Radix sort is a sorting technique that sorts the elements by first grouping the individual digits of same place value. Then, sort the elements according to their increasing/decreasing order.
Suppose, we have an array of 8 elements. First, we will sort elements based on the value of the unit place. Then, we will sort elements based on the value of the tenth place. This process goes on until the last significant place.
Let the initial array be [121, 432, 564, 23, 1, 45, 788]. It is sorted according to radix sort as shown in the figure below.
Please go through the counting sort before reading this article because counting sort is used as an intermediate sort in radix sort.
X be the number of digits in max. X is calculated because we have to go through all the significant places of all elements.[121, 432, 564, 23, 1, 45, 788], we have the largest number 788. It has 3 digits. Therefore, the loop should go up to hundreds place (3 times).X=0).
radixSort(array)
d <- maximum number of digits in the largest element
create d buckets of size 0-9
for i <- 0 to d
sort the elements according to ith place digits using countingSort
countingSort(array, d)
max <- find largest element among dth place elements
initialize count array with all zeros
for j <- 0 to size
find the total count of each unique digit in dth place of elements and
store the count at jth index in count array
for i <- 1 to max
find the cumulative sum and store it in count array itself
for j <- size down to 1
restore the elements to array
decrease count of each element restored by 1
# Radix sort in Python
def countingSort(array, place):
size = len(array)
output = [0] * (size)
count = [0] * (10)
for i in range(0, size):
index = (array[i]//place)
count[(index) % 10] += 1
for i in range(1, 10):
count[i] += count[i-1]
i = size-1
while i >= 0:
index = (array[i]//place)
output[count[(index) % 10] - 1] = array[i]
count[(index) % 10] -= 1
i -= 1
for i in range(0, size):
array[i] = output[i]
def radixSort(array):
max_element = max(array)
place = 1
while max_element//place > 0:
countingSort(array, place)
place *= 10
data = [121, 432, 564, 23, 1, 45, 788]
radixSort(data)
print(data)
// Radix Sort in Java Programming
class RadixSort {
void countingSort(int array[], int size, int place) {
int[] output = new int[size + 1];
int max = array[0];
for (int i = 1; i < size; i++) {
if (array[i] > max)
max = array[i];
}
int[] count = new int[max + 1];
for (int i = 0; i < max; ++i)
count[i] = 0;
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;
for (int i = 1; i < 10; i++)
count[i] += count[i - 1];
for (int i = size - 1; i >= 0; i--) {
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}
for (int i = 0; i < size; i++)
array[i] = output[i];
}
int getMax(int array[], int n) {
int max = array[0];
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}
void radixSort(int array[], int size) {
int max = getMax(array, size);
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}
void printArray(int array[], int size) {
for (int i = 0; i < size; ++i)
System.out.print(array[i] + " ");
System.out.println();
}
public static void main(String args[]) {
int[] data = { 121, 432, 564, 23, 1, 45, 788 };
int size = data.length;
RadixSort rs = new RadixSort();
rs.radixSort(data, size);
System.out.println("Sorted Array in Ascending Order: ");
rs.printArray(data, size);
}
}
// Radix Sort in C Programming
#include <stdio.h>
int getMax(int array[], int n)
{
int max = array[0];
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}
void countingSort(int array[], int size, int place)
{
int output[size + 1];
int max = (array[0] / place) % 10;
for (int i = 1; i < size; i++)
{
if (((array[i] / place) % 10) > max)
max = array[i];
}
int count[max + 1];
for (int i = 0; i < max; ++i)
count[i] = 0;
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;
for (int i = 1; i < 10; i++)
count[i] += count[i - 1];
for (int i = size - 1; i >= 0; i--)
{
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}
for (int i = 0; i < size; i++)
array[i] = output[i];
}
void radixsort(int array[], int size)
{
int max = getMax(array, size);
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}
void printArray(int array[], int size)
{
for (int i = 0; i < size; ++i)
{
printf("%d ", array[i]);
}
printf("\n");
}
int main()
{
int array[] = {121, 432, 564, 23, 1, 45, 788};
int n = sizeof(array) / sizeof(array[0]);
radixsort(array, n);
printArray(array, n);
}
// Radix Sort in C++ Programming
#include <iostream>
using namespace std;
int getMax(int array[], int n)
{
int max = array[0];
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}
void countingSort(int array[], int size, int place)
{
const int max = 10;
int output[size];
int count[max];
for (int i = 0; i < max; ++i)
count[i] = 0;
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;
for (int i = 1; i < max; i++)
count[i] += count[i - 1];
for (int i = size - 1; i >= 0; i--)
{
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}
for (int i = 0; i < size; i++)
array[i] = output[i];
}
void radixsort(int array[], int size)
{
int max = getMax(array, size);
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}
void printArray(int array[], int size)
{
int i;
for (i = 0; i < size; i++)
cout << array[i] << " ";
cout << endl;
}
int main()
{
int array[] = {121, 432, 564, 23, 1, 45, 788};
int n = sizeof(array) / sizeof(array[0]);
radixsort(array, n);
printArray(array, n);
}
Since radix sort is a non-comparative algorithm, it has advantages over comparative sorting algorithms.
For the radix sort that uses counting sort as an intermediate stable sort, the time complexity is O(d(n+k)).
Here, d is the number passes and O(n+k) is the time complexity of counting sort.
Thus, radix sort has linear time complexity which is better than O(nlog n) of comparative sorting algorithms.
If we take very large digit numbers or the number of other bases like 32-bit and 64-bit numbers then it can perform in linear time however the intermediate sort takes large space.
This makes radix sort space inefficient. This is the reason why this sort is not used in software libraries.
Radix sort is implemented in