Implement a Simple Memory Allocator

Design and implement a simplified memory allocator with `malloc(size)` and `free(ptr)` for a fixed-size heap. Requirements: 1. The allocator manages a contiguous memory region, such as a byte array. 2. `malloc(size)` should return a pointer or offset to a block of at least `size` bytes, or fail if no suitable block exists. 3. `free(ptr)` should mark a previously allocated block as reusable. 4. Start with a simple first-fit implementation that linearly scans the heap or free list and chooses the first free block large enough to satisfy the request. 5. Support block splitting when a free block is larger than requested. 6. Discuss how to handle adjacent free blocks and reduce fragmentation. 7. Then propose an optimization using a best-fit strategy: choose the smallest free block that can satisfy the allocation request, using an appropriate ordered data structure such as a heap, balanced tree, or size-indexed free list. 8. Analyze the time complexity, space overhead, and trade-offs between first-fit and best-fit allocation.