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Interactive Algorithm & Data Structure Visualizer

Visual step-by-step tutor for Sorting, Pathfinding, and AVL Trees. Inspect comparisons, swaps, audio pitch frequencies, and polyglot code execution.

Quick Answer & Summary

An algorithm visualizer is an interactive educational tool that transforms abstract computer science code into dynamic, animated state machines. It graphically depicts comparison pointers, recursive stack partitioning, graph wavefront traversals, and tree balance rotations to build deep pedagogical intuition for time and space complexity.

Master Theorem Divide-and-Conquer Recurrence
T(N) = a * T(N/b) + f(N) ⟹ O(N^log_b(a))

Characterizes the asymptotic time complexity of recursive algorithms like MergeSort (a=2, b=2 ⟹ O(N log N)) and QuickSort.

Elements (20)
Speed (60ms)
Step 1 / 147
Normal Comparing Swapping / Insert Sorted
Array Length: 20
[0]: 56
56
0
[1]: 73
73
1
[2]: 81
81
2
[3]: 85
85
3
[4]: 83
83
4
[5]: 12
12
5
[6]: 40
40
6
[7]: 24
24
7
[8]: 17
17
8
[9]: 39
39
9
[10]: 6
6
10
[11]: 31
31
11
[12]: 33
33
12
[13]: 98
98
13
[14]: 38
38
14
[15]: 66
66
15
[16]: 48
48
16
[17]: 62
62
17
[18]: 63
63
18
[19]: 7
7
19
Current Execution State

Starting QuickSort with Lomuto partitioning.

Comparisons
0
Swaps / Shifts
0
Array Accesses
0
Asymptotic Complexity
Average Time:O(N log N)
Worst Time:O(N²)
Space:O(log N)
Stable:No
1function quickSort(arr, low, high):
2 if low < high:
3 pivotIndex = partition(arr, low, high)
4 quickSort(arr, low, pivotIndex - 1)
5 quickSort(arr, pivotIndex + 1, high)
6
7function partition(arr, low, high):
8 pivot = arr[high]
9 i = low - 1
10 for j = low to high - 1:
11 if arr[j] < pivot:
12 i = i + 1
13 swap(arr[i], arr[j])
14 swap(arr[i + 1], arr[high])
15 return i + 1

Algorithm Step-Challenge #1

1 / 4

In QuickSort with Lomuto partitioning, what is the time complexity when the input array is already sorted?

Asymptotic Big-O Complexity Master Matrix

Comprehensive benchmark summary of time, space, stability, and recurrence relations for standard CS algorithms.

AlgorithmBest TimeAverage TimeWorst TimeSpaceStable
QuickSortO(N log N)O(N log N)O(N²)O(log N)No
MergeSortO(N log N)O(N log N)O(N log N)O(N)Yes
HeapSortO(N log N)O(N log N)O(N log N)O(1)No
BubbleSortO(N)O(N²)O(N²)O(1)Yes
InsertionSortO(N)O(N²)O(N²)O(1)Yes
RadixSortO(d·(N+k))O(d·(N+k))O(d·(N+k))O(N+k)Yes

Mathematical Recurrence Relations (Master Theorem)

MergeSort Recurrence
T(N) = 2T(N/2) + Θ(N) ⟹ O(N log N)

By Master Theorem Case 2: a=2, b=2, c=1 ⟹ log_b(a) = 1 = c.

QuickSort Recurrence (Worst Case)
T(N) = T(N-1) + T(0) + Θ(N) ⟹ O(N²)

Occurs when the chosen pivot is always the maximum or minimum element.

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Documentation & Guide

How to Use Interactive Algorithm & Data Structure Visualizer

1

Select an Algorithmic Mode

Choose between the Sorting Studio, Multi-Algorithm Battle Race, 2D Grid Pathfinding, or the AVL Tree Balancer.

2

Choose a Dataset Distribution or Draw Custom Obstacles

Select Random, Reversed, or Worst-Case QuickSort array distributions, or draw walls and weighted swamps on the pathfinding grid.

3

Control Playback & Audio Synthesis

Use Play/Pause or Step Forward/Back buttons to step through execution, enable Sound of Sorting, and inspect synchronized polyglot code.

Practical Examples & Conversions

Input
Input: Uniform Random Array [35 elements]
Output
QuickSort finishes in ~140 operations (O(N log N)); BubbleSort requires ~595 comparisons (O(N²)).

Frequently Asked Questions (PAA)

Related Tools & Converters

Authoritative Standards & Citations

Calculations and algorithms on this page are implemented and verified in strict accordance with the following official technical specifications: