kapitals-pi & SEN: x̄ - > 12 foundational data structures used in computer science

Linear and Non-Linear Data Structures Visualization

This page presents common data structures with simple visual descriptions, practical uses, and a Python script for generating diagrams.

  Focus: clean visual explanation of arrays, queues, stacks, trees, graphs, and related structures.

1) Linear Data Structures

Structure	Visualization	How it is used
Array	Contiguous memory cells containing values like 6, 3, 8, 12 mapped to positions 0, 1, 2, 3.	Used for random access, lookup tables, and as a base for matrices.
Queue	A horizontal tunnel where elements enter from the rear and exit from the front.	Implements FIFO processing for scheduling and asynchronous tasks.
Stack	A vertical container where elements are added and removed from the top.	Implements LIFO processing for function calls, undo/redo, and parsing.
Linked List	A sequence of nodes, each holding data and a pointer to the next node.	Useful for dynamic memory allocation and efficient insertion/deletion.

2) Tabular and Key-Value Structures

Structure	Visualization	How it is used
Matrix	A 2D grid arranged in rows and columns.	Used in image processing, coordinate systems, adjacency matrices, and linear algebra.
HashMap	A key directly maps to a value.	Provides near-instant lookup for caching, indexing, and session management.

3) Hierarchical Structures

Structure	Visualization	How it is used
Tree	A parent node branching downward into child nodes.	Represents hierarchical systems such as file systems, DOM trees, and organizations.
BST	A binary tree ordered by value, with smaller values on the left and larger on the right.	Supports efficient search, insertion, and sorting.
Heap	A complete binary tree ordered by priority.	Used in priority queues, scheduling, and heapsort.
Trie	A prefix tree where paths spell parts of words or keys.	Useful for autocomplete, spell-checking, and routing tables.

4) Network and Grouping Structures

Structure	Visualization	How it is used
Graph	A network of nodes interconnected by edges.	Models social networks, transport systems, and internet routing.
Union Find	Elements partitioned into independent, non-overlapping subsets.	Useful for connectivity, clustering, and cycle detection.

Python Script

The following Python code generates the structure diagrams using Matplotlib and NetworkX.

import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle, Circle
import networkx as nx
import numpy as np

fig, axes = plt.subplots(4, 3, figsize=(18, 22))
axes = axes.flatten()

def clean_ax(ax, title):
    ax.set_title(title, fontsize=14, fontweight='bold')
    ax.set_xticks([])
    ax.set_yticks([])
    ax.set_xlim(0, 10)
    ax.set_ylim(0, 10)
    ax.set_frame_on(False)

# 1. Array
ax = axes[0]
clean_ax(ax, "Array")
arr = [6, 3, 8, 12]
for i, v in enumerate(arr):
    ax.add_patch(Rectangle((1.5 + i*1.8, 4), 1.5, 1.2, edgecolor='black', facecolor='#7bed9f'))
    ax.text(2.25 + i*1.8, 4.6, str(v), ha='center', va='center', fontsize=12)
    ax.text(2.25 + i*1.8, 3.5, str(i), ha='center', va='center', fontsize=10, color='gray')

# 2. Queue
ax = axes[1]
clean_ax(ax, "Queue")
queue = [6, 5, 8]
for i, v in enumerate(queue):
    ax.add_patch(Rectangle((2, 2 + i*1.5), 4, 1, edgecolor='black', facecolor='#fd79a8'))
    ax.text(4, 2.5 + i*1.5, str(v), ha='center', va='center', fontsize=12)
ax.text(6.5, 2.5, "front", fontsize=10)
ax.text(6.5, 5.5, "rear", fontsize=10)
ax.text(1.2, 4, "FIFO", fontsize=11)

# 3. Stack
ax = axes[2]
clean_ax(ax, "Stack")
stack = [3, 8, 1]
for i, v in enumerate(stack):
    ax.add_patch(Rectangle((3, 2 + i*1.2), 4, 1, edgecolor='black', facecolor='#feca57'))
    ax.text(5, 2.5 + i*1.2, str(v), ha='center', va='center', fontsize=12)
ax.text(7.2, 2.5, "top", fontsize=10)
ax.text(1.2, 4, "LIFO", fontsize=11)

# 4. Linked List
ax = axes[3]
clean_ax(ax, "Linked List")
vals = [6, 3, 5, 8, 12]
for i, v in enumerate(vals):
    x = 1 + i*1.6
    ax.add_patch(Circle((x, 5), 0.45, edgecolor='black', facecolor='#81ecec'))
    ax.text(x, 5, str(v), ha='center', va='center', fontsize=11)
    if i < len(vals)-1:
        ax.arrow(x+0.5, 5, 0.7, 0, head_width=0.15, head_length=0.15, fc='black', ec='black')

# 5. Matrix
ax = axes[4]
clean_ax(ax, "Matrix")
mat = np.array([[2,7,3],[4,7,5],[8,9,6]])
for i in range(mat.shape[0]):
    for j in range(mat.shape[1]):
        ax.add_patch(Rectangle((2 + j*1.5, 3 + (2-i)*1.2), 1.2, 1, edgecolor='black', facecolor='#a29bfe'))
        ax.text(2.6 + j*1.5, 3.5 + (2-i)*1.2, str(mat[i, j]), ha='center', va='center', fontsize=11)

# 6. Tree
ax = axes[5]
clean_ax(ax, "Tree")
nodes = {(5,8):"5",(3,6):"3",(7,6):"4",(2,4):"1",(4,4):"4"}
for (x,y), val in nodes.items():
    ax.add_patch(Circle((x,y), 0.4, edgecolor='black', facecolor='#55efc4'))
    ax.text(x, y, val, ha='center', va='center', fontsize=11)
ax.plot([5,3],[7.6,6.4], 'k-')
ax.plot([5,7],[7.6,6.4], 'k-')
ax.plot([3,2],[5.6,4.4], 'k-')
ax.plot([3,4],[5.6,4.4], 'k-')

# 7. HashMap
ax = axes[6]
clean_ax(ax, "HashMap")
keys = [("K1","V1"),("K2","V2")]
for i, (k,v) in enumerate(keys):
    ax.add_patch(Rectangle((1.5, 6-i*2), 2, 1, edgecolor='black', facecolor='#fab1a0'))
    ax.text(2.5, 6.5-i*2, k, ha='center', va='center')
    ax.add_patch(Rectangle((6, 6-i*2), 2, 1, edgecolor='black', facecolor='#74b9ff'))
    ax.text(7, 6.5-i*2, v, ha='center', va='center')
    ax.text(4.2, 6.5-i*2, "=>", fontsize=14)

# 8. BST
ax = axes[7]
clean_ax(ax, "BST")
coords = {(5,8):5,(3,6):2,(7,6):6,(2,4):1,(4,4):3,(6,4):5,(8,4):7}
for (x,y), v in coords.items():
    ax.add_patch(Circle((x,y), 0.35, edgecolor='black', facecolor='#ffeaa7'))
    ax.text(x, y, str(v), ha='center', va='center')
edges = [((5,8),(3,6)),((5,8),(7,6)),((3,6),(2,4)),((3,6),(4,4)),((7,6),(6,4)),((7,6),(8,4))]
for (x1,y1),(x2,y2) in edges:
    ax.plot([x1,x2],[y1-0.35,y2+0.35],'k-')

# 9. Heap
ax = axes[8]
clean_ax(ax, "Heap")
vals = [9,5,8,2,3]
coords = [(5,8),(3,6),(7,6),(2,4),(4,4)]
for (x,y), v in zip(coords, vals):
    ax.add_patch(Circle((x,y), 0.35, edgecolor='black', facecolor='#ff7675'))
    ax.text(x, y, str(v), ha='center', va='center')
for (x1,y1),(x2,y2) in [((5,8),(3,6)),((5,8),(7,6)),((3,6),(2,4)),((3,6),(4,4))]:
    ax.plot([x1,x2],[y1-0.35,y2+0.35],'k-')

# 10. Trie
ax = axes[9]
clean_ax(ax, "Trie")
pts = {(5,8):"root",(3,6):"a",(5,6):"b",(7,6):"c",(2,4):"t",(3.8,4):"i",(5,4):"o",(6.2,4):"n"}
for (x,y), v in pts.items():
    ax.add_patch(Circle((x,y), 0.3, edgecolor='black', facecolor='#dfe6e9'))
    ax.text(x, y, v, ha='center', va='center', fontsize=8)
for (x1,y1),(x2,y2) in [((5,8),(3,6)),((5,8),(5,6)),((5,8),(7,6)),((3,6),(2,4)),((3,6),(3.8,4)),((5,6),(5,4)),((7,6),(6.2,4))]:
    ax.plot([x1,x2],[y1-0.3,y2+0.3],'k-')

# 11. Graph
ax = axes[10]
clean_ax(ax, "Graph")
G = nx.Graph()
G.add_edges_from([("A","B"),("A","C"),("B","D"),("C","E")])
pos = {"A":(3,7),"B":(7,7),"C":(3,3),"D":(7,3),"E":(5,1.5)}
nx.draw(G, pos, ax=ax, with_labels=True, node_color='#55efc4', node_size=900, font_size=12)

# 12. Union Find
ax = axes[11]
clean_ax(ax, "Union Find")
vals = [1,2,3,4,5,6]
for i, v in enumerate(vals):
    ax.add_patch(Circle((1.5+i*1.3, 5), 0.35, edgecolor='black', facecolor='#ffeaa7'))
    ax.text(1.5+i*1.3, 5, str(v), ha='center', va='center')
ax.plot([1.5,2.8],[4.65,4.65],'k-')
ax.plot([1.5,4.1],[4.65,4.65],'k-')
ax.plot([5.4,6.7],[4.65,4.65],'k-')

plt.tight_layout()
plt.show()

For Blogger, place the HTML inside the post’s HTML view so the CSS, script, and code blocks render correctly.

Why this format works

This structure matches the article-style template: a title, a horizontally scrolling image strip, section headings, tables, a toggleable hidden section, and a code block area. It is also more maintainable than embedding everything as one long HTML fragment inside a single paragraph.