2261. K Divisible Elements Subarrays
Description
Given an integer array nums
and two integers k
and p
, return the number of distinct subarrays, which have at most k
elements that are divisible by p
.
Two arrays nums1
and nums2
are said to be distinct if:
- They are of different lengths, or
- There exists at least one index
i
wherenums1[i] != nums2[i]
.
A subarray is defined as a non-empty contiguous sequence of elements in an array.
Example 1:
Input: nums = [2,3,3,2,2], k = 2, p = 2 Output: 11 Explanation: The elements at indices 0, 3, and 4 are divisible by p = 2. The 11 distinct subarrays which have at most k = 2 elements divisible by 2 are: [2], [2,3], [2,3,3], [2,3,3,2], [3], [3,3], [3,3,2], [3,3,2,2], [3,2], [3,2,2], and [2,2]. Note that the subarrays [2] and [3] occur more than once in nums, but they should each be counted only once. The subarray [2,3,3,2,2] should not be counted because it has 3 elements that are divisible by 2.
Example 2:
Input: nums = [1,2,3,4], k = 4, p = 1 Output: 10 Explanation: All element of nums are divisible by p = 1. Also, every subarray of nums will have at most 4 elements that are divisible by 1. Since all subarrays are distinct, the total number of subarrays satisfying all the constraints is 10.
Constraints:
1 <= nums.length <= 200
1 <= nums[i], p <= 200
1 <= k <= nums.length
Follow up:
Can you solve this problem in O(n2) time complexity?
Solutions
Solution 1: Enumeration + String Hashing
We can enumerate the left endpoint $i$ of the subarray, and then enumerate the right endpoint $j$ in the range $[i, n)$. During the enumeration of the right endpoint, we use double hashing to store the hash value of the subarray into a set. Finally, we return the size of the set.
The time complexity is $O(n^2)$, and the space complexity is $O(n^2)$. Here, $n$ is the length of the array.
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