guest@cp-base:~/home/data-structures$
templates/binary-search-tree.cpp
compilable
$cat templates/binary-search-tree

Binary Search Tree

Basic BST with insert, delete, search, min/max, and all four traversal orders.

[Data Structures]|
Jul 9, 2026
|explanatory_notes.md|
#bst#binary-search-tree#traversal
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$cat source_code/
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#include <bits/stdc++.h>
using namespace std;

struct Node {
    int val;
    Node *L, *R;
    Node(int v) : val(v), L(nullptr), R(nullptr) {}
};

Node* insert(Node* root, int v) {
    if (!root) return new Node(v);
    if (v < root->val) root->L = insert(root->L, v);
    else root->R = insert(root->R, v);
    return root;
}

bool search(Node* root, int v) {
    if (!root) return false;
    if (root->val == v) return true;
    return v < root->val ? search(root->L, v) : search(root->R, v);
}

Node* minNode(Node* root) {
    while (root && root->L) root = root->L;
    return root;
}

Node* maxNode(Node* root) {
    while (root && root->R) root = root->R;
    return root;
}

Node* erase(Node* root, int v) {
    if (!root) return root;
    if (v < root->val) root->L = erase(root->L, v);
    else if (v > root->val) root->R = erase(root->R, v);
    else {
        if (!root->L) { Node* t = root->R; delete root; return t; }
        if (!root->R) { Node* t = root->L; delete root; return t; }
        Node* succ = minNode(root->R);
        root->val = succ->val;
        root->R = erase(root->R, succ->val);
    }
    return root;
}

void inorder(Node* root) {
    if (!root) return;
    inorder(root->L);
    cout << root->val << " ";
    inorder(root->R);
}

void preorder(Node* root) {
    if (!root) return;
    cout << root->val << " ";
    preorder(root->L);
    preorder(root->R);
}
59 linesutf-8
$cat explanation_notes.md
notes_viewer --renderedmarkdown (math enabled)

Binary Search Tree

For every node, all values in the left subtree are strictly less and all in the right subtree are strictly greater.

Operations

  • insert(val) — insert value

  • erase(val) — delete node (handles leaf, one child, two children cases)

  • search(val) — check if value exists

  • minVal() / maxVal() — find min/max

  • inorder() / preorder() / postorder() / levelOrder() — traversals

    • Deletion Cases

  • Leaf — remove directly

  • One child — bypass node, connect parent to child

  • Two children — replace with in-order successor (min of right subtree), then delete successor

    • When to Use

  • Learning/educational purposes

  • When you need a simple ordered container

  • In contests, prefer set/map or balanced BSTs (splay, treap)

    • Complexity

  • Average — O(log⁡n)O(\log n) per operation

  • Worst case (skewed) — O(n)O(n)

  • Space — O(n)O(n)