In this sorting algorithm, Hash Function f is used with the property of Order Preserving Function which states that if 
.
Hash Function:
f(x) = floor( (x/maximum) * SIZE )
where maximum => maximum value in the array,
SIZE => size of the address table (10 in our case),
floor => floor function
This algorithm uses an address table to store the values which is simply a list (or array) of Linked lists. The Hash function is applied to each value in the array to find its corresponding address in the address table. Then the values are inserted at their corresponding addresses in a sorted manner by comparing them to the values which are already present at that address.
Examples:
Input : arr = [29, 23, 14, 5, 15, 10, 3, 18, 1]
Output:
After inserting all the values in the address table, the address table looks like this:
ADDRESS 0: 1 --> 3
ADDRESS 1: 5
ADDRESS 2:
ADDRESS 3: 10
ADDRESS 4: 14 --> 15
ADDRESS 5: 18
ADDRESS 6:
ADDRESS 7: 23
ADDRESS 8:
ADDRESS 9: 29
The below figure shows the representation of the address table for the example discussed above:
After insertion, the values at each address in the address table are sorted. Hence we iterate through each address one by one and insert the values at that address in the input array. Below is the implementation of the above approach
Implementation:
C++
// C++ code for implementation of// Address Calculation Sorting using Hashing#include <bits/stdc++.h>#include <vector>using namespace std;// Size of the address table (In this case 0-9)const int SIZE = 10;class Node {public: int data; Node* nextNode; Node(int data = 0) { this->data = data; this->nextNode = nullptr; }};class LinkedList {public: Node* head; LinkedList() { this->head = nullptr; } // Insert values in such a way that the list remains sorted void insert(int data) { Node* newNode = new Node(data); // If there is no node or new Node's value // is smaller than the first value in the list, // Insert new Node in the first place if (this->head == nullptr || data < this->head->data) { newNode->nextNode = this->head; this->head = newNode; } else { Node* current = this->head; // If the next node is null or its value // is greater than the new Node's value, // Insert new Node in that place while (current->nextNode != nullptr && current->nextNode->data < data) { current = current->nextNode; } newNode->nextNode = current->nextNode; current->nextNode = newNode; } }};// This function returns the corresponding address// of given value in the address tableint hashFunction(int num, int maximum) { // Scale the value such that address is between 0 to 9 int address = static_cast<int>((num * 1.0 / maximum) * (SIZE - 1)); return address;}// This function sorts the given list// using Address Calculation Sorting using Hashingvoid addressCalculationSort(vector<int>& arr) { // Declare a list of Linked Lists of given SIZE vector<LinkedList*> listOfLinkedLists(SIZE, nullptr); for (int i = 0; i < SIZE; ++i) { listOfLinkedLists[i] = new LinkedList(); } // Calculate maximum value in the array int maximum = *max_element(arr.begin(), arr.end()); // Find the address of each value // in the address table // and insert it in that list for (int val : arr) { int address = hashFunction(val, maximum); listOfLinkedLists[address]->insert(val); } // Print the address table // after all the values have been inserted for (int i = 0; i < SIZE; ++i) { Node* current = listOfLinkedLists[i]->head; cout << "ADDRESS " << i << ": "; while (current != nullptr) { cout << current->data << " "; current = current->nextNode; } cout << endl; } // Assign the sorted values to the input array int index = 0; for (int i = 0; i < SIZE; ++i) { Node* current = listOfLinkedLists[i]->head; while (current != nullptr) { arr[index] = current->data; index++; current = current->nextNode; } }}// Driver codeint main() { // giving the input address as follows vector<int> arr = {29, 23, 14, 5, 15, 10, 3, 18, 1}; cout << "Input array: "; for(auto x : arr) cout << x << " "; cout << endl; // Function call addressCalculationSort(arr); cout << endl; cout << "Sorted array: "; for(auto x : arr) cout << x << " "; cout << endl;} |
Java
// Java code for implementation of// Address Calculation Sorting using Hashingimport java.util.ArrayList;class Node { int data; Node nextNode; Node(int data) { this.data = data; this.nextNode = null; }}class LinkedList { Node head; LinkedList() { this.head = null; } // Insert values in such a way that the list remains // sorted void insert(int data) { Node newNode = new Node(data); // If there is no node or new Node's value // is smaller than the first value in the list, // Insert new Node in the first place if (this.head == null || data < this.head.data) { newNode.nextNode = this.head; this.head = newNode; } else { Node current = this.head; // If the next node is null or its value // is greater than the new Node's value, // Insert new Node in that place while (current.nextNode != null && current.nextNode.data < data) { current = current.nextNode; } newNode.nextNode = current.nextNode; current.nextNode = newNode; } }}public class AddressCalculationSorting { // Size of the address table (In this case 0-9) static final int SIZE = 10; // This function returns the corresponding address // of given value in the address table static int hashFunction(int num, int maximum) { // Scale the value such that address is between 0 to // 9 int address = (int)((num * 1.0 / maximum) * (SIZE - 1)); return address; } // This function sorts the given list // using Address Calculation Sorting using Hashing static void addressCalculationSort(ArrayList<Integer> arr) { // Declare a list of Linked Lists of given SIZE ArrayList<LinkedList> listOfLinkedLists = new ArrayList<>(SIZE); for (int i = 0; i < SIZE; ++i) { listOfLinkedLists.add(new LinkedList()); } // Calculate maximum value in the array int maximum = arr.stream() .mapToInt(Integer::intValue) .max() .getAsInt(); // Find the address of each value // in the address table // and insert it in that list for (int val : arr) { int address = hashFunction(val, maximum); listOfLinkedLists.get(address).insert(val); } // Print the address table // after all the values have been inserted for (int i = 0; i < SIZE; ++i) { Node current = listOfLinkedLists.get(i).head; System.out.print("ADDRESS " + i + ": "); while (current != null) { System.out.print(current.data + " "); current = current.nextNode; } System.out.println(); } // Assign the sorted values to the input array int index = 0; for (int i = 0; i < SIZE; ++i) { Node current = listOfLinkedLists.get(i).head; while (current != null) { arr.set(index, current.data); index++; current = current.nextNode; } } } // Driver code public static void main(String[] args) { ArrayList<Integer> arr = new ArrayList<>(); // giving the input address as follows arr.add(29); arr.add(23); arr.add(14); arr.add(5); arr.add(15); arr.add(10); arr.add(3); arr.add(18); arr.add(1); System.out.print("Input array: "); for (int x : arr) { System.out.print(x + " "); } System.out.println(); // Function call addressCalculationSort(arr); System.out.println(); System.out.print("Sorted array: "); for (int x : arr) { System.out.print(x + " "); } System.out.println(); }}// This code is contributed by Samim Hossain Mondal. |
Python3
# Python3 code for implementation of# Address Calculation Sorting using Hashing# Size of the address table (In this case 0-9)SIZE = 10class Node(object): def __init__(self, data = None): self.data = data self.nextNode = Noneclass LinkedList(object): def __init__(self): self.head = None # Insert values in such a way that the list remains sorted def insert(self, data): newNode = Node(data) # If there is no node or new Node's value # is smaller than the first value in the list, # Insert new Node in the first place if self.head == None or data < self.head.data: newNode.nextNode = self.head self.head = newNode else: current = self.head # If the next node is null or its value # is greater than the new Node's value, # Insert new Node in that place while current.nextNode != None \ and \ current.nextNode.data < data: current = current.nextNode newNode.nextNode = current.nextNode current.nextNode = newNode # This function sorts the given list# using Address Calculation Sorting using Hashingdef addressCalculationSort(arr): # Declare a list of Linked Lists of given SIZE listOfLinkedLists = [] for i in range(SIZE): listOfLinkedLists.append(LinkedList()) # Calculate maximum value in the array maximum = max(arr) # Find the address of each value # in the address table # and insert it in that list for val in arr: address = hashFunction(val, maximum) listOfLinkedLists[address].insert(val) # Print the address table # after all the values have been inserted for i in range(SIZE): current = listOfLinkedLists[i].head print("ADDRESS " + str(i), end = ": ") while current != None: print(current.data, end = " ") current = current.nextNode print() # Assign the sorted values to the input array index = 0 for i in range(SIZE): current = listOfLinkedLists[i].head while current != None: arr[index] = current.data index += 1 current = current.nextNode # This function returns the corresponding address# of given value in the address tabledef hashFunction(num, maximum): # Scale the value such that address is between 0 to 9 address = int((num * 1.0 / maximum) * (SIZE-1)) return address# -------------------------------------------------------# Driver code# giving the input address as followsarr = [29, 23, 14, 5, 15, 10, 3, 18, 1]# Printing the Input arrayprint("\nInput array: " + " ".join([str(x) for x in arr]))# Performing address calculation sortaddressCalculationSort(arr)# printing the result sorted arrayprint("\nSorted array: " + " ".join([str(x) for x in arr])) |
C#
using System;using System.Collections.Generic;using System.Linq;class Node{ public int Data; public Node NextNode; public Node(int data) { this.Data = data; this.NextNode = null; }}class LinkedList{ public Node Head; public LinkedList() { this.Head = null; } // Insert values in such a way that the list remains // sorted public void Insert(int data) { Node newNode = new Node(data); // If there is no node or new Node's value // is smaller than the first value in the list, // Insert new Node in the first place if (this.Head == null || data < this.Head.Data) { newNode.NextNode = this.Head; this.Head = newNode; } else { Node current = this.Head; // If the next node is null or its value // is greater than the new Node's value, // Insert new Node in that place while (current.NextNode != null && current.NextNode.Data < data) { current = current.NextNode; } newNode.NextNode = current.NextNode; current.NextNode = newNode; } }}class AddressCalculationSorting{ // Size of the address table (In this case 0-9) static readonly int SIZE = 10; // This function returns the corresponding address // of the given value in the address table static int HashFunction(int num, int maximum) { // Scale the value such that the address is between 0 to 9 int address = (int)((num * 1.0 / maximum) * (SIZE - 1)); return address; } // This function sorts the given list // using Address Calculation Sorting using Hashing static void AddressCalculationSort(List<int> arr) { // Declare a list of Linked Lists of given SIZE List<LinkedList> listOfLinkedLists = new List<LinkedList>(SIZE); for (int i = 0; i < SIZE; ++i) { listOfLinkedLists.Add(new LinkedList()); } // Calculate the maximum value in the array int maximum = arr.Max(); // Find the address of each value // in the address table // and insert it in that list foreach (int val in arr) { int address = HashFunction(val, maximum); listOfLinkedLists[address].Insert(val); } // Print the address table // after all the values have been inserted for (int i = 0; i < SIZE; ++i) { Node current = listOfLinkedLists[i].Head; Console.Write("ADDRESS " + i + ": "); while (current != null) { Console.Write(current.Data + " "); current = current.NextNode; } Console.WriteLine(); } // Assign the sorted values to the input array int index = 0; for (int i = 0; i < SIZE; ++i) { Node current = listOfLinkedLists[i].Head; while (current != null) { arr[index] = current.Data; index++; current = current.NextNode; } } } // Driver code public static void Main(string[] args) { List<int> arr = new List<int>(); // giving the input address as follows arr.Add(29); arr.Add(23); arr.Add(14); arr.Add(5); arr.Add(15); arr.Add(10); arr.Add(3); arr.Add(18); arr.Add(1); Console.Write("Input array: "); foreach (int x in arr) { Console.Write(x + " "); } Console.WriteLine(); // Function call AddressCalculationSort(arr); Console.WriteLine(); Console.Write("Sorted array: "); foreach (int x in arr) { Console.Write(x + " "); } Console.WriteLine(); }}// This code is contributed by Samim Hossain Mondal. |
Javascript
// Python3 code for implementation of// Address Calculation Sorting using Hashing// Size of the address table (In this case 0-9)const SIZE = 10;class Node { constructor(data) { this.data = data; this.nextNode = null; }}class LinkedList { constructor() { this.head = null; } // Insert values in such a way that the list remains sorted insert(data) { const newNode = new Node(data); // If there is no node or new Node's value // is smaller than the first value in the list, // Insert new Node in the first place if (this.head === null || data < this.head.data) { newNode.nextNode = this.head; this.head = newNode; } else { let current = this.head; // If the next node is null or its value // is greater than the new Node's value, // Insert new Node in that place while (current.nextNode !== null && current.nextNode.data < data) { current = current.nextNode; } newNode.nextNode = current.nextNode; current.nextNode = newNode; } }}// This function sorts the given list// using Address Calculation Sorting using Hashingfunction addressCalculationSort(arr) { // Declare a list of Linked Lists of given SIZE const listOfLinkedLists = []; for (let i = 0; i < SIZE; i++) { listOfLinkedLists.push(new LinkedList()); } const maximum = Math.max(...arr); // Find the address of each value // in the address table // and insert it in that list for (const val of arr) { const address = hashFunction(val, maximum); listOfLinkedLists[address].insert(val); } // Print the address table // after all the values have been inserted for (let i = 0; i < SIZE; i++) { let current = listOfLinkedLists[i].head; process.stdout.write(`ADDRESS ${i}: `); while (current !== null) { process.stdout.write(`${current.data} `); current = current.nextNode; } process.stdout.write('\n'); } // Assign the sorted values to the input array let index = 0; for (let i = 0; i < SIZE; i++) { let current = listOfLinkedLists[i].head; while (current !== null) { arr[index] = current.data; index += 1; current = current.nextNode; } }}// This function returns the corresponding address// of given value in the address tablefunction hashFunction(num, maximum) { // Scale the value such that address is between 0 to 9 const address = Math.floor((num * 1.0 / maximum) * (SIZE - 1)); return address;}// Driver code// giving the input address as followsconst arr = [29, 23, 14, 5, 15, 10, 3, 18, 1];process.stdout.write(`\nInput array: ${arr.join(' ')}\n`);// Performing address calculation sortaddressCalculationSort(arr);// printing the result sorted arrayprocess.stdout.write(`\nSorted array: ${arr.join(' ')}\n`);//contributed by Aditya Sharma |
Output
Input array: 29 23 14 5 15 10 3 18 1 ADDRESS 0: 1 3 ADDRESS 1: 5 ADDRESS 2: ADDRESS 3: 10 ADDRESS 4: 14 15 ADDRESS 5: 18 ADDRESS 6: ADDRESS 7: 23 ADDRESS 8: ADDRESS 9: 29 Sorted array: 1 3 5 10 14 15 18 23 29
Time Complexity: The time complexity of this algorithm is 
in the best case. This happens when the values in the array are uniformly distributed within a specific range.
Whereas the worst-case time complexity is 
. This happens when most of the values occupy 1 or 2 addresses because then significant work is required to insert each value at its proper place.
