bit operations. Because each element is processed at most twice (entering and leaving the window), the total runtime remains linear. This technique is common in problems mixing array traversal with incremental state updates.

The algorithm benefits from properties of bit manipulation. Bitwise operations are associative and cheap to compute, allowing the running value to be updated efficiently without recomputing the entire sequence each time.

Recommended for interviews: Interviewers typically expect the optimized greedy or dynamic approach because it shows you understand how bitwise contributions accumulate and how to maintain the optimal candidate while scanning the array. A sorting‑based method demonstrates the core intuition, but the linear sliding window solution better reflects mastery of dynamic programming style state tracking and greedy optimization.