Find max min-plus-max over all subarrays
Problem Statement
You are given an array arr of n integers.
A subarray is defined as a contiguous non-empty segment of the array. For any subarray arr[l..r] (0-indexed), we define a value X(l, r) as:
X(l, r) = min(arr[l..r]) + max(arr[l..r])
Your task is to compute the maximum possible value of X(l, r) over all possible subarrays of arr.
Input
- An integer
n, representing the length of the array. - An array
arrofnintegers. These integers can be positive, zero, or negative.
Output
- A single integer: the maximum value of
min(subarray) + max(subarray)found across all non-empty contiguous subarrays.
Requirements
- Describe an efficient algorithm and analyze its time and space complexity.
- The algorithm should aim for better than O(n^2) time complexity, especially for large
n(e.g.,nup to approximately2 * 10^5).
AI interview prep
Core dilemma
The central engineering conflict is identifying the subtle mathematical property that allows for an O(N) solution, avoiding the brute-force O(N^2) iteration over all subarrays, which is too slow for the given constraints. It's about recognizing that the maximum `min(S) + max(S)` is always achieved by a subarray of length 1 or 2.
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Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Find max min-plus-max over all subarrays
Problem Statement
You are given an array arr of n integers.
A subarray is defined as a contiguous non-empty segment of the array. For any subarray arr[l..r] (0-indexed), we define a value X(l, r) as:
X(l, r) = min(arr[l..r]) + max(arr[l..r])
Your task is to compute the maximum possible value of X(l, r) over all possible subarrays of arr.
Input
- An integer
n, representing the length of the array. - An array
arrofnintegers. These integers can be positive, zero, or negative.
Output
- A single integer: the maximum value of
min(subarray) + max(subarray)found across all non-empty contiguous subarrays.
Requirements
- Describe an efficient algorithm and analyze its time and space complexity.
- The algorithm should aim for better than O(n^2) time complexity, especially for large
n(e.g.,nup to approximately2 * 10^5).