Count the subarrays whose center satisfies the problem’s balancing condition.
Problem
Given an integer array, count how many subarrays are centered according to the condition described in the original problem.
A subarray is any contiguous slice of the array. Your task is to examine all possible subarrays and return the number that satisfy the centered-subarray property.
Because the exact centered condition can often be expressed by comparing values symmetrically around a middle point, efficient solutions typically rely on prefix-style aggregation or counting relationships between positions rather than checking every subarray naively.
Goal
Return the total number of valid centered subarrays.
Input Format
- An integer array
nums. - The exact centered condition is defined over contiguous subarrays of
nums.
Output Format
- Return a single integer: the number of centered subarrays.
Constraints
- The array contains a finite number of integers.
- Solve efficiently enough to avoid enumerating every subarray in the worst case.
Example 1
Input
nums = [1, 2, 1]
Output
1
Explanation
The whole array forms one centered subarray, while the shorter subarrays do not satisfy the centered condition.
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