📚 Classic Data Structures: Definitions, Diagrams, and Trade-offs

📚 Classic Data Structures: Definitions, Diagrams, and Trade-offs#

This module introduces foundational data structures, their conceptual diagrams, strengths and weaknesses, and real-world use cases.

🧮 Array#

Definition: A linear structure storing elements in contiguous memory, accessed via indices.

Diagram: Index: 0 1 2 3 4 Array: [10, 20, 30, 40, 50]

Advantages:

  • ✅ Fast indexed access: O(1)

  • ✅ Simple and memory-efficient for fixed-size data

Disadvantages:

  • ❌ Fixed size; resizing is costly

  • ❌ Insertion/deletion is expensive (O(n))

Applications:

  • 📊 Image pixel grids

  • 📈 Lookup tables

  • 📉 Time-series data

🧱 Stack#

Definition: A Last-In-First-Out (LIFO) structure where the last element added is the first removed.

Diagram: Top → [5] [4] [3] [2] Bottom→[1]

Advantages:

  • ✅ Simple implementation

  • ✅ Great for backtracking and recursion

Disadvantages:

  • ❌ Limited access (only top element)

  • ❌ Not ideal for random access

Applications:

  • ↩️ Undo operations

  • 🧮 Expression parsing

  • 🌐 Browser history

🚦 Queue#

Definition: A First-In-First-Out (FIFO) structure where the first element added is the first removed.

Diagram: Front → [A] [B] [C] [D] ← Rear

Advantages:

  • ✅ Ideal for scheduling and buffering

  • ✅ Predictable order of processing

Disadvantages:

  • ❌ Slow search

  • ❌ Fixed size in static queues

Applications:

  • 🖨️ Print job scheduling

  • 🧵 Task queues

  • 📡 Real-time data streams

🔗 Linked List#

Definition: A dynamic structure of nodes, each pointing to the next.

Diagram: [10] → [20] → [30] → [40] → None

Advantages:

  • ✅ Dynamic size

  • ✅ Fast insert/delete at ends

Disadvantages:

  • ❌ Slow access (O(n))

  • ❌ Extra memory for pointers

Applications:

  • 🎵 Music playlists

  • ↩️ Undo/redo stacks

  • 🧠 Memory-efficient queues

🌳 Tree#

Definition: A hierarchical structure with parent-child relationships.

Diagram: [A] / [B] [C] / \ \ [D] [E] [F]

Advantages:

  • ✅ Fast search, insert, delete (balanced trees)

  • ✅ Represents hierarchical data naturally

Disadvantages:

  • ❌ Complex balancing logic

  • ❌ Traversal can be tricky

Applications:

  • 📁 File systems

  • 🧠 Decision trees

  • 🧬 XML/HTML parsing

🌐 Graph#

Definition: A set of nodes connected by edges, modeling relationships.

Diagram: A — B | | C — D

Advantages:

  • ✅ Models complex relationships

  • ✅ Supports rich traversal algorithms

Disadvantages:

  • ❌ Can be memory-intensive

  • ❌ Algorithms may be slow (e.g., cycle detection)

Applications:

  • 👥 Social networks

  • 🗺️ Routing algorithms

  • 🔗 Dependency graphs

🔍 Visualization Tools#

To explore these structures interactively, try:

📊 Comparison of Classic Data Structures#

This table compares five foundational data structures used in computer science. Each row outlines their core characteristics, strengths, limitations, and practical use cases.

Data Structure

Definition

Key Operations

Advantages

Disadvantages

Real-World Applications

🧱 Stack

LIFO structure where last added is first removed

Push, Pop, Peek

Simple to implement; great for backtracking

Limited access (only top); not suitable for random access

Undo functionality, expression parsing, browser history

🚦 Queue

FIFO structure where first added is first removed

Enqueue, Dequeue, Peek

Ideal for scheduling; predictable order

Slow search; fixed size in static queues

Task scheduling, print queues, real-time data streams

🔗 Linked List

Dynamic node-based structure with pointers

Insert, Delete, Traverse

Dynamic size; efficient insert/delete at ends

Slow access; extra memory for pointers

Music playlists, memory-efficient queues, undo stacks

🌳 Tree

Hierarchical structure with parent-child relationships

Insert, Delete, Traverse (inorder, preorder, postorder)

Fast search in balanced trees; models hierarchy

 

import ipywidgets as widgets
from IPython.display import display, Markdown

# 📂 Problem categories
categories = {
    "Array": [
        "Find the maximum subarray sum (Kadane’s Algorithm)",
        "Rotate array by k steps",
        "Find duplicate elements"
    ],
    "Stack": [
        "Evaluate postfix expression",
        "Check for balanced parentheses",
        "Implement min stack"
    ],
    "Queue": [
        "Implement circular queue",
        "Sliding window maximum",
        "First non-repeating character in stream"
    ],
    "Linked List": [
        "Reverse a linked list",
        "Detect cycle in linked list",
        "Merge two sorted linked lists"
    ],
    "Tree": [
        "Inorder traversal of binary tree",
        "Check if tree is balanced",
        "Lowest common ancestor"
    ],
    "Graph": [
        "Depth-first search (DFS)",
        "Breadth-first search (BFS)",
        "Detect cycle in directed graph"
    ]
}

# 🎛️ Widgets with wider labels
category_dropdown = widgets.Dropdown(
    options=list(categories.keys()),
    value="Array",
    description="📂 Choose Category:",
    style={'description_width': '150px'},
    layout=widgets.Layout(width='350px')
)

problem_dropdown = widgets.Dropdown(
    options=categories["Array"],
    description="🧩 Choose Problem:",
    style={'description_width': '150px'},
    layout=widgets.Layout(width='500px')
)

output = widgets.Output()

def update_problems(change):
    problem_dropdown.options = categories[change.new]

category_dropdown.observe(update_problems, names='value')

def show_problem(b):
    output.clear_output()
    with output:
        display(Markdown(f"### 🧩 Problem: {problem_dropdown.value}"))
        print("Try implementing this problem using the appropriate data structure.")
        print("You can start by writing a function and testing it with sample inputs.")

run_button = widgets.Button(
    description="🔍 Show Selected Problem",
    button_style='success',
    layout=widgets.Layout(width='220px')
)
run_button.on_click(show_problem)

# 🚀 Display UI
display(category_dropdown, problem_dropdown, run_button, output)
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