Contiguous Subarray with Largest Min + Max

A custom 30-minute coding question: given a positive integer array, find a contiguous subarray (length ≥ 2) maximizing `min + max`, return the sum. Requirements Given an array of n positive integers, find a contiguous subarray containing more than one number with the largest min + max. Return that sum. def largestMinMaxSum(nums: List[int]) -> int: ... Example: Input: [5, 12, 9, 6, 4] Output: 21 (subarray [12, 9], min=9 max=12, 9+12=21) Notes The trick is to realize that for any subarray of length ≥ 2, the answer reduces to picking any pair of indices (i, j) with i < j and computing min(nums[i..j]) + max(nums[i..j]). The largest sum is achieved by adjacent pairs: max(nums[i] + nums[i+1]) for all i. Why adjacency works: extending a subarray can only decrease min (never increase it) and increase max by at most as much as a fresh single new max. Pair-wise adjacent gives both min + max simultaneously without loss. Linear O(n) scan suffices; no need for a sliding window or segment tree. Common trap: candidates jump to two pointers or sliding window because of "contiguous subarray," but the structure of the cost function (min + max) makes the answer purely local. Be careful to clarify the "length ≥ 2" requirement up front — single-element subarrays trivially give 2 * nums[i] and change the answer. Preparation Practice noticing when "contiguous subarray" problems collapse to adjacent pairs — this is a recurring trick across interviews. Drill the one-pass scan; be able to write it in under 5 minutes with explicit tracking of both elements. Be ready to argue the correctness reduction crisply: "extending never helps, so two-element subarrays are sufficient."