Longest Mountain in Array - Video Solutions

Problem Overview: You are given an integer array and need the length of the longest mountain. A mountain is a subarray where values strictly increase to a peak and then strictly decrease. The subarray must contain at least three elements and the peak cannot be at the ends.

The challenge is identifying valid peaks while ensuring the left side strictly rises and the right side strictly falls. Efficient solutions avoid recomputing slopes for every position and instead track increasing and decreasing segments using linear scans. This problem mainly relies on array traversal patterns from Array problems combined with pointer movement techniques from Two Pointers.

Approach 1: Two-Pass Approach with Peak Detection (O(n) time, O(n) space)

This approach precomputes how long the array increases and decreases at every index. First pass from left to right builds an up[] array where up[i] stores the length of the increasing slope ending at i. Second pass from right to left builds a down[] array where down[i] stores the length of the decreasing slope starting at i. A valid mountain peak exists where both values are greater than zero. The total mountain length becomes up[i] + down[i] + 1. Iterate through all indices and track the maximum.

This method is easy to reason about because each direction is handled independently. The tradeoff is extra memory for two arrays, but the logic stays simple and deterministic. The idea resembles prefix-style preprocessing seen in Dynamic Programming problems where partial results are reused.

Approach 2: Single-Pass Gradient Tracking (O(n) time, O(1) space)

This approach scans the array once while tracking the current uphill and downhill lengths. When the sequence is increasing, increment the up counter. When it switches to decreasing, increment the down. A valid mountain appears only if both counters are positive. If the slope resets (equal values or a new increasing segment after decreasing), reset the counters accordingly.

During each step, update the answer when both up > 0 and down > 0. The length of the current mountain is up + down + 1. This solution effectively performs inline Enumeration of slope segments while maintaining only constant state. Because it avoids auxiliary arrays, it is memory efficient and performs a clean linear traversal.

Recommended for interviews: Interviewers usually expect the single-pass gradient solution. It demonstrates that you recognize the slope pattern and can maintain state while scanning once. The two-pass approach still shows strong understanding of the problem structure and is often a stepping stone toward the optimal O(1) space solution.