B-Tree Node Structure

Write a C program that defines and prints a B-tree node structure.

Requirements:

• Define MAX_KEYS as 3 (for demonstration; real databases use much larger)
• Define a BTreeNode struct with:
  • int keys[MAX_KEYS]
  • int values[MAX_KEYS]
  • struct BTreeNode* children[MAX_KEYS + 1]
  • int num_keys
  • int is_leaf
• Implement create_node() that allocates and initializes a node
• Implement print_node() that shows:
  • Whether the node is a leaf or internal
  • All keys and values
  • Number of children (if internal)
• Create and print three example nodes:
  • Root (internal): keys=[10, 20], values=[100, 200], children=[leaf1, leaf2, leaf3]
  • Leaf1: keys=[1, 5, 8], values=[10, 50, 80], is_leaf=1
  • Leaf2: keys=[12, 15, 18], values=[120, 150, 180], is_leaf=1
  • Leaf3: keys=[25, 30], values=[250, 300], is_leaf=1
• Print the tree structure showing parent-child relationships
• Calculate and print the maximum number of keys a tree of height 2 can hold with MAX_KEYS=3
• Include a note about why real databases use larger MAX_KEYS