3209. Number of Subarrays With AND Value of K
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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.
Example 1:
Input: nums = [1,1,1], k = 1
Output: 6
Explanation:
All subarrays contain only 1's.
Example 2:
Input: nums = [1,1,2], k = 1
Output: 3
Explanation:
Subarrays having an AND value of 1 are: [1,1,2], [1,1,2], [1,1,2].
Example 3:
Input: nums = [1,2,3], k = 2
Output: 2
Explanation:
Subarrays having an AND value of 2 are: [1,2,3], [1,2,3].
Constraints:
1 <= nums.length <= 1050 <= nums[i], k <= 109
Hints
Hint 1
Let’s say we want to count the number of pairs
(l, r) such that nums[l] & nums[l + 1] & … & nums[r] == k.Hint 2
Fix the left index
l.Hint 3
Note that if you increase
r for a fixed l, then the AND value of the subarray either decreases or remains unchanged.Hint 4
Therefore, consider using binary search.
Hint 5
To calculate the AND value of a subarray, use sparse tables.