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You are given a 0-indexed array of positive integers nums. A subarray of nums is called incremovable if nums becomes strictly increasing on removing the subarray. For example, the subarray [3, 4] is an incremovable subarray of [5, 3, 4, 6, 7] because removing this subarray changes the array [5, 3, 4, 6, 7] to [5, 6, 7] which is strictly increasing. Return the total number of *incremovable* subarrays of nums. Note that an empty array is considered strictly increasing. A subarray is a contiguous non-empty sequence of elements within an array. Example 1: Input: nums = [1,2,3,4] Output: 10 Explanation: The 10 incremovable subarrays are: [1], [2], [3], [4], [1,2], [2,3], [3,4], [1,2,3], [2,3,4], and [1,2,3,4], because on removing any one of these subarrays nums becomes strictly increasing. Note that you cannot select an empty subarray. Example 2: Input: nums = [6,5,7,8] Output: 7 Explanation: The 7 incremovable subarrays are: [5], [6], [5,7], [6,5], [5,7,8], [6,5,7] and [6,5,7,8]. It can be shown that there are only 7 incremovable subarrays in nums. Example 3: Input: nums = [8,7,6,6] Output: 3 Explanation: The 3 incremovable subarrays are: [8,7,6], [7,6,6], and [8,7,6,6]. Note that [8,7] is not an incremovable subarray because after removing [8,7] nums becomes [6,6], which is sorted in ascending order but not strictly increasing.

Apple

Let's delve into the fascinating world of computer systems. I'd like you to design a simplified operating system. Assume you're building this OS for a resource-constrained embedded system, like a smart thermostat or a simple microcontroller-based device. Your design should address the following key aspects: Memory Management: Describe your approach to memory allocation and deallocation. How would you prevent memory leaks and fragmentation in this environment? Would you use static allocation, dynamic allocation, or a combination of both? Explain your reasoning, giving specific examples of how your chosen methods would work in practice. Process/Task Scheduling: How would you schedule tasks to run on the processor? Would you opt for a preemptive or non-preemptive scheduler? What scheduling algorithm (e.g., Round Robin, Priority-based) would you use, and why? Consider the trade-offs between responsiveness, fairness, and overhead. Imagine you have three tasks: Task A (high priority, short bursts), Task B (medium priority, longer computation), and Task C (low priority, background task). How would your scheduler handle these tasks? Interrupt Handling: Explain how your OS would handle interrupts from hardware devices (e.g., a temperature sensor, a button press). How would you ensure that interrupt handlers are efficient and don't disrupt the normal operation of the system? Describe the steps involved in processing an interrupt, from the moment it occurs to the point where the interrupted task resumes execution. File System (Optional): If your embedded system requires persistent storage, outline a simple file system design. How would you organize files and directories? What data structures would you use to track file metadata (e.g., name, size, location)? How would you handle file creation, deletion, and reading/writing operations? Assume the storage medium is a small flash memory chip with limited write cycles. Inter-Process Communication (IPC): How would different tasks or processes communicate with each other within your OS? Would you use message queues, shared memory, or another mechanism? Explain the advantages and disadvantages of your chosen approach. For example, consider a scenario where one task needs to send sensor data to another task for processing. How would you implement this communication? Remember to justify your design choices based on the constraints of the embedded system, such as limited memory, processing power, and energy consumption. Aim for simplicity, efficiency, and reliability in your design. Your explanation should demonstrate a solid understanding of operating system principles and their practical application in a real-world scenario.

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