MSD( Most Significant Digit ) Radix Sort

Last Updated : 26 Mar, 2024

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 stringÂ

• 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 <iostream> #include <vector> 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 <stdio.h> #include <stdlib.h> // For using malloc #include <string.h> // 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<Integer,Integer> 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[c + 2]++; } // 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[c + 1]+1)) temp.put(count[c + 1]++, arr[i]); else temp.put(count[c + 1]++, 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 ``` 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[c + 2]++; } // 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[c + 1] + 1)) temp.Add(count[c + 1]++, arr[i]); else temp.Add(count[c + 1]++, 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 ```// javascript implementation of MSD Radix Sort // of MSD Radix Sort using counting sort() // A utility function to print an array function print(arr , n) { for (var i = 0; i < n; i++) { document.write(arr[i] + " "); } document.write(); } // A utility function to get the digit // at index d in a integer function digit_at(x , d) { return parseInt( x / Math.pow(10, d - 1)) % 10; } // The main function to sort array using // MSD Radix Sort recursively function MSD_sort(arr , lo , hi , d) { // recursion break condition if (hi <= lo) { return arr; } var count = Array(10 + 2).fill(0); // temp is created to easily swap Strings in arr var temp = new Map(); // Store occurrences of most significant character // from each integer in count for (var i = lo; i <= hi; i++) { var c = digit_at(arr[i], d); count[c + 2]++; } // Change count so that count now contains actual // position of this digits in temp for (var r = 0; r < 10 + 1; r++) count[r + 1] += count[r]; // Build the temp for (i = lo; i <= hi; i++) { var c = digit_at(arr[i], d); if (temp.has(count[c + 1] + 1)) temp.set(count[c + 1]++, arr[i]); else temp.set(count[c + 1]++, arr[i]); } // Copy all integers of temp to arr, so that arr now // contains partially sorted integers for (i = lo; i <= hi; i++) if (temp.has(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 (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 function getMax(arr , n) { var mx = arr[0]; for (i = 1; i < n; i++) if (arr[i] > mx) mx = arr[i]; return mx; } // Main function to call MSD_sort function radixsort(arr , n) { // Find the maximum number to know number of digits var m = getMax(arr, n); // get the length of the largest integer var d = parseInt( Math.floor(Math.log10(Math.abs(m)))) + 1; // function call return MSD_sort(arr, 0, n - 1, d); } // Driver Code // Input array var arr = [ 9330, 9950, 718, 8977, 6790, 95, 9807, 741, 8586, 5710 ]; // Size of the array var n = arr.length; document.write("Unsorted array : "); // Print the unsorted array print(arr, n); // Function Call arr = radixsort(arr, n); document.write("<br/>Sorted array : "); // Print the sorted array print(arr, n); // This code is contributed by Rajput-Ji ``` 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[c + 2] += 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[c + 1]] = arr[i] count[c + 1] += 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. ```

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:Â

For string:

C++ ```// C++ implementation of MSD Radix Sort #include <iostream> #include <unordered_map> 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[c + 2]++; } // 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[c + 1]++] = 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; } ``` 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<Integer, String> 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[c + 2]++; } // 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[c + 1]++, 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[c + 2]++; } // 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[c + 1]++, 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 ``` Javascript ```// JS implementation of MSD Radix Sort // A utility function to print an array function print(str, n) { for (let i = 0; i < n; i++) { console.log(str[i] + " "); } console.log("<br>"); } // A utility function to get the ASCII value // of the character at index d in a string function char_at( str, d) { if (str.length <= d) return -1; else return str.charCodeAt(d); } // The main function to sort array using // MSD Radix Sort recursively function MSD_sort( str, lo, hi, d) { // recursion break condition if (hi <= lo) { return; } let count = new Array(256 + 2).fill(0); // temp is created to easily swap strings in str[] // int temp[n] can also be used but, // it will take more space. let temp = new Map(); // Store occurrences of most significant character // from each string in count[] for (let i = lo; i <= hi; i++) { let c = char_at(str[i], d); count[c + 2]++; } // Change count[] so that count[] now contains actual // position of this digits in temp[] for (let r = 0; r < 256 + 1; r++) count[r + 1] += count[r]; // Build the temp for (let i = lo; i <= hi; i++) { let c = char_at(str[i], d); temp.set(count[c + 1]++,str[i]); } // Copy all strings of temp to str[], so that str[] now // contains partially sorted strings for (let 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 (let r = 0; r < 256; r++) MSD_sort(str, lo + count[r], lo + count[r + 1] - 1, d + 1); } let str = [ "midnight", "badge", "bag", "worker", "banner", "wander" ]; let n = str.length; console.log("Unsorted array : "); // print the unsorted array print(str, n); // Function call MSD_sort(str, 0, n - 1, 0); console.log("Sorted array : "); // print the sorted array print(str, n); ``` Python3 ```import collections # Utility function to get the ASCII value of the character at index d in the string def char_at(string, d): if len(string) <= d: return -1 else: return ord(string[d]) # Function to sort the array using MSD Radix Sort recursively def MSD_sort(string_list, lo, hi, d): # Recursive break condition if hi <= lo: return # Stores the ASCII Values count = [0] * (256 + 1) # Temp is created to easily swap strings in str[] temp = collections.defaultdict(str) # Store the occurrences of the most significant character from each string in count[] for i in range(lo, hi+1): c = char_at(string_list[i], d) count[c + 2] += 1 # Change count[] so that count[] now contains actual position of this digits in temp[] for r in range(256): count[r + 1] += count[r] # Build the temp for i in range(lo, hi+1): c = char_at(string_list[i], d) temp[count[c + 1]] = string_list[i] count[c + 1] += 1 # Copy all strings of temp to str[], so that str[] now contains partially sorted strings for i in range(lo, hi+1): string_list[i] = temp[i - lo] # Recursively MSD_sort() on each partially sorted strings set to sort them by their next character for r in range(256): MSD_sort(string_list, lo + count[r], lo + count[r + 1] - 1, d + 1) # Function to print an array def print_list(string_list): for i in string_list: print(i, end=" ") print() # Driver Code if __name__ == '__main__': # Input String string_list = ["midnight", "badge", "bag", "worker", "banner", "wander"] # Size of the string n = len(string_list) print("Unsorted array : ", end="") # Print the unsorted array print_list(string_list) # Function Call MSD_sort(string_list, 0, n - 1, 0) print("Sorted array : ", end="") # Print the sorted array print_list(string_list) ```

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

```

For Integer:

C++ ```// C++ implementation of MSD Radix Sort // of MSD Radix Sort using counting sort() #include <iostream> #include <math.h> #include <unordered_map> 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[c + 2]++; } // 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[c + 1]++] = 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; } ``` 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<Integer,Integer> 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[c + 2]++; } // 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[c + 1]++, 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 ``` Python ```# A utility function to print an array def print_array(arr): for num in arr: print num, # A utility function to get the digit at index d in an integer def digit_at(x, d): return (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 count = [0] * (10 + 2) temp = {} # 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[c + 2] += 1 # Change count[] so that count[] now contains actual position of these 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[c + 1]] = arr[i] count[c + 1] += 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.get(i - lo + 1, 0) # Recursively MSD_sort() on each partially sorted integers set to sort them by their next digit for r in range(10): MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1, d - 1) # Function to find the largest integer def getMax(arr): mx = arr[0] for num in arr: if num > mx: mx = num return mx # Main function to call MSD_sort def radixsort(arr): # Find the maximum number to know the number of digits m = getMax(arr) # Get the length of the largest integer d = len(str(abs(m))) # Function call MSD_sort(arr, 0, len(arr) - 1, d) # Driver Code if __name__ == "__main__": # Input array arr = [9330, 9950, 718, 8977, 6790, 95, 9807, 741, 8586, 5710] print "Unsorted array:", print_array(arr) # Function Call radixsort(arr) print "Sorted array:", print_array(arr) ``` 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[c + 2]++; } // 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[c + 1]++, 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 ``` Javascript ```// JS implementation of MSD Radix Sort // of MSD Radix Sort using counting sort() function print(arr, n) { console.log(arr.join(" ")) } function digit_at(x, d) { return Math.floor(x / Math.pow(10, d - 1)) % 10; } function MSD_sort(arr, lo, hi, d) { // recursion break condition if (hi <= lo) { return; } let count = new Array(10 + 2).fill(0); // temp is created to easily swap Strings in []arr let temp = {}; // Store occurrences of most significant character // from each integer in []count for (let i = lo; i <= hi; i++) { let c = digit_at(arr[i], d); count[c + 2]++; } // Change []count so that []count now contains actual // position of this digits in []temp for (let r = 0; r < 10 + 1; r++) count[r + 1] += count[r]; // Build the temp for (let i = lo; i <= hi; i++) { let c = digit_at(arr[i], d); temp[count[c + 1]++] = arr[i]; } // Copy all integers of temp to []arr, so that []arr now // contains partially sorted integers for (let 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 (let r = 0; r < 10; r++) MSD_sort(arr, lo + count[r], lo + count[r + 1] - 1, d - 1); } function getMax(arr, n) { let mx = arr[0]; for (let i = 1; i < n; i++) if (arr[i] > mx) mx = arr[i]; return mx; } function radixsort(arr, n) { // Find the maximum number to know number of digits let m = getMax(arr, n); // get the length of the largest integer let d = Math.floor(Math.log10(Math.abs(m))) + 1; // function call MSD_sort(arr, 0, n - 1, d); } // Driver Code let arr = [9330, 9950, 718, 8977, 6790, 95, 9807, 741, 8586, 5710]; // Size of the array let n = arr.length; console.log("Unsorted array : "); // Print the unsorted array print(arr, n); // Function Call radixsort(arr, n); console.log("Sorted array : "); // Print the sorted array print(arr, n); // This code is contributed by phasing17 ```

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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