You are asked to solve two coding problems. ### Problem 1: Find the Minimum Constant Processing Speed You are given an array `piles`, where `piles[i]` is the number of items in the `i`-th pile, and an integer `h`, the maximum number of hours available. Each hour, you may choose exactly one non-empty pile and process up to `k` items from that pile. If the pile has fewer than `k` items remaining, you finish that pile during the hour and do not use the remaining capacity on another pile. Return the minimum positive integer speed `k` such that all piles can be processed within `h` hours. Example: ```text Input: piles = [3, 6, 7, 11], h = 8 Output: 4 ``` Explain both a brute-force approach and an optimized approach. For the optimized approach, analyze the time complexity carefully. ### Problem 2: Compute the Product of Two Large Non-Negative Integers You are given two non-negative integers `num1` and `num2` represented as decimal strings. The integers may be too large to fit into built-in numeric types. Return their product as a decimal string. Constraints: - `num1` and `num2` contain only digits `0-9`. - Neither string contains leading zeros unless the number is exactly `"0"`. - You may not directly convert the full strings into built-in integer types. Example: ```text Input: num1 = "123", num2 = "456" Output: "56088" ``` Write several test cases, including edge cases, and explain the algorithmic complexity.