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.
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.
Characterizes the asymptotic time complexity of recursive algorithms like MergeSort (a=2, b=2 ⟹ O(N log N)) and QuickSort.
Starting QuickSort with Lomuto partitioning.
Algorithm Step-Challenge #1
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.
| Algorithm | Best Time | Average Time | Worst Time | Space | Stable |
|---|---|---|---|---|---|
| QuickSort | O(N log N) | O(N log N) | O(N²) | O(log N) | No |
| MergeSort | O(N log N) | O(N log N) | O(N log N) | O(N) | Yes |
| HeapSort | O(N log N) | O(N log N) | O(N log N) | O(1) | No |
| BubbleSort | O(N) | O(N²) | O(N²) | O(1) | Yes |
| InsertionSort | O(N) | O(N²) | O(N²) | O(1) | Yes |
| RadixSort | O(d·(N+k)) | O(d·(N+k)) | O(d·(N+k)) | O(N+k) | Yes |
Mathematical Recurrence Relations (Master Theorem)
By Master Theorem Case 2: a=2, b=2, c=1 ⟹ log_b(a) = 1 = c.
Occurs when the chosen pivot is always the maximum or minimum element.
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How to Use Interactive Algorithm & Data Structure Visualizer
Select an Algorithmic Mode
Choose between the Sorting Studio, Multi-Algorithm Battle Race, 2D Grid Pathfinding, or the AVL Tree Balancer.
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.
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: Uniform Random Array [35 elements]
QuickSort finishes in ~140 operations (O(N log N)); BubbleSort requires ~595 comparisons (O(N²)).
Frequently Asked Questions (PAA)
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Authoritative Standards & Citations
Calculations and algorithms on this page are implemented and verified in strict accordance with the following official technical specifications:
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