Number of Subarrays With AND Value of K

Problem Description

Given an array of integers nums and an integer k, return the number of subarrays of nums where the bitwise AND of the elements of the subarray equals k.

Key Insights

• The AND operation between numbers results in bits being set to 1 only if both corresponding bits are 1.
• A subarray's AND can only equal k if every element in that subarray has the bits set that are present in k.
• The problem can be approached by iterating through the array and checking all possible subarrays while maintaining the current AND value.
• Efficient pruning of search space is possible: if the current AND value falls below k, further extensions of the subarray will not yield valid subarrays.

Space and Time Complexity

Time Complexity: O(n^2) in the worst case, but optimized checks can lead to better performance in practice.
Space Complexity: O(1) since we're only using a few variables to maintain state.

Solution

To solve this problem, we will use a brute-force approach optimized with early stopping. We will iterate through each starting index of the subarray, calculate the AND value progressively, and track how many subarrays yield the desired AND value of k.

We can utilize a nested loop where the outer loop picks the starting index and the inner loop extends the subarray until either the AND value equals k or decreases below k.

Code Solutions