Radix Sort

Radix Sort Algorithm in C++ (Complete Implementation)

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C++ Radix Sort Program

This program helps you to learn the fundamental structure and syntax of C++ programming.

Try This Code
#include <iostream>
#include <algorithm>
using namespace std;

int getMax(int arr[], int n) {
    int max = arr[0];
    for (int i = 1; i < n; i++) {
        if (arr[i] > max)
            max = arr[i];
    }
    return max;
}

void countSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};
    
    // Store count of occurrences
    for (int i = 0; i < n; i++)
        count[(arr[i] / exp) % 10]++;
    
    // Change count to position
    for (int i = 1; i < 10; i++)
        count[i] += count[i - 1];
    
    // Build output array
    for (int i = n - 1; i >= 0; i--) {
        output[count[(arr[i] / exp) % 10] - 1] = arr[i];
        count[(arr[i] / exp) % 10]--;
    }
    
    // Copy output to original array
    for (int i = 0; i < n; i++)
        arr[i] = output[i];
}

void radixSort(int arr[], int n) {
    int max = getMax(arr, n);
    
    // Do counting sort for every digit
    for (int exp = 1; max / exp > 0; exp *= 10)
        countSort(arr, n, exp);
}

void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;
}

int main() {
    int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
    int n = sizeof(arr) / sizeof(arr[0]);
    
    cout << "Original array: ";
    printArray(arr, n);
    
    radixSort(arr, n);
    
    cout << "Sorted array: ";
    printArray(arr, n);
    
    return 0;
}
Output
Original array: 170 45 75 90 802 24 2 66
Sorted array: 2 24 45 66 75 90 170 802

Understanding Radix Sort

This program teaches you how to implement the Radix Sort algorithm in C++. Radix Sort is a non-comparative sorting algorithm that sorts numbers by processing individual digits from least significant to most significant. It uses Counting Sort as a subroutine for each digit position. Radix Sort is efficient for integers with a limited number of digits.

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1. What This Program Does

The program sorts an array of integers using the Radix Sort algorithm. For example:

Input array: [170, 45, 75, 90, 802, 24, 2, 66]
Output array: [2, 24, 45, 66, 75, 90, 170, 802]

Radix Sort processes digits from right to left (least significant to most significant), using Counting Sort for each digit position.

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2. Header Files Used

1.#include <iostream>
Provides cout and cin for input/output operations.
2.#include <algorithm>
Provides max_element() and min_element() functions (used in some implementations).

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3. Understanding Radix Sort

Algorithm Concept

:

Sorts by processing individual digits
Starts with least significant digit (rightmost)
Moves to more significant digits (leftward)
Uses Counting Sort for each digit position
Stable sorting algorithm

Visual Example

:

Array: [170, 45, 75, 90, 802, 24, 2, 66]
Pass 1 (ones place): [170, 90, 802, 2, 24, 45, 75, 66]
Pass 2 (tens place): [802, 2, 24, 45, 66, 170, 75, 90]
Pass 3 (hundreds place): [2, 24, 45, 66, 75, 90, 170, 802]

---

4. Function: getMax()

int getMax(int arr[], int n) {

int max = arr[0];

for (int i = 1; i < n; i++) {

if (arr[i] > max)

max = arr[i];

}

}

    return max;

How it works

:

Finds the maximum element in the array
Needed to determine number of digits to process
Example: max = 802 → 3 digits → 3 passes needed

---

5. Function: countSort()

void countSort(int arr[], int n, int exp) {

int output[n];

int count[10] = {0};

for (int i = 0; i < n; i++)

count[(arr[i] / exp) % 10]++;

// Change count to position

for (int i = 1; i < 10; i++)

count[i] += count[i - 1];

// Build output array

for (int i = n - 1; i >= 0; i--) {

output[count[(arr[i] / exp) % 10] - 1] = arr[i];

count[(arr[i] / exp) % 10]--;

}

// Copy output to original array

for (int i = 0; i < n; i++)

arr[i] = output[i];

}

    // Store count of occurrences

How it works

:

exp: current digit position (1, 10, 100, ...)
(arr[i] / exp) % 10: extracts digit at current position
Uses Counting Sort for the current digit
Maintains stability by processing from right to left

Example

(exp = 1, ones place):

Extract ones digit: 170 → 0, 45 → 5, 75 → 5
Count occurrences: count[0]=1, count[5]=2, ...
Build sorted output based on ones digit

---

6. Function: radixSort()

void radixSort(int arr[], int n) {

int max = getMax(arr, n);

for (int exp = 1; max / exp > 0; exp *= 10)

countSort(arr, n, exp);

}

How it works

:

Gets maximum element to determine number of passes
exp starts at 1 (ones place)
Each iteration: exp *= 10 (tens, hundreds, ...)
Continues until max / exp > 0 (all digits processed)

Example

(max = 802):

Pass 1: exp = 1 (ones place)
Pass 2: exp = 10 (tens place)
Pass 3: exp = 100 (hundreds place)
Pass 4: exp = 1000, max/exp = 0 → stop

---

7. Time and Space Complexity

Time Complexity

: O(d * (n + k))

d: number of digits in maximum element
n: number of elements
k: range of digits (0-9, so k = 10)
Each pass: O(n + k) for Counting Sort
Total: O(d * (n + k)) ≈ O(d * n) for integers

Space Complexity

: O(n + k)

Output array: O(n)
Count array: O(k) = O(10) = O(1)
Total: O(n)

Stability

: Stable

Counting Sort maintains relative order
Important for sorting objects with multiple fields

---

8. When to Use Radix Sort

Best For

:

Integers with limited digit range
When number of digits is small compared to array size
When stability is required
Fixed-width integers

Not Recommended For

:

Floating-point numbers (without modification)
Strings (requires different approach)
Very large digit ranges
When d is large (many passes needed)

---

9. Important Considerations

Digit Extraction

:

(arr[i] / exp) % 10 extracts digit at position exp
exp = 1: ones place
exp = 10: tens place
exp = 100: hundreds place

Stability

:

Processing from right to left (i = n-1 to 0) maintains stability
Equal digits preserve relative order from previous pass

Number of Passes

:

Determined by maximum element's digit count
Example: max = 802 → 3 passes
Example: max = 9999 → 4 passes

---

10. return 0;

This ends the program successfully.

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Summary

Radix Sort processes digits from least to most significant.
Uses Counting Sort as subroutine for each digit position.
Time complexity: O(d * (n + k)) where d is number of digits.
Space complexity: O(n + k) - requires temporary arrays.
Stable algorithm - preserves relative order of equal elements.
Efficient for integers with limited digit range.
Number of passes equals number of digits in maximum element.
Understanding Radix Sort demonstrates non-comparative sorting techniques.

This program is fundamental for learning non-comparative sorting algorithms, understanding digit-based sorting, and preparing for advanced sorting techniques in C++ programs.

Let us now understand every line and the components of the above program.

Note: To write and run C++ programs, you need to set up the local environment on your computer. Refer to the complete article Setting up C++ Development Environment. If you do not want to set up the local environment on your computer, you can also use online IDE to write and run your C++ programs.

Practical Learning Notes for Radix Sort

This C++ program is part of the "Sorting & Searching Programs" topic and is designed to help you build real problem-solving confidence, not just memorize syntax. Start by understanding the goal of the program in plain language, then trace the logic line by line with a custom input of your own. Once you can predict the output before running the code, your understanding becomes much stronger.

A reliable practice pattern is to run the original version first, then modify only one condition or variable at a time. Observe how that single change affects control flow and output. This deliberate style helps you understand loops, conditions, and data movement much faster than copying full solutions repeatedly.

For interview preparation, explain this solution in three layers: the high-level approach, the step-by-step execution, and the time-space tradeoff. If you can teach these three layers clearly, you are ready to solve close variations of this problem under time pressure.

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