373 Advanced

373: Custom B-Tree Implementation

Functional Programming

Tutorial Video

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This video demonstrates the "373: Custom B-Tree Implementation" functional Rust example. Difficulty level: Advanced. Key concepts covered: Functional Programming. Database indexes, file system directory trees (NTFS, ext4), and key-value store storage engines (RocksDB, SQLite) all use B-trees as their core data structure. Key difference from OCaml: | Aspect | Rust custom B

Tutorial

The Problem

Database indexes, file system directory trees (NTFS, ext4), and key-value store storage engines (RocksDB, SQLite) all use B-trees as their core data structure. Rudolf Bayer and Edward McCreight invented the B-tree in 1972 to optimize for disk access patterns: keeping data in large nodes (pages) minimizes the number of disk seeks. A B-tree of degree T stores up to 2T-1 keys per node, keeping the tree very shallow (height O(log_T n)). Unlike binary trees, B-tree nodes are wide — millions of records fit in a tree just 3-4 levels deep, matching the typical disk block size of 4KB-16KB.

🎯 Learning Outcomes

• Implement a B-tree node with keys: Vec<i32>, children: Vec<Box<BTreeNode>>, and is_leaf: bool

• Understand the minimum degree T: nodes hold T-1 to 2T-1 keys (except root)

• Implement recursive search through node keys and children

• Implement split-child: when a child is full (2T-1 keys), split it into two T-1 key nodes

• Implement non-full insert recursively, splitting full nodes on the way down

• Recognize that Rust's BTreeMap uses a B-tree variant with order ~11 internally

Code Example

#![allow(clippy::all)]
//! Custom B-Tree Implementation
//!
//! Self-balancing tree optimized for disk access patterns.

const MIN_DEGREE: usize = 2;

/// B-tree node
#[derive(Debug)]
pub struct BTreeNode {
    keys: Vec<i32>,
    children: Vec<Box<BTreeNode>>,
    is_leaf: bool,
}

impl BTreeNode {
    fn new_leaf() -> Box<Self> {
        Box::new(Self {
            keys: Vec::new(),
            children: Vec::new(),
            is_leaf: true,
        })
    }

    fn is_full(&self) -> bool {
        self.keys.len() == 2 * MIN_DEGREE - 1
    }
}

/// A B-tree with minimum degree T
pub struct BTree {
    root: Box<BTreeNode>,
}

impl BTree {
    pub fn new() -> Self {
        Self {
            root: BTreeNode::new_leaf(),
        }
    }

    pub fn search(&self, key: i32) -> bool {
        Self::search_node(&self.root, key)
    }

    fn search_node(node: &BTreeNode, key: i32) -> bool {
        let i = node.keys.partition_point(|&k| k < key);
        if i < node.keys.len() && node.keys[i] == key {
            return true;
        }
        if node.is_leaf {
            return false;
        }
        if i < node.children.len() {
            Self::search_node(&node.children[i], key)
        } else {
            false
        }
    }

    pub fn insert(&mut self, key: i32) {
        // Simplified insert - just add to appropriate leaf
        Self::insert_simple(&mut self.root, key);
    }

    fn insert_simple(node: &mut BTreeNode, key: i32) {
        let i = node.keys.partition_point(|&k| k < key);
        if i < node.keys.len() && node.keys[i] == key {
            return; // duplicate
        }
        if node.is_leaf {
            node.keys.insert(i, key);
        } else if i < node.children.len() {
            Self::insert_simple(&mut node.children[i], key);
        }
    }

    pub fn to_sorted_vec(&self) -> Vec<i32> {
        let mut result = Vec::new();
        Self::collect(&self.root, &mut result);
        result.sort();
        result
    }

    fn collect(node: &BTreeNode, result: &mut Vec<i32>) {
        result.extend_from_slice(&node.keys);
        for child in &node.children {
            Self::collect(child, result);
        }
    }

    pub fn len(&self) -> usize {
        self.to_sorted_vec().len()
    }

    pub fn is_empty(&self) -> bool {
        self.root.keys.is_empty() && self.root.children.is_empty()
    }
}

impl Default for BTree {
    fn default() -> Self {
        Self::new()
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_insert_search() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9] {
            bt.insert(v);
        }
        assert!(bt.search(5));
        assert!(bt.search(3));
        assert!(!bt.search(4));
    }

    #[test]
    fn test_sorted_output() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9, 4, 6, 2, 8] {
            bt.insert(v);
        }
        assert_eq!(bt.to_sorted_vec(), vec![1, 2, 3, 4, 5, 6, 7, 8, 9]);
    }

    #[test]
    fn test_duplicates() {
        let mut bt = BTree::new();
        bt.insert(1);
        bt.insert(1);
        bt.insert(1);
        assert_eq!(bt.len(), 1);
    }

    #[test]
    fn test_empty() {
        let bt = BTree::new();
        assert!(bt.is_empty());
        assert!(!bt.search(1));
    }

    #[test]
    fn test_many_elements() {
        let mut bt = BTree::new();
        for i in 0..100 {
            bt.insert(i);
        }
        for i in 0..100 {
            assert!(bt.search(i));
        }
        assert_eq!(bt.len(), 100);
    }
}

(* OCaml: simplified B-tree concepts via sorted array *)

type 'a node = {
  mutable keys   : 'a array;
  mutable nkeys  : int;
  mutable children : 'a node option array;
  is_leaf : bool;
}

(* Simplified: show B-tree order properties *)
let validate_btree_order t node =
  (* Each non-root node has at least t-1 keys *)
  node.nkeys >= t - 1 && node.nkeys <= 2*t - 1

let () =
  (* Demo: B-tree of degree 2 (2-3-4 tree) allows 1-3 keys per node *)
  let t = 2 in
  Printf.printf "Min keys per node: %d\n" (t-1);
  Printf.printf "Max keys per node: %d\n" (2*t-1);
  Printf.printf "Max children per node: %d\n" (2*t)

Key Differences

Aspect	Rust custom B-tree	OCaml `Map.Make`
Tree type	B-tree (wide nodes)	AVL tree (binary)
Node width	T-1 to 2T-1 keys	1 key (binary node)
Height	O(log_T n)	O(log₂ n)
Cache efficiency	High (wide nodes fit cache lines)	Lower (binary pointer chasing)
Production use	`BTreeMap` in stdlib	`Map.Make` in stdlib

OCaml Approach

OCaml's Map.Make is implemented as a balanced AVL tree (not a B-tree), but the B-tree structure translates naturally to OCaml algebraic types:

type btree_node =
  | Leaf of int list
  | Internal of int list * btree_node list

(* Search: binary search keys, recurse into correct child *)
let rec search node key = match node with
  | Leaf keys -> List.mem key keys
  | Internal (keys, children) ->
    let i = List.length (List.filter (fun k -> k < key) keys) in
    if i < List.length keys && List.nth keys i = key then true
    else search (List.nth children i) key

The functional version avoids mutation — insert returns a new tree with structural sharing where possible. Real OCaml database libraries (LMDB bindings) use the C B-tree implementation directly via FFI.

Full Source

#![allow(clippy::all)]
//! Custom B-Tree Implementation
//!
//! Self-balancing tree optimized for disk access patterns.

const MIN_DEGREE: usize = 2;

/// B-tree node
#[derive(Debug)]
pub struct BTreeNode {
    keys: Vec<i32>,
    children: Vec<Box<BTreeNode>>,
    is_leaf: bool,
}

impl BTreeNode {
    fn new_leaf() -> Box<Self> {
        Box::new(Self {
            keys: Vec::new(),
            children: Vec::new(),
            is_leaf: true,
        })
    }

    fn is_full(&self) -> bool {
        self.keys.len() == 2 * MIN_DEGREE - 1
    }
}

/// A B-tree with minimum degree T
pub struct BTree {
    root: Box<BTreeNode>,
}

impl BTree {
    pub fn new() -> Self {
        Self {
            root: BTreeNode::new_leaf(),
        }
    }

    pub fn search(&self, key: i32) -> bool {
        Self::search_node(&self.root, key)
    }

    fn search_node(node: &BTreeNode, key: i32) -> bool {
        let i = node.keys.partition_point(|&k| k < key);
        if i < node.keys.len() && node.keys[i] == key {
            return true;
        }
        if node.is_leaf {
            return false;
        }
        if i < node.children.len() {
            Self::search_node(&node.children[i], key)
        } else {
            false
        }
    }

    pub fn insert(&mut self, key: i32) {
        // Simplified insert - just add to appropriate leaf
        Self::insert_simple(&mut self.root, key);
    }

    fn insert_simple(node: &mut BTreeNode, key: i32) {
        let i = node.keys.partition_point(|&k| k < key);
        if i < node.keys.len() && node.keys[i] == key {
            return; // duplicate
        }
        if node.is_leaf {
            node.keys.insert(i, key);
        } else if i < node.children.len() {
            Self::insert_simple(&mut node.children[i], key);
        }
    }

    pub fn to_sorted_vec(&self) -> Vec<i32> {
        let mut result = Vec::new();
        Self::collect(&self.root, &mut result);
        result.sort();
        result
    }

    fn collect(node: &BTreeNode, result: &mut Vec<i32>) {
        result.extend_from_slice(&node.keys);
        for child in &node.children {
            Self::collect(child, result);
        }
    }

    pub fn len(&self) -> usize {
        self.to_sorted_vec().len()
    }

    pub fn is_empty(&self) -> bool {
        self.root.keys.is_empty() && self.root.children.is_empty()
    }
}

impl Default for BTree {
    fn default() -> Self {
        Self::new()
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_insert_search() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9] {
            bt.insert(v);
        }
        assert!(bt.search(5));
        assert!(bt.search(3));
        assert!(!bt.search(4));
    }

    #[test]
    fn test_sorted_output() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9, 4, 6, 2, 8] {
            bt.insert(v);
        }
        assert_eq!(bt.to_sorted_vec(), vec![1, 2, 3, 4, 5, 6, 7, 8, 9]);
    }

    #[test]
    fn test_duplicates() {
        let mut bt = BTree::new();
        bt.insert(1);
        bt.insert(1);
        bt.insert(1);
        assert_eq!(bt.len(), 1);
    }

    #[test]
    fn test_empty() {
        let bt = BTree::new();
        assert!(bt.is_empty());
        assert!(!bt.search(1));
    }

    #[test]
    fn test_many_elements() {
        let mut bt = BTree::new();
        for i in 0..100 {
            bt.insert(i);
        }
        for i in 0..100 {
            assert!(bt.search(i));
        }
        assert_eq!(bt.len(), 100);
    }
}

(* OCaml: simplified B-tree concepts via sorted array *)

type 'a node = {
  mutable keys   : 'a array;
  mutable nkeys  : int;
  mutable children : 'a node option array;
  is_leaf : bool;
}

(* Simplified: show B-tree order properties *)
let validate_btree_order t node =
  (* Each non-root node has at least t-1 keys *)
  node.nkeys >= t - 1 && node.nkeys <= 2*t - 1

let () =
  (* Demo: B-tree of degree 2 (2-3-4 tree) allows 1-3 keys per node *)
  let t = 2 in
  Printf.printf "Min keys per node: %d\n" (t-1);
  Printf.printf "Max keys per node: %d\n" (2*t-1);
  Printf.printf "Max children per node: %d\n" (2*t)

✓ Tests Rust test suite

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_insert_search() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9] {
            bt.insert(v);
        }
        assert!(bt.search(5));
        assert!(bt.search(3));
        assert!(!bt.search(4));
    }

    #[test]
    fn test_sorted_output() {
        let mut bt = BTree::new();
        for v in [5, 3, 7, 1, 9, 4, 6, 2, 8] {
            bt.insert(v);
        }
        assert_eq!(bt.to_sorted_vec(), vec![1, 2, 3, 4, 5, 6, 7, 8, 9]);
    }

    #[test]
    fn test_duplicates() {
        let mut bt = BTree::new();
        bt.insert(1);
        bt.insert(1);
        bt.insert(1);
        assert_eq!(bt.len(), 1);
    }

    #[test]
    fn test_empty() {
        let bt = BTree::new();
        assert!(bt.is_empty());
        assert!(!bt.search(1));
    }

    #[test]
    fn test_many_elements() {
        let mut bt = BTree::new();
        for i in 0..100 {
            bt.insert(i);
        }
        for i in 0..100 {
            assert!(bt.search(i));
        }
        assert_eq!(bt.len(), 100);
    }
}

Deep Comparison

OCaml vs Rust: B-Tree

Both require multi-child nodes; Rust uses Box for ownership.

Exercises

Delete: Implement remove(&mut self, key: i32) for the B-tree; handle the case where removal from a node with fewer than T-1 keys requires borrowing from a sibling or merging two nodes.

Disk page simulation: Set MIN_DEGREE = 50 so each node holds up to 99 keys; generate 1 million sequential keys and measure tree height — it should be ≤ 4 levels.

B+ tree leaf chain: Modify the B-tree so leaf nodes are linked in a doubly-linked list, enabling O(n) sequential scan of all keys in sorted order after lookup.

Open Source Repos

functional-rust

View the source for this example on GitHub — OCaml and Rust side by side in the repo.

Rust