What is the memory management model in Java? Describe how it works, specifically focusing on the heap and stack memory. What are the differences between them and how does garbage collection fit into this model?

**LeetCode #75 - Sort Colors** \nBackground: You are given an array consisting of red, white, and blue, represented by 0, 1, and 2 respectively. Your task is to sort them in-place so that objects of the same color are adjacent, with the colors in the order red, white, and blue. \nProblem Statement: Implement a function `void sortColors(int[] nums)` that sorts the array in a single pass with O(n) time complexity and O(1) space complexity. \nExample 1: \nInput: nums = [2,0,2,1,1,0] \nOutput: [0,0,1,1,2,2] \nExplanation: The numbers are sorted in order where 0 represents red, 1 represents white, and 2 represents blue. \nExample 2: \nInput: nums = [2,0,1] \nOutput: [0,1,2] \nConstraints: `1 <= nums.length <= 300`, `nums[i]` is either 0, 1, or 2.

**Design a URL Shortener** \nBackground: A URL shortener takes a long URL and converts it into a shorter, unique URL that redirects to the original URL. This process makes sharing URLs easier, especially on platforms with character limits. \nProblem Statement: Design a URL shortening service with the following functionalities: `shorten(url: String): String` to shorten a URL and `retrieve(shortened: String): String` to retrieve the original URL. Focus on scalability, storage, and handle issues like collisions. \nConstraints: The service should support up to billions of URLs and provide low latency.