Hashing is an improvement technique over the Direct Access Table. The idea is to use a hash function that converts a given phone number or any other key to a smaller number and uses the small number as the index in a table called a hash table.
Hash Function:
A function that converts a given big number to a small practical integer value. The mapped integer value is used as an index in the hash table. In simple terms, a hash function maps a big number or string to a small integer that can be used as an index in the hash table. In this article, the collision technique, quadratic probing is discussed:
Quadratic Probing:
Quadratic probing is an open-addressing scheme where we look for the i2‘th slot in the i’th iteration if the given hash value x collides in the hash table.
How Quadratic Probing is done?
Let hash(x) be the slot index computed using the hash function.
- If the slot hash(x) % S is full, then we try (hash(x) + 1*1) % S.
- If (hash(x) + 1*1) % S is also full, then we try (hash(x) + 2*2) % S.
- If (hash(x) + 2*2) % S is also full, then we try (hash(x) + 3*3) % S.
- This process is repeated for all the values of i until an empty slot is found.
For example: Let us consider a simple hash function as “key mod 7” and sequence of keys as 50, 700, 76, 85, 92, 73, 101
Below is the implementation of the above approach:
C++
// C++ implementation of// the Quadratic Probing#include <bits/stdc++.h>using namespace std;// Function to print an arrayvoid printArray(int arr[], int n){ // Iterating and printing the array for (int i = 0; i < n; i++) { cout << arr[i] << " "; }}// Function to implement the// quadratic probingvoid hashing(int table[], int tsize, int arr[], int N){ // Iterating through the array for (int i = 0; i < N; i++) { // Computing the hash value int hv = arr[i] % tsize; // Insert in the table if there // is no collision if (table[hv] == -1) table[hv] = arr[i]; else { // If there is a collision // iterating through all // possible quadratic values for (int j = 0; j < tsize; j++) { // Computing the new hash value int t = (hv + j * j) % tsize; if (table[t] == -1) { // Break the loop after // inserting the value // in the table table[t] = arr[i]; break; } } } } printArray(table, N);}// Driver codeint main(){ int arr[] = { 50, 700, 76, 85, 92, 73, 101 }; int N = 7; // Size of the hash table int L = 7; int hash_table[7]; // Initializing the hash table for (int i = 0; i < L; i++) { hash_table[i] = -1; } // Function call hashing(hash_table, L, arr, N); return 0;}// This code is contributed by gauravrajput1 |
Java
// Java implementation of the Quadratic Probingclass GFG { // Function to print an array static void printArray(int arr[]) { // Iterating and printing the array for (int i = 0; i < arr.length; i++) { System.out.print(arr[i] + " "); } } // Function to implement the // quadratic probing static void hashing(int table[], int tsize, int arr[], int N) { // Iterating through the array for (int i = 0; i < N; i++) { // Computing the hash value int hv = arr[i] % tsize; // Insert in the table if there // is no collision if (table[hv] == -1) table[hv] = arr[i]; else { // If there is a collision // iterating through all // possible quadratic values for (int j = 0; j < tsize; j++) { // Computing the new hash value int t = (hv + j * j) % tsize; if (table[t] == -1) { // Break the loop after // inserting the value // in the table table[t] = arr[i]; break; } } } } printArray(table); } // Driver code public static void main(String args[]) { int arr[] = { 50, 700, 76, 85, 92, 73, 101 }; int N = 7; // Size of the hash table int L = 7; int hash_table[] = new int[L]; // Initializing the hash table for (int i = 0; i < L; i++) { hash_table[i] = -1; } // Function call hashing(hash_table, L, arr, N); }} |
Python3
# Python3 implementation of# the Quadratic Probing# Function to print an arraydef printArray(arr, n): # Iterating and printing the array for i in range(n): print(arr[i], end=" ")# Function to implement the# quadratic probingdef hashing(table, tsize, arr, N): # Iterating through the array for i in range(N): # Computing the hash value hv = arr[i] % tsize # Insert in the table if there # is no collision if (table[hv] == -1): table[hv] = arr[i] else: # If there is a collision # iterating through all # possible quadratic values for j in range(tsize): # Computing the new hash value t = (hv + j * j) % tsize if (table[t] == -1): # Break the loop after # inserting the value # in the table table[t] = arr[i] break printArray(table, N)# Driver codeif __name__ == "__main__": arr = [50, 700, 76, 85, 92, 73, 101] N = 7 # Size of the hash table L = 7 hash_table = [0] * 7 # Initializing the hash table for i in range(L): hash_table[i] = -1 # Function call hashing(hash_table, L, arr, N)# This code is contributed by code_hunt |
C#
// C# implementation of the Quadratic Probingusing System;class GFG { // Function to print an array static void printArray(int[] arr) { // Iterating and printing the array for (int i = 0; i < arr.Length; i++) { Console.Write(arr[i] + " "); } } // Function to implement the // quadratic probing static void hashing(int[] table, int tsize, int[] arr, int N) { // Iterating through the array for (int i = 0; i < N; i++) { // Computing the hash value int hv = arr[i] % tsize; // Insert in the table if there // is no collision if (table[hv] == -1) table[hv] = arr[i]; else { // If there is a collision // iterating through all // possible quadratic values for (int j = 0; j < tsize; j++) { // Computing the new hash value int t = (hv + j * j) % tsize; if (table[t] == -1) { // Break the loop after // inserting the value // in the table table[t] = arr[i]; break; } } } } printArray(table); } // Driver code public static void Main(String[] args) { int[] arr = { 50, 700, 76, 85, 92, 73, 101 }; int N = 7; // Size of the hash table int L = 7; int[] hash_table = new int[L]; // Initializing the hash table for (int i = 0; i < L; i++) { hash_table[i] = -1; } // Function call hashing(hash_table, L, arr, N); }}// This code is contributed by Rajput-Ji |
Javascript
<script>// Javascript implementation of the Quadratic Probing // Function to print an array function printArray(arr) { // Iterating and printing the array for (let i = 0; i < arr.length; i++) { document.write(arr[i] + " "); } } // Function to implement the // quadratic probing function hashing(table, tsize, arr, N) { // Iterating through the array for (let i = 0; i < N; i++) { // Computing the hash value let hv = arr[i] % tsize; // Insert in the table if there // is no collision if (table[hv] == -1) table[hv] = arr[i]; else { // If there is a collision // iterating through all // possible quadratic values for (let j = 0; j < tsize; j++) { // Computing the new hash value let t = (hv + j * j) % tsize; if (table[t] == -1) { // Break the loop after // inserting the value // in the table table[t] = arr[i]; break; } } } } printArray(table); } // Driver Code let arr = [ 50, 700, 76, 85, 92, 73, 101 ]; let N = 7; // Size of the hash table let L = 7; let hash_table = []; // Initializing the hash table for (let i = 0; i < L; i++) { hash_table[i] = -1; } // Quadratic probing hashing(hash_table, L, arr, N);// This code is contributed by splevel62.</script> |
Output
700 50 85 73 101 92 76
Time Complexity: O(N * L), where N is the length of the array and L is the size of the hash table.
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
