Radix Sort Visualizer

Setup Array

Sort Controls

Array Visualization

Current Array:

Buckets (Digit: 1):

Algorithm Steps

How to Use

Setup: Enter numbers separated by commas or click "Random" to generate an array
Sort: Click "Start Sort" to begin the radix sort process
Step Through: Click "Next Step" to see each step of the algorithm execution
Run Through: Click "Run Through" to automatically execute all steps in sequence
Observe: Watch elements being sorted by each digit position
Reset: Click "Reset" to start over with a new sort

Colors: Orange = Current Digit, Different Colors = Buckets 0-9, Green = Sorted

Radix Sort Concept

Radix Sort is a non-comparison sorting algorithm that sorts numbers by processing individual digits from least to most significant.

How it works:

Find maximum number to determine digit count
Sort by each digit position (units, tens, hundreds)
Use counting sort for each digit (0-9)
Distribute elements into buckets by digit value
Collect elements from buckets in order

Time Complexity: O(d Ã— (n + k)) where d is digits, k is range

Use Cases

Integer Sorting: Optimal for sorting integers and numbers within fixed digit ranges
Large Integer Keys: Sorting very large numbers (1 billion to 1 trillion) efficiently without comparison
Fixed-Width Strings: Sorting fixed-length strings (like postal codes, product IDs, ISBN) digit-by-digit
Linear Time Guarantee: O(d × n) where d is digits ensures predictable performance for bounded data
Stable Sorting Required: Preserves relative order of equal elements through digit-based passes
Specialized Hardware: Efficient on systems with limited comparison operations but fast digit manipulation
Historical Data Sorting: Sorting by timestamps, years, or date components without comparison
Educational Algorithms: Learning non-comparison sorting paradigms and digit manipulation techniques

Real-World Example

Scenario: A postal service needs to sort 100,000 parcels by their 5-digit postal codes for efficient delivery route organization.

Input: Parcel records with postal codes [42857, 19384, 67921, 35412, 82746, 51234, 29876, 73451...]
Process: Sort by digit position (ones, tens, hundreds, thousands, ten-thousands) using counting sort at each step
Output: Parcels sorted by postal code [19384, 29876, 35412, 42857, 51234, 67921, 73451, 82746...]

Radix sort is ideal for postal code sorting because codes are fixed-length integers (5 digits), and radix sort processes them in O(d × n) = O(5 × 100,000) = O(500,000) operations versus comparison sort's O(n log n) ≈ O(1.66M) operations. Radix sort also naturally groups parcels by digit significance - after processing the ten-thousands digit, parcels are already pre-grouped by region. Postal services worldwide use radix sort variants for sorting mail codes efficiently.

Benefits: Linear time O(d × n), efficient for fixed-width keys, stable sorting, excellent for bounded integer ranges