# MSD( Most Significant Digit ) Radix Sort

• Last Updated : 24 Jan, 2023

Approach: The idea is to perform the following steps for each digit i where the value of i varies from the most significant digit to the least significant digit:

• Store elements in different buckets according to their ith digit.
• Recursively sort each bucket that has more than one element.

### Most vs Least Significant Digit Radix Sort:

• The idea is to sort the fixed-length integers, MSD is more efficient than LSD because it may not have to examine every digit of each integer:

• MSD can be used to sort strings of variable length, unlike LSD. LSD has to be stable in order to work correctly, but MSD can either be made stable or unstable and MSD can work with random strings.

MSD Radix sort variable length string

• Time Complexity:
• Auxiliary Space:
• LSD Radix sort: O(N + B)
• MSD Radix sort: O(N + MB), where M = length of the longest string and B = size of radix (B=10 possible numbers or B=256 characters or B=2 for Binary).
• MSD uses recursion, so it requires more space than LSD. This means that MSD is much slower than LSD when working with a few inputs.

Using linked list: This implementation is for integers using linked list. A fixed-length array for every node will take a very large amount of storage.

Below is the implementation of MSD Radix Sort using a linked list:

## C++

 `// C++ program for the implementation``// of MSD Radix Sort using linked list``#include ``#include ` `using` `namespace` `std;` `// Linked list node structure``struct` `node {``    ``vector<``int``> arr;``    ``struct` `node* nxt[10];``};` `// Function to create a new node of``// the Linked List``struct` `node* new_node(``void``)``{``    ``struct` `node* tempNode = ``new` `node;` `    ``for` `(``int` `i = 0; i < 10; i++) {``        ``tempNode->nxt[i] = NULL;``    ``}` `    ``// Return the created node``    ``return` `tempNode;``}` `// Function to sort the given array``// using MSD Radix Sort recursively``void` `msd_sort(``struct` `node* root, ``int` `exp``,``              ``vector<``int``>& sorted_arr)``{``    ``if` `(``exp` `<= 0) {``        ``return``;``    ``}` `    ``int` `j;` `    ``// Stores the numbers in different``    ``// buckets according their MSD``    ``for` `(``int` `i = 0;``         ``i < root->arr.size();``         ``i++) {` `        ``// Get the MSD in j``        ``j = (root->arr[i] / ``exp``) % 10;` `        ``// If j-th index in the node``        ``// array is empty create and``        ``// link a new node in index``        ``if` `(root->nxt[j] == NULL) {``            ``root->nxt[j] = new_node();``        ``}` `        ``// Store the number in j-th node``        ``root->nxt[j]->arr.push_back(``            ``root->arr[i]);``    ``}` `    ``// Sort again every child node that``    ``// has more than one number``    ``for` `(``int` `i = 0; i < 10; i++) {` `        ``// If root->next is NULL``        ``if` `(root->nxt[i] != NULL) {` `            ``if` `(root->nxt[i]->arr.size()``                ``> 1) {` `                ``// Sort recursively``                ``msd_sort(root->nxt[i],``                         ``exp` `/ 10,``                         ``sorted_arr);``            ``}` `            ``// If any node have only``            ``// one number then it means``            ``// the number is sorted``            ``else` `{``                ``sorted_arr.push_back(``                    ``root->nxt[i]->arr[0]);``            ``}``        ``}``    ``}``}` `// Function to calculate the MSD of the``// maximum  value in the array``int` `get_max_exp(vector<``int``> arr)``{``    ``// Stores the maximum element``    ``int` `mx = arr[0];` `    ``// Traverse the given array``    ``for` `(``int` `i = 1; i < arr.size(); i++) {` `        ``// Update the value of maximum``        ``if` `(arr[i] > mx) {``            ``mx = arr[i];``        ``}``    ``}` `    ``int` `exp` `= 1;` `    ``while` `(mx > 10) {``        ``mx /= 10;``        ``exp` `*= 10;``    ``}` `    ``// Return the resultant value``    ``return` `exp``;``}` `// Function to print an array``void` `print(vector<``int``> arr)``{``    ``for` `(``int` `i = 0; i < arr.size(); i++)``        ``cout << arr[i] << ``" "``;` `    ``cout << endl;``}` `// Driver Code``int` `main()``{``    ``// create the root node``    ``struct` `node* root = new_node();` `    ``// Stores the unsorted array``    ``// in the root node``    ``root->arr.insert(root->arr.end(),``                     ``{ 9330, 9950, 718,``                       ``8977, 6790, 95,``                       ``9807, 741, 8586,``                       ``5710 });` `    ``cout << ``"Unsorted array : "``;` `    ``// Print the unsorted array``    ``print(root->arr);` `    ``// Find the optimal longest exponent``    ``int` `exp` `= get_max_exp(root->arr);` `    ``// Stores the sorted numbers``    ``vector<``int``> sorted_arr;` `    ``// Function Call``    ``msd_sort(root, ``exp``, sorted_arr);` `    ``cout << ``"Sorted array : "``;` `    ``// Print the sorted array``    ``print(sorted_arr);` `    ``return` `0;``}`

## C

 `// C program for the implementation``// of MSD Radix Sort using linked list``// Linked list node structure``#include ``#include // For using malloc``#include // For using memset` `// Output array filled length``int` `sorted_array_length = 0;` `struct` `node {``    ``int` `arr[100];``    ``int` `arr_length;``    ``struct` `node* nxt[10];``};` `// Function to create a new node of``// the Linked List``struct` `node* new_node(``void``)``{``    ``struct` `node* tempNode``        ``= (``struct` `node*)``malloc``(``sizeof``(``struct` `node));` `    ``tempNode->arr_length = 0;` `    ``for` `(``int` `i = 0; i < 10; i++) {``        ``tempNode->nxt[i] = NULL;``    ``}` `    ``// Return the created node``    ``return` `tempNode;``}` `// Function to sort the given array``// using MSD Radix Sort recursively``void` `msd_sort(``struct` `node* root, ``int` `exp``, ``int``* sorted_arr)``{``    ``if` `(``exp` `<= 0) {``        ``return``;``    ``}` `    ``int` `j;` `    ``// Stores the numbers in different``    ``// buckets according their MSD``    ``for` `(``int` `i = 0; i < root->arr_length; i++) {` `        ``// Get the MSD in j``        ``j = (root->arr[i] / ``exp``) % 10;` `        ``// If j-th index in the node``        ``// array is empty create and``        ``// link a new node in index``        ``if` `(root->nxt[j] == NULL) {``            ``root->nxt[j] = new_node();``        ``}` `        ``// Store the number in j-th node``        ``root->nxt[j]->arr[root->nxt[j]->arr_length++]``            ``= root->arr[i];``    ``}` `    ``// Sort again every child node that``    ``// has more than one number``    ``for` `(``int` `i = 0; i < 10; i++) {` `        ``// If root->next is NULL``        ``if` `(root->nxt[i] != NULL) {` `            ``if` `(root->nxt[i]->arr_length > 1) {` `                ``// Sort recursively``                ``msd_sort(root->nxt[i], ``exp` `/ 10,``                         ``sorted_arr);``            ``}` `            ``// If any node have only``            ``// one number then it means``            ``// the number is sorted``            ``else` `{``                ``sorted_arr[sorted_array_length++]``                    ``= root->nxt[i]->arr[0];``            ``}``        ``}``    ``}``}` `// Function to calculate the MSD of the``// maximum value in the array``int` `get_max_exp(``int``* arr, ``int` `n)``{``    ``// Stores the maximum element``    ``int` `mx = arr[0];` `    ``// Traverse the given array``    ``for` `(``int` `i = 1; i < n; i++) {` `        ``// Update the value of maximum``        ``if` `(arr[i] > mx) {``            ``mx = arr[i];``        ``}``    ``}` `    ``int` `exp` `= 1;` `    ``while` `(mx > 10) {``        ``mx /= 10;``        ``exp` `*= 10;``    ``}` `    ``// Return the resultant value``    ``return` `exp``;``}` `// Function to print an array``void` `print(``int``* arr, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``printf``(``"%d "``, arr[i]);` `    ``printf``(``"\n"``);``}` `// Driver Code``int` `main()``{``    ``// Unsorted array``    ``int` `array[] = { 9330, 9950, 718, 8977, 6790,``                    ``95,   9807, 741, 8586, 5710 };` `    ``// Input array length``    ``int` `n = ``sizeof``(array) / ``sizeof``(array[0]);` `    ``// create the root node``    ``struct` `node* root = new_node();` `    ``// Stores the unsorted array``    ``// in the root node and``    ``// set arr_length``    ``memcpy``(root->arr, array, ``sizeof``(array));``    ``root->arr_length = n;` `    ``printf``(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(root->arr, n);` `    ``// Find the optimal longest exponent``    ``int` `exp` `= get_max_exp(root->arr, root->arr_length);` `    ``// Stores the sorted numbers``    ``int` `output[n];``    ``int``* sorted_arr = &output[0];` `    ``// Function Call``    ``msd_sort(root, ``exp``, sorted_arr);` `    ``printf``(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(sorted_arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of MSD Radix Sort``// of MSD Radix Sort using counting sort()``import` `java.util.*;` `class` `GFG{` `// A utility function to print an array``static` `void` `print(``int``[] arr, ``int` `n)``{``    ``for` `(``int` `i = ``0``; i < n; i++) {``        ``System.out.print(arr[i]+ ``" "``);``    ``}``    ``System.out.println();``}` `// A utility function to get the digit``// at index d in a integer``static` `int` `digit_at(``int` `x, ``int` `d)``{``    ``return` `(``int``)(x / Math.pow(``10``, d - ``1``)) % ``10``;``}` `// The main function to sort array using``// MSD Radix Sort recursively``static` `int``[] MSD_sort(``int``[] arr, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo) {``        ``return` `arr;``    ``}` `    ``int` `count[] = ``new` `int``[``10` `+ ``2``];` `    ``// temp is created to easily swap Strings in arr[]``    ``HashMap temp = ``new` `HashMap<>();` `    ``// Store occurrences of most significant character``    ``// from each integer in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = ``0``; r < ``10` `+ ``1``; r++)``        ``count[r + ``1``] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``if``(temp.containsKey(count+``1``))``            ``temp.put(count++, arr[i]);``        ``else``        ``temp.put(count++, arr[i]);``    ``}` `    ``// Copy all integers of temp to arr[], so that arr[] now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++)``        ``if``(temp.containsKey(i-lo))``        ``arr[i] = temp.get(i - lo);` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = ``0``; r < ``10``; r++)``        ``arr = MSD_sort(arr, lo + count[r], lo + count[r + ``1``] - ``1``,``                 ``d - ``1``);``    ``return` `arr;``}` `// function find the largest integer``static` `int` `getMax(``int` `arr[], ``int` `n)``{``    ``int` `mx = arr[``0``];``    ``for` `(``int` `i = ``1``; i < n; i++)``        ``if` `(arr[i] > mx)``            ``mx = arr[i];``    ``return` `mx;``}` `// Main function to call MSD_sort``static` `int``[] radixsort(``int``[] arr, ``int` `n)``{``    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = (``int``)Math.floor(Math.log10(Math.abs(m))) + ``1``;` `    ``// function call``    ``return` `MSD_sort(arr, ``0``, n - ``1``, d);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Input array``    ``int` `arr[] = { ``9330``, ``9950``, ``718``, ``8977``, ``6790``,``                  ``95``,   ``9807``, ``741``, ``8586``, ``5710` `};` `    ``// Size of the array``    ``int` `n = arr.length;` `    ``System.out.printf(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``   ``arr =  radixsort(arr, n);` `    ``System.out.printf(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);` `}``}` `// This code is contributed by gauravrajput1`

## Python3

 `# Python implementation of MSD Radix Sort``import` `math` `# A utility function to get the digit at index d in a integer``def` `digit_at(x, d):``    ``return` `int``(x ``/` `(``10``*``*``(d``-``1``))) ``%` `10` `# The main function to sort array using MSD Radix Sort recursively``def` `MSD_sort(arr, lo, hi, d):``  ` `    ``# recursion break condition``    ``if` `hi <``=` `lo:``        ``return` `arr` `    ``count ``=` `[``0``] ``*` `(``10` `+` `2``)``    ``temp ``=` `[``0``] ``*` `(hi ``-` `lo ``+` `1``)` `    ``# Store occurrences of most significant character``    ``# from each integer in count``    ``for` `i ``in` `range``(lo, hi``+``1``):``        ``c ``=` `digit_at(arr[i], d)``        ``count ``+``=` `1` `    ``# Change count so that count now contains actual``    ``# position of this digits in temp``    ``for` `r ``in` `range``(``10` `+` `1``):``        ``count[r ``+` `1``] ``+``=` `count[r]` `    ``# Build the temp``    ``for` `i ``in` `range``(lo, hi``+``1``):``        ``c ``=` `digit_at(arr[i], d)``        ``temp[count] ``=` `arr[i]``        ``count ``+``=` `1` `    ``# Copy all integers of temp to arr, so that arr now``    ``# contains partially sorted integers``    ``for` `i ``in` `range``(lo, hi``+``1``):``        ``arr[i] ``=` `temp[i ``-` `lo]` `    ``# Recursively MSD_sort() on each partially sorted``    ``# integers set to sort them by their next digit``    ``for` `r ``in` `range``(``10``):``        ``arr ``=` `MSD_sort(arr, lo ``+` `count[r], lo ``+` `count[r ``+` `1``] ``-` `1``, d ``-` `1``)``    ``return` `arr` `# function find the largest integer``def` `getMax(arr):``    ``mx ``=` `arr[``0``]``    ``for` `i ``in` `range``(``1``, ``len``(arr)):``        ``if` `arr[i] > mx:``            ``mx ``=` `arr[i]``    ``return` `mx` `# Main function to call MSD_sort``def` `radixsort(arr):``    ``# Find the maximum number to know number of digits``    ``m ``=` `getMax(arr)` `    ``# get the length of the largest integer``    ``d ``=` `int``(math.floor(math.log10(``abs``(m)))) ``+` `1` `    ``# function call``    ``return` `MSD_sort(arr, ``0``, ``len``(arr) ``-` `1``, d)` `# Driver Code` `# Input array``arr ``=` `[``9330``, ``9950``, ``718``, ``8977``, ``6790``, ``95``, ``9807``, ``741``, ``8586``, ``5710``]``print``(``"Unsorted array: "``,arr)` `# Function Call``arr ``=` `radixsort(arr)` `print``(``"Sorted array : "``,arr)` `# This code is contributed by lokeshpotta20.`

## C#

 `// C# implementation of MSD Radix Sort``// of MSD Radix Sort using counting sort()``using` `System;``using` `System.Collections.Generic;` `public` `class` `GFG {` `  ``// A utility function to print an array``  ``static` `void` `print(``int``[] arr, ``int` `n) {``    ``for` `(``int` `i = 0; i < n; i++) {``      ``Console.Write(arr[i] + ``" "``);``    ``}``    ``Console.WriteLine();``  ``}` `  ``// A utility function to get the digit``  ``// at index d in a integer``  ``static` `int` `digit_at(``int` `x, ``int` `d) {``    ``return` `(``int``) (x / Math.Pow(10, d - 1)) % 10;``  ``}` `  ``// The main function to sort array using``  ``// MSD Radix Sort recursively``  ``static` `int``[] MSD_sort(``int``[] arr, ``int` `lo, ``int` `hi, ``int` `d) {` `    ``// recursion break condition``    ``if` `(hi <= lo) {``      ``return` `arr;``    ``}` `    ``int` `[]count = ``new` `int``[10 + 2];` `    ``// temp is created to easily swap Strings in []arr``    ``Dictionary<``int``, ``int``> temp = ``new` `Dictionary<``int``, ``int``>();` `    ``// Store occurrences of most significant character``    ``// from each integer in []count``    ``for` `(``int` `i = lo; i <= hi; i++) {``      ``int` `c = digit_at(arr[i], d);``      ``count++;``    ``}` `    ``// Change []count so that []count now contains actual``    ``// position of this digits in []temp``    ``for` `(``int` `r = 0; r < 10 + 1; r++)``      ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``      ``int` `c = digit_at(arr[i], d);``      ``if` `(temp.ContainsKey(count + 1))``        ``temp.Add(count++, arr[i]);``      ``else``        ``temp.Add(count++, arr[i]);``    ``}` `    ``// Copy all integers of temp to []arr, so that []arr now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++)``      ``if` `(temp.ContainsKey(i - lo))``        ``arr[i] = temp[i - lo];` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = 0; r < 10; r++)``      ``arr = MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1, d - 1);``    ``return` `arr;``  ``}` `  ``// function find the largest integer``  ``static` `int` `getMax(``int` `[]arr, ``int` `n)``  ``{``    ``int` `mx = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``      ``if` `(arr[i] > mx)``        ``mx = arr[i];``    ``return` `mx;``  ``}` `  ``// Main function to call MSD_sort``  ``static` `int``[] radixsort(``int``[] arr, ``int` `n)``  ``{` `    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = (``int``) Math.Floor(Math.Log10(Math.Abs(m))) + 1;` `    ``// function call``    ``return` `MSD_sort(arr, 0, n - 1, d);``  ``}` `  ``// Driver Code``  ``public` `static` `void` `Main(String[] args)``  ``{` `    ``// Input array``    ``int` `[]arr = { 9330, 9950, 718, 8977, 6790, 95, 9807, 741, 8586, 5710 };` `    ``// Size of the array``    ``int` `n = arr.Length;` `    ``Console.Write(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``    ``arr = radixsort(arr, n);` `    ``Console.Write(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);` `  ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

```Unsorted array : 9330 9950 718 8977 6790 95 9807 741 8586 5710
Sorted array : 95 718 741 5710 6790 8586 8977 9330 9807 9950 ```

Using Counting Sort() method: This implementation is for the strings based on the counting sort() method. As C style ASCII character is 1 byte. So, the 256 size array is used to count occurrences of characters, and it sorts the strings lexicographically.

Below is the implementation of MSD Radix Sort using the counting sort() method:

## C++

 `// C++ implementation of MSD Radix Sort``#include ``#include ` `using` `namespace` `std;` `// A utility function to print an array``void` `print(string* str, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``cout << str[i] << ``" "``;``    ``}``    ``cout << endl;``}` `// A utility function to get the ASCII value``// of the character at index d in a string``int` `char_at(string str, ``int` `d)``{``    ``if` `(str.size() <= d)``        ``return` `-1;``    ``else``        ``return` `str.at(d);``}` `// The main function to sort array using``// MSD Radix Sort recursively``void` `MSD_sort(string* str, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo) {``        ``return``;``    ``}` `    ``int` `count[256 + 2] = { 0 };` `    ``// temp is created to easily swap strings in str[]``    ``// int temp[n] can also be used but,``    ``// it will take more space.``    ``unordered_map<``int``, string> temp;` `    ``// Store occurrences of most significant character``    ``// from each string in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = char_at(str[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = 0; r < 256 + 1; r++)``        ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = char_at(str[i], d);``        ``temp[count++] = str[i];``    ``}` `    ``// Copy all strings of temp to str[], so that str[] now``    ``// contains partially sorted strings``    ``for` `(``int` `i = lo; i <= hi; i++)``        ``str[i] = temp[i - lo];` `    ``// Recursively MSD_sort() on each partially sorted``    ``// strings set to sort them by their next character``    ``for` `(``int` `r = 0; r < 256; r++)``        ``MSD_sort(str, lo + count[r], lo + count[r + 1] - 1,``                 ``d + 1);``}` `int` `main()``{``    ``string str[] = { ``"midnight"``, ``"badge"``,  ``"bag"``,``                     ``"worker"``,   ``"banner"``, ``"wander"` `};` `    ``int` `n = ``sizeof``(str) / ``sizeof``(str[0]);` `    ``cout << ``"Unsorted array : "``;``    ``// print the unsorted array``    ``print(str, n);` `    ``// Function call``    ``MSD_sort(str, 0, n - 1, 0);` `    ``cout << ``"Sorted array : "``;``    ``// print the sorted array``    ``print(str, n);` `    ``return` `0;``}`

## C

 `// C program for the implementation``// of MSD Radix Sort using counting sort()``#include ``#include ` `// A utility function to get the ASCII value``// of the character at index d in a string``int` `char_at(``char``* str, ``int` `d)``{``    ``if` `(``sizeof``(str) / ``sizeof``(str[0]) <= d)``        ``return` `-1;``    ``else``        ``return` `str[d];``}` `int` `n;` `// The main function to sort array using``// MSD Radix Sort recursively``void` `MSD_sort(``char``** str, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo + 1) {``        ``return``;``    ``}` `    ``int` `count[256 + 2] = { 0 };` `    ``// temp is created to easily swap strings in str[]``    ``char` `temp[n][100];` `    ``// Store occurrences of most significant character``    ``// from each string in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = char_at(str[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = 0; r < 256 + 1; r++)``        ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = char_at(str[i], d);``        ``memcpy``(temp[count++], str[i],``               ``strlen``(str[i]) + 1);``    ``}` `    ``// Copy all strings of temp to str[], so that str[] now``    ``// contains partially sorted strings``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``str[i] = strdup(temp[i - lo]);``    ``}` `    ``// Recursively MSD_sort() on each partially sorted``    ``// strings set to sort them by their next character``    ``for` `(``int` `r = 0; r < 256; r++)``        ``MSD_sort(str, lo + count[r], lo + count[r + 1] - 1,``                 ``d + 1);``}` `// Function to print an array``void` `print(``char``** str, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``printf``(``"%s "``, str[i]);``    ``}``    ``printf``(``"\n"``);``}` `// Driver Code``int` `main()``{``    ``// Input String``    ``char``* str[] = { (``char``*)``"midnight"``, (``char``*)``"badge"``,``                    ``(``char``*)``"bag"``,      (``char``*)``"worker"``,``                    ``(``char``*)``"banner"``,   (``char``*)``"wander"` `};` `    ``// Size of the string``    ``n = ``sizeof``(str) / ``sizeof``(str[0]);` `    ``printf``(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(str, n);` `    ``// Function Call``    ``MSD_sort(str, 0, n - 1, 0);` `    ``printf``(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(str, n);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;``import` `java.lang.*;``import` `java.util.*;` `public` `class` `GFG {` `    ``// Utility function to get the ASCII``    ``// value of the character at index d``    ``// in the string``    ``static` `int` `char_at(String str, ``int` `d)``    ``{``        ``if` `(str.length() <= d)``            ``return` `-``1``;``        ``else``            ``return` `(``int``)(str.charAt(d));``    ``}` `    ``// Function to sort the array using``    ``// MSD Radix Sort recursively``    ``static` `void` `MSD_sort(String str[], ``int` `lo, ``int` `hi,``                         ``int` `d)``    ``{``        ``// Recursive break condition``        ``if` `(hi <= lo) {``            ``return``;``        ``}` `        ``// Stores the ASCII Values``        ``int` `count[] = ``new` `int``[``256` `+ ``1``];` `        ``// Temp is created to easily``        ``// swap strings in str[]``        ``HashMap temp = ``new` `HashMap<>();` `        ``// Store the occurrences of the most``        ``// significant character from``        ``// each string in count[]``        ``for` `(``int` `i = lo; i <= hi; i++) {``            ``int` `c = char_at(str[i], d);``            ``count++;``        ``}` `        ``// Change count[] so that count[]``        ``// now contains actual position``        ``// of this digits in temp[]``        ``for` `(``int` `r = ``0``; r < ``256``; r++)``            ``count[r + ``1``] += count[r];` `        ``// Build the temp``        ``for` `(``int` `i = lo; i <= hi; i++) {``            ``int` `c = char_at(str[i], d);``            ``temp.put(count++, str[i]);``        ``}` `        ``// Copy all strings of temp to str[],``        ``// so that str[] now contains``        ``// partially sorted strings``        ``for` `(``int` `i = lo; i <= hi; i++)``            ``str[i] = temp.get(i - lo);` `        ``// Recursively MSD_sort() on each``        ``// partially sorted strings set to``        ``// sort them by their next character``        ``for` `(``int` `r = ``0``; r < ``256``; r++)``            ``MSD_sort(str, lo + count[r],``                     ``lo + count[r + ``1``] - ``1``, d + ``1``);``    ``}` `    ``// Function to print an array``    ``static` `void` `print(String str[], ``int` `n)``    ``{``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``System.out.print(str[i] + ``" "``);``        ``}``        ``System.out.println();``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``// Input String``        ``String str[] = { ``"midnight"``, ``"badge"``,  ``"bag"``,``                         ``"worker"``,   ``"banner"``, ``"wander"` `};` `        ``// Size of the string``        ``int` `n = str.length;` `        ``System.out.print(``"Unsorted array : "``);` `        ``// Print the unsorted array``        ``print(str, n);` `        ``// Function Call``        ``MSD_sort(str, ``0``, n - ``1``, ``0``);` `        ``System.out.print(``"Sorted array : "``);` `        ``// Print the sorted array``        ``print(str, n);``    ``}``}` `// This code is contributed by Kingash.`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG{` `// Utility function to get the ASCII``// value of the character at index d``// in the string``static` `int` `char_at(String str, ``int` `d)``{``    ``if` `(str.Length <= d)``        ``return` `-1;``    ``else``        ``return``(``int``)(str[d]);``}` `// Function to sort the array using``// MSD Radix Sort recursively``static` `void` `MSD_sort(String []str, ``int` `lo,``                           ``int` `hi, ``int` `d)``{``    ` `    ``// Recursive break condition``    ``if` `(hi <= lo)``    ``{``        ``return``;``    ``}` `    ``// Stores the ASCII Values``    ``int` `[]count = ``new` `int``[256 + 1];` `    ``// Temp is created to easily``    ``// swap strings in []str``    ``Dictionary<``int``,``               ``String> temp = ``new` `Dictionary<``int``,``                                             ``String>();` `    ``// Store the occurrences of the most``    ``// significant character from``    ``// each string in []count``    ``for``(``int` `i = lo; i <= hi; i++)``    ``{``        ``int` `c = char_at(str[i], d);``        ``count++;``    ``}` `    ``// Change []count so that []count``    ``// now contains actual position``    ``// of this digits in []temp``    ``for``(``int` `r = 0; r < 256; r++)``        ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for``(``int` `i = lo; i <= hi; i++)``    ``{``        ``int` `c = char_at(str[i], d);``        ``temp.Add(count++, str[i]);``    ``}` `    ``// Copy all strings of temp to []str,``    ``// so that []str now contains``    ``// partially sorted strings``    ``for``(``int` `i = lo; i <= hi; i++)``        ``str[i] = temp[i - lo];` `    ``// Recursively MSD_sort() on each``    ``// partially sorted strings set to``    ``// sort them by their next character``    ``for``(``int` `r = 0; r < 256; r++)``        ``MSD_sort(str, lo + count[r],``                      ``lo + count[r + 1] - 1,``                       ``d + 1);``}` `// Function to print an array``static` `void` `print(String []str, ``int` `n)``{``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``Console.Write(str[i] + ``" "``);``    ``}``    ``Console.WriteLine();``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{` `    ``// Input String``    ``String []str = { ``"midnight"``, ``"badge"``, ``"bag"``,``                     ``"worker"``, ``"banner"``, ``"wander"` `};` `    ``// Size of the string``    ``int` `n = str.Length;` `    ``Console.Write(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(str, n);` `    ``// Function Call``    ``MSD_sort(str, 0, n - 1, 0);` `    ``Console.Write(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(str, n);``}``}` `// This code is contributed by shikhasingrajput`

Output

```Unsorted array : midnight badge bag worker banner wander
Sorted array : badge bag banner midnight wander worker ```

## C++

 `// C++ implementation of MSD Radix Sort``// of MSD Radix Sort using counting sort()``#include ``#include ``#include ` `using` `namespace` `std;` `// A utility function to print an array``void` `print(``int``* arr, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``cout << arr[i] << ``" "``;``    ``}``    ``cout << endl;``}` `// A utility function to get the digit``// at index d in a integer``int` `digit_at(``int` `x, ``int` `d)``{``    ``return` `(``int``)(x / ``pow``(10, d - 1)) % 10;``}` `// The main function to sort array using``// MSD Radix Sort recursively``void` `MSD_sort(``int``* arr, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo) {``        ``return``;``    ``}` `    ``int` `count[10 + 2] = { 0 };` `    ``// temp is created to easily swap strings in arr[]``    ``unordered_map<``int``, ``int``> temp;` `    ``// Store occurrences of most significant character``    ``// from each integer in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = 0; r < 10 + 1; r++)``        ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``temp[count++] = arr[i];``    ``}` `    ``// Copy all integers of temp to arr[], so that arr[] now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++)``        ``arr[i] = temp[i - lo];` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = 0; r < 10; r++)``        ``MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1,``                 ``d - 1);``}` `// function find the largest integer``int` `getMax(``int` `arr[], ``int` `n)``{``    ``int` `mx = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``        ``if` `(arr[i] > mx)``            ``mx = arr[i];``    ``return` `mx;``}` `// Main function to call MSD_sort``void` `radixsort(``int``* arr, ``int` `n)``{``    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = ``floor``(``log10``(``abs``(m))) + 1;` `    ``// function call``    ``MSD_sort(arr, 0, n - 1, d);``}` `// Driver Code``int` `main()``{``    ``// Input array``    ``int` `arr[] = { 9330, 9950, 718, 8977, 6790,``                  ``95,   9807, 741, 8586, 5710 };` `    ``// Size of the array``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``    ``radixsort(arr, n);` `    ``printf``(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);` `    ``return` `0;``}`

## C

 `// C program for the implementation``// of MSD Radix Sort using counting sort()``#include ``#include ``#include ``#include ` `// A utility function to print an array``void` `print(``int``* arr, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``printf``(``"%d, "``, arr[i]);``    ``}``    ``printf``(``"\n"``);``}` `// A utility function to get the digit``// at index d in a integer``int` `digit_at(``int` `x, ``int` `d)``{``    ``return` `(``int``)(x / ``pow``(10, d - 1)) % 10;``}` `// array length``int` `n;` `// function to sort array using``// MSD Radix Sort recursively``void` `MSD_sort(``int``* arr, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo || d < 1) {``        ``return``;``    ``}` `    ``int` `count[10 + 2] = { 0 };` `    ``// temp is created to easily swap strings in arr[]``    ``int` `temp[n];` `    ``// Store occurrences of most significant character``    ``// from each integer in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = 0; r < 10 + 1; r++)``        ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``temp[count++] = arr[i];``    ``}` `    ``// Copy all integer of temp to arr[], so that arr[] now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``arr[i] = temp[i - lo];``    ``}` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = 0; r < 10; r++)``        ``MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1,``                 ``d - 1);``}` `// function find the largest integer``int` `getMax(``int` `arr[], ``int` `n)``{``    ``int` `mx = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``        ``if` `(arr[i] > mx)``            ``mx = arr[i];``    ``return` `mx;``}` `// Main function to call MSD_sort``void` `radixsort(``int``* arr, ``int` `n)``{``    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = ``floor``(``log10``(``abs``(m))) + 1;` `    ``// function call``    ``MSD_sort(arr, 0, n - 1, d);``}` `// Driver Code``int` `main()``{``    ``// Input array``    ``int` `arr[] = { 9330, 9950, 718, 8977, 6790,``                  ``95,   9807, 741, 8586, 5710 };` `    ``// Size of the array``    ``n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``    ``radixsort(arr, n);` `    ``printf``(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of MSD Radix Sort``// of MSD Radix Sort using counting sort()``import` `java.util.*;` `class` `GFG{` `// A utility function to print an array``static` `void` `print(``int``[] arr, ``int` `n)``{``    ``for` `(``int` `i = ``0``; i < n; i++) {``        ``System.out.print(arr[i]+ ``" "``);``    ``}``    ``System.out.println();``}` `// A utility function to get the digit``// at index d in a integer``static` `int` `digit_at(``int` `x, ``int` `d)``{``    ``return` `(``int``)(x / Math.pow(``10``, d - ``1``)) % ``10``;``}` `// The main function to sort array using``// MSD Radix Sort recursively``static` `void` `MSD_sort(``int``[] arr, ``int` `lo, ``int` `hi, ``int` `d)``{` `    ``// recursion break condition``    ``if` `(hi <= lo) {``        ``return``;``    ``}` `    ``int` `count[] = ``new` `int``[``10` `+ ``2``];` `    ``// temp is created to easily swap Strings in arr[]``    ``HashMap temp = ``new` `HashMap<>();` `    ``// Store occurrences of most significant character``    ``// from each integer in count[]``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``count++;``    ``}` `    ``// Change count[] so that count[] now contains actual``    ``//  position of this digits in temp[]``    ``for` `(``int` `r = ``0``; r < ``10` `+ ``1``; r++)``        ``count[r + ``1``] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``        ``int` `c = digit_at(arr[i], d);``        ``temp.put(count++, arr[i]);``    ``}` `    ``// Copy all integers of temp to arr[], so that arr[] now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++)``        ``arr[i] = temp.get(i - lo);` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = ``0``; r < ``10``; r++)``        ``MSD_sort(arr, lo + count[r], lo + count[r + ``1``] - ``1``,``                 ``d - ``1``);``}` `// function find the largest integer``static` `int` `getMax(``int` `arr[], ``int` `n)``{``    ``int` `mx = arr[``0``];``    ``for` `(``int` `i = ``1``; i < n; i++)``        ``if` `(arr[i] > mx)``            ``mx = arr[i];``    ``return` `mx;``}` `// Main function to call MSD_sort``static` `void` `radixsort(``int``[] arr, ``int` `n)``{``    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = (``int``)Math.floor(Math.log10(Math.abs(m))) + ``1``;` `    ``// function call``    ``MSD_sort(arr, ``0``, n - ``1``, d);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Input array``    ``int` `arr[] = { ``9330``, ``9950``, ``718``, ``8977``, ``6790``,``                  ``95``,   ``9807``, ``741``, ``8586``, ``5710` `};` `    ``// Size of the array``    ``int` `n = arr.length;` `    ``System.out.printf(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``    ``radixsort(arr, n);` `    ``System.out.printf(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);` `}``}` `// This code is contributed by Rajput-Ji`

## C#

 `// C# implementation of MSD Radix Sort``// of MSD Radix Sort using counting sort()``using` `System;``using` `System.Collections.Generic;` `public` `class` `GFG {` `  ``// A utility function to print an array``  ``static` `void` `print(``int``[] arr, ``int` `n) {``    ``for` `(``int` `i = 0; i < n; i++) {``      ``Console.Write(arr[i] + ``" "``);``    ``}``    ``Console.WriteLine();``  ``}` `  ``// A utility function to get the digit``  ``// at index d in a integer``  ``static` `int` `digit_at(``int` `x, ``int` `d) {``    ``return` `(``int``) (x / Math.Pow(10, d - 1)) % 10;``  ``}` `  ``// The main function to sort array using``  ``// MSD Radix Sort recursively``  ``static` `void` `MSD_sort(``int``[] arr, ``int` `lo, ``int` `hi, ``int` `d) {` `    ``// recursion break condition``    ``if` `(hi <= lo) {``      ``return``;``    ``}` `    ``int` `[]count = ``new` `int``[10 + 2];` `    ``// temp is created to easily swap Strings in []arr``    ``Dictionary<``int``, ``int``> temp = ``new` `Dictionary<``int``, ``int``>();` `    ``// Store occurrences of most significant character``    ``// from each integer in []count``    ``for` `(``int` `i = lo; i <= hi; i++) {``      ``int` `c = digit_at(arr[i], d);``      ``count++;``    ``}` `    ``// Change []count so that []count now contains actual``    ``// position of this digits in []temp``    ``for` `(``int` `r = 0; r < 10 + 1; r++)``      ``count[r + 1] += count[r];` `    ``// Build the temp``    ``for` `(``int` `i = lo; i <= hi; i++) {``      ``int` `c = digit_at(arr[i], d);``      ``temp.Add(count++, arr[i]);``    ``}` `    ``// Copy all integers of temp to []arr, so that []arr now``    ``// contains partially sorted integers``    ``for` `(``int` `i = lo; i <= hi; i++)``      ``arr[i] = temp[i - lo];` `    ``// Recursively MSD_sort() on each partially sorted``    ``// integers set to sort them by their next digit``    ``for` `(``int` `r = 0; r < 10; r++)``      ``MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1, d - 1);``  ``}` `  ``// function find the largest integer``  ``static` `int` `getMax(``int` `[]arr, ``int` `n) {``    ``int` `mx = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``      ``if` `(arr[i] > mx)``        ``mx = arr[i];``    ``return` `mx;``  ``}` `  ``// Main function to call MSD_sort``  ``static` `void` `radixsort(``int``[] arr, ``int` `n)``  ``{` `    ``// Find the maximum number to know number of digits``    ``int` `m = getMax(arr, n);` `    ``// get the length of the largest integer``    ``int` `d = (``int``) Math.Floor(Math.Log10(Math.Abs(m))) + 1;` `    ``// function call``    ``MSD_sort(arr, 0, n - 1, d);``  ``}` `  ``// Driver Code``  ``public` `static` `void` `Main(String[] args)``  ``{` `    ``// Input array``    ``int` `[]arr = { 9330, 9950, 718, 8977, 6790, 95, 9807, 741, 8586, 5710 };` `    ``// Size of the array``    ``int` `n = arr.Length;` `    ``Console.Write(``"Unsorted array : "``);` `    ``// Print the unsorted array``    ``print(arr, n);` `    ``// Function Call``    ``radixsort(arr, n);` `    ``Console.Write(``"Sorted array : "``);` `    ``// Print the sorted array``    ``print(arr, n);``  ``}``}` `// This code is contributed by Rajput-Ji`

Output

```Unsorted array : 9330 9950 718 8977 6790 95 9807 741 8586 5710
Sorted array : 95 718 741 5710 6790 8586 8977 9330 9807 9950 ```

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