Code Question 1: Optimizing AWS Server Scaling
AWS provides scalable systems. A set of n servers are used for horizontally scaling an application. The goal is to have the computational power of the servers in non-decreasing order. To do so, you can increase the computational power of each server in any contiguous segment by x. Choose the values of x such that after the computational powers are in non-decreasing order, the sum of the x values is minimum.
Example
There are n = 5 servers and their computational power = [3, 4, 1, 6, 2].
Add 3 units to the subarray (2, 4) and 4 units to the subarray (4, 4). The final arrangement of the servers is: [3, 4, 4, 9, 9]. The answer is 3 + 4 = 7.
Code Question 2：Amazon Cart Management
As an aspiring developer at Amazon, you are building a prototype for a cart management service. There is an array of integers, items, that represents the item ids present in the cart initially. Given an array of q integers, query, your service must perform as follows. Each integer is an item id to be added to or removed from the cart.
- If the query integer is positive, add the integer representing an item id to the back of the cart.
- If the integer is negative, remove the first occurrence of the integer from the cart.
Report an array that represents the final cart after processing all the queries. It is guaranteed that the final cart is non-empty and the integers in the queries are not equal to 0.
Example
For example, initially, there are n = 5 items in the cart represented as cart = [1, 2, 1, 2, 1] and queries = [-1, -1, 3, 4, -3].
| Query | Task | Cart |
|---|---|---|
| -1 | Delete first 1 from cart | [2, 1, 2, 1] |
| -1 | Delete first 1 from cart | [2, 2, 1] |
| 3 | Append 3 to cart | [2, 2, 1, 3] |
| 4 | Append 4 to cart | [2, 2, 1, 3, 4] |
| -3 | Delete first 3 from cart | [2, 2, 1, 4] |
Conclusion
These two algorithmic problems highlight the importance of efficient data manipulation and optimization in real-world applications like server scaling and cart management. By understanding and applying the right algorithms, we can ensure optimal performance and user experience.
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