Is Number of Centered Subarrays easy or hard?

Number of Centered Subarrays is generally rated Medium difficulty. The main challenge is recognizing that brute force enumeration is too slow and that the centered condition can be represented using a balance value and hash map lookups.

Number of Centered Subarrays Python/Java solution

The solution is typically implemented by iterating over each index as a center, maintaining a running balance for elements greater or smaller than that center, and storing balance frequencies in a hash map. The same algorithm translates directly across Python, Java, C++, Go, and TypeScript with identical O(n^2) time complexity.

How to solve Number of Centered Subarrays in O(n)?

Most implementations solve it in O(n^2) by enumerating each possible center and using a hash table to match balance values. Achieving O(n) for the fully general version is difficult because every element can potentially serve as a center. The hash-based enumeration method is typically considered optimal for this formulation.

What is the best approach for Number of Centered Subarrays?

The most practical approach uses hash table + enumeration. Fix each index as the potential center and track the balance between elements greater and smaller than the center while expanding the subarray. A hash map stores previously seen balances so complementary states can be matched quickly. This reduces repeated scanning and runs in O(n^2) time with O(n) space.

Is Number of Centered Subarrays asked at Google/Amazon/Meta?

Problems involving median-based subarrays and balance counting appear frequently in interviews at companies like Google, Amazon, and Meta. Variants often require counting subarrays where a particular element behaves like a median, which uses the same hash map and balance-difference technique.

What data structure is used in Number of Centered Subarrays?

The key data structure is a hash table (hash map). It stores frequency counts of balance values representing how many elements are greater or smaller than the chosen center. This allows constant-time lookups to determine whether a valid centered configuration exists.

What is the time complexity of Number of Centered Subarrays?

The optimized solution runs in O(n^2) time and O(n) space. Each index is treated as a center and the algorithm expands around it while updating a balance value. Hash table lookups allow constant-time matching of valid configurations, avoiding the O(n^3) brute force check.

3804. Number of Centered Subarrays - Practice Online

You are given an integer array nums.

A subarray of nums is called centered if the sum of its elements is equal to at least one element within that same subarray.

Return the number of centered subarrays of nums.

Example 1:

Input: nums = [-1,1,0]

Output: 5

Explanation:

All single-element subarrays ([-1], [1], [0]) are centered.
The subarray [1, 0] has a sum of 1, which is present in the subarray.
The subarray [-1, 1, 0] has a sum of 0, which is present in the subarray.
Thus, the answer is 5.

Example 2:

Input: nums = [2,-3]

Output: 2

Explanation:

Only single-element subarrays ([2], [-3]) are centered.

Constraints:

1 <= nums.length <= 500
-10⁵ <= nums[i] <= 10⁵