Interactive Data Structures & Algorithms

Binary Search Tree Deep Dive

Understanding BST operations through interactive visualizations

BST Foundation

What is a Binary Search Tree?

A Binary Search Tree (BST) is a hierarchical data structure where:

Each node has at most two children
Left child < Parent < Right child
All operations average O(log n) time
In-order traversal gives sorted sequence

BST Search Operation

How Search Works

Starting from root, compare target with current node:

If equal: Found!
If target < current: Go left
If target > current: Go right
If null reached: Not found

BST Insert Operation

Building a Tree Step by Step

Watch how values [8,3,10,1,6,14,4,7,13] build our BST:

🧩 Visual Problem

Where would value 5 be inserted in our tree?

BST Delete Operation

Three Deletion Cases

Leaf node: Simply remove
One child: Replace with child
Two children: Replace with inorder successor

BST Traversals

Three Traversal Methods

Inorder: Left → Root → Right (sorted)
Preorder: Root → Left → Right
Postorder: Left → Right → Root

DFS on Large Graph

DFS on Complex Graph Structure

See how DFS works on the larger graph from the tutorial with 10 nodes:

Stack-based execution shows deep exploration
Creates a spanning tree structure
Back edges connect to already visited vertices
Similar to pre-order traversal pattern

Stack State:

🧩 DFS Pattern Recognition

What traversal pattern does DFS resemble?

Depth-First Search Exploration

Master DFS with stack-based traversal techniques

What are Graphs?

Graph Fundamentals

A graph is a collection of vertices (nodes) connected by edges:

Vertices: The individual points or nodes
Edges: Connections between vertices
Adjacent vertices: Vertices connected by an edge
Path: Sequence of vertices connected by edges

Key Concepts from Tutorial:

Visiting: Going to a particular vertex
Exploring: Visiting all adjacent vertices of current vertex

🧩 Graph Understanding

Which statement is true about trees?

DFS Fundamentals

How DFS Works

Depth-First Search explores as far as possible along each branch before backtracking:

Uses a stack (LIFO) structure
Goes deep before going wide
Can be implemented recursively
Time: O(V + E), Space: O(h)

Stack State:

DFS vs BFS Comparison

Side-by-Side Analysis

Watch how DFS and BFS traverse the same graph differently:

DFS (Stack)

BFS (Queue)

Complex DFS Examples

Advanced DFS Applications

Explore complex scenarios with larger graphs:

DFS Applications

Real-World DFS Usage

See how DFS solves practical problems:

🧩 Interactive Challenge

Select an application to see the challenge

Breadth-First Search Exploration

Master BFS with queue-based level-order traversal

BFS Fundamentals

How BFS Works

Breadth-First Search explores level by level before going deeper:

Uses a queue (FIFO) structure
Goes wide before going deep
Finds shortest paths in unweighted graphs
Time: O(V + E), Space: O(w)

Queue State:

BFS vs DFS Direct Comparison

DFS (Depth-First)

Stack:

Key Differences:

DFS: Stack (LIFO), goes deep
BFS: Queue (FIFO), goes wide
Space: DFS O(h), BFS O(w)
Path: BFS finds shortest

BFS (Breadth-First)

Queue:

Complex BFS Examples

Advanced BFS Scenarios

Explore BFS in complex graph structures:

🧩 Path Challenge

What's the shortest path from A to F?

BFS Applications

Real-World BFS Usage

Discover how BFS powers everyday applications:

🧩 Application Challenge

Select an application to see the challenge

BFS on Large Graph

BFS on Complex Graph Structure

See BFS on the same large graph - compare with DFS results:

Queue-based execution shows level-by-level exploration
Creates a different spanning tree than DFS
Cross edges connect to already visited vertices
Similar to level-order traversal pattern

Queue State:

🧩 BFS vs DFS Comparison

On the same graph, how do BFS and DFS spanning trees compare?