B-Tree Insertion with Node Splitting

Write a C program that implements B-tree insertion with node splitting.

Requirements:

• Use MAX_KEYS=3 (so split when a node has 4 keys temporarily)
• Implement btree_insert(root, key, value) that inserts a key-value pair
• Implement split_child(parent, child_index) that splits a full child
• When inserting into a full root, create a new root and split the old root
• Start with an empty tree and insert these keys in order: 10, 20, 5, 6, 12, 30, 7, 17
• After each insertion that causes a split, print "SPLIT: promoted key X"
• After all insertions, print the tree level by level showing keys in each node
• Verify that all leaves are at the same depth
• Count and print the total number of nodes and the tree height
• Test searching for a few keys to verify the tree is correct