POTD_12_OCT_2024_TwoSmallestsInEverySubarray

[Avnee29]

📝 Description

Given an array of integers arr, the task is to find and return the maximum sum of the smallest and second smallest element among all possible subarrays of size greater than one. If it is not possible, then return -1.

💡 Enhancement / Feature Request (if applicable)

Why It's Useful
Finding the maximum sum of the smallest and second smallest elements in subarrays is useful in various applications such as:

Data Analysis: Understanding the distribution and relationships of values in datasets.
Algorithm Optimization: Enhancing sorting or searching algorithms by focusing on key elements.
Competitive Programming: Addressing complex problem-solving scenarios efficiently.
How It Should Work
Iterate through Subarrays: For each possible subarray of size greater than one, identify the smallest and second smallest elements.
Calculate Sums: Compute the sum of these two elements.
Track Maximum Sum: Keep track of the maximum sum found across all subarrays.
Return Result: If at least one valid subarray is found, return the maximum sum; otherwise, return -1 if no valid subarrays exist.

🌐 Additional Context

Complexity: A brute force approach to generate all subarrays and calculate sums has a time complexity of
𝑂(𝑛^3)(where 𝑛 is the size of the array), which may be inefficient for large arrays.)
Optimized Approach: Consider using a sliding window technique or maintaining a priority queue to efficiently find the two smallest elements in each subarray, potentially reducing the time complexity to
𝑂(𝑛^2)

Edge Cases: Ensure to handle cases where the array has fewer than two elements, as valid subarrays of size greater than one wouldn't exist, leading to a return value of -1.
This problem encourages efficient data handling and can serve as a stepping stone to more advanced algorithmic techniques.

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