This project implements a self-balancing binary search tree (Red-Black Tree) to ensure $O(\log n)$ operational complexity for dynamic sets. The implementation adheres to the following invariant properties:

• Each node is assigned a color attribute: Red or Black.
• The root and all NIL leaf nodes are Black.
• Red nodes must have Black children (No consecutive Red nodes).
• Black-height consistency: Every path from a node to descendant NIL nodes contains an identical number of Black nodes.

The system provides the following primitives:

• Insertion: Standard BST insertion followed by insertFixup (recoloring and rotations).
• Deletion: Node removal followed by deleteFixup to restore structural properties.
• Search: $O(\log n)$ value retrieval.
• Extrema: Retrieval and removal of minimum and maximum elements.
• Visualization: Formatted CLI output representing tree hierarchy and node metadata.

typedef enum { RED, BLACK } NodeColor;

typedef struct Node {
    int data;
    NodeColor color;
    struct Node *left, *right, *parent;
} Node;

typedef struct RBTree {
    Node *root;
    Node *NIL;
} RBTree;

The project is modularized into header, implementation, and driver files.

Compilation:

gcc -Wall -Wextra -o rbtree_system main.c rbtree.c

Execution:

./rbtree_system

The command-line interface (CLI) provides a structured menu for tree manipulation.

• Input: Integer-based data entry.
• Output: ANSI-coded terminal representation.
  • Red nodes: Displayed in Red.
  • Black nodes: Displayed in Blue/Black.
• Balancing: The system automatically triggers left/right rotations and recoloring upon any structural modification.

• Memory Management: Utilizes dynamic allocation (malloc) and requires manual deallocation for nodes.
• Sentinel Nodes: Employs a single NIL sentinel node to represent all leaf nodes, optimizing memory and simplifying boundary condition logic.