Persist B-Trees to Disk with Fixed-Size Pages

Write a C program that serializes and deserializes B-tree nodes to fixed-size pages.

Requirements:

• Define PAGE_SIZE as 128 bytes (small for demonstration)
• Define a page header struct: page_id (int), is_leaf (int), num_keys (int), reserved (padding to 16 bytes)
• Implement serialize_node(node, page_id, char* buffer) that writes:
  • Header at offset 0
  • Keys at offset 16 (4 bytes each)
  • Values at offset 16 + MAX_KEYS*4 (4 bytes each)
  • Child page IDs at offset 16 + MAX_KEYS*8 (4 bytes each, internal nodes only)
• Implement deserialize_node(char* buffer) that reconstructs a node
• Create a node: page_id=1, is_leaf=0, keys=[10, 20], values=[100, 200], children=[2, 3, 4]
• Serialize it to a byte buffer and print the buffer as hex dump (16 bytes per line)
• Deserialize the buffer back into a node
• Print the deserialized node and verify it matches the original
• Calculate and print the space utilization: bytes used / PAGE_SIZE
• Include a note about why real databases use 4KB-16KB pages