Fullstack Developer

There are n mountains in a row, with their heights given by an array h. You are planning a hang gliding route and want to find the longest possible trip, measured by the number of mountains visited.

A trip consists of a sequence of glides. You can start your trip at any mountain. From a mountain a at index i, you can glide to a mountain b at index j if and only if:

Mountain a is strictly taller than mountain b (h[i] > h[j]).

All mountains physically located between a and b are also strictly shorter than mountain a.

A route can change direction. For example, a valid route could be starting at mountain i, gliding left to mountain j, and then gliding left again to mountain k. Another valid route could start at i, glide right to j, and then glide right again. A third valid route could involve a path that goes left from a peak and a path that goes right from the same peak.

Your task is to find the maximum number of distinct mountains that can be visited in a single continuous route.

You are given an array of n integers. Your task is to calculate a specific cost for each sliding window of k elements, from left to right.

The cost for a single window is defined as the minimum total cost to make all elements in that window equal. The cost to change an element is the absolute difference between its new value and its original value. The total cost is the sum of these individual costs.

Mathematical Insight: The cost sum(|xi - y|) for a set of numbers xi is minimized when y is the median of the set. Therefore, for each window, you must find its median and then calculate the sum of absolute differences of all elements from that median.

You need to return a list of these costs for each of the n-k+1 windows.

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