Thu Sep 26 15:00:00 UTC 2024: ## Efficiently Counting Subarrays with a Specific Mean in Java
A new algorithm has been developed to efficiently count contiguous subarrays within a given array that have a specific arithmetic mean. This problem, commonly encountered in data analysis, can be challenging for large datasets.
**The Challenge:**
Given an array X and an integer S, the goal is to find the number of subarrays within X whose arithmetic mean equals S. While a brute-force approach iterating through all possible subarrays works for small datasets, it becomes inefficient for larger arrays with up to 100,000 elements.
**The Solution:**
The solution leverages the concept of **prefix sums** and a **hash map**. This optimized approach significantly reduces the time complexity from O(n²) to O(n), making it suitable for handling large datasets efficiently.
**Key Features:**
* **Prefix sums:** Calculate the sum of all elements up to a specific index, allowing for faster subarray sum calculations.
* **Hash map:** Tracks the frequency of each prefix sum, enabling efficient counting of valid subarrays.
**Implementation:**
The `countSubarraysWithMean` method utilizes a hash map to store adjusted prefix sums. It iterates through the array, updating the running sum and calculating the required sum for each subarray. By checking the presence of the required sum in the hash map, the method efficiently determines the number of valid subarrays.
**Benefits:**
This optimized approach provides a practical solution for counting subarrays with a specific mean, even in large datasets. Its efficient time complexity ensures quick computation, making it valuable for real-world applications.
First Piper 