Maximum OR

Problem Description

You are given a 0-indexed integer array nums of length n and an integer k. In an operation, you can choose an element and multiply it by 2. Return the maximum possible value of nums[0] | nums[1] | ... | nums[n - 1] that can be obtained after applying the operation on nums at most k times. Note that a | b denotes the bitwise or between two integers a and b.

Key Insights

• The operation of multiplying an element by 2 effectively shifts its bits to the left, thus increasing its value in terms of bitwise representation.
• The bitwise OR operation accumulates bits set to 1 from all numbers, meaning that to maximize the OR value, we should focus on maximizing the values of the highest contributing elements in the array.
• Since k is small (maximum of 15), we can afford to try all combinations of applying the operation up to k times on different elements.

Space and Time Complexity

Time Complexity: O(n * k)
Space Complexity: O(1)

Solution

To solve this problem, we can iterate through each element in the nums array and for each element, we will consider applying the multiplication operation up to k times. For each application, we will calculate the new potential value of the array and compute the OR value for that configuration. The maximum OR value encountered during these iterations will be our result. We will use a greedy approach to focus on the highest values that contribute the most to the OR operation.

Code Solutions