Quadratic Probing in Hashing
Hashing is an improvement over 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 i2‘th slot in 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; } // Quadratic probing 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; } // Quadratic probing hashing(hash_table, L, arr, N); }} |
Python3
# Python3 implementation of# the Quadratic Probing# Function to pran 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 codearr = [ 50, 700, 76, 85, 92, 73, 101 ]N = 7# Size of the hash tableL = 7hash_table = [0] * 7# Initializing the hash tablefor i in range(L): hash_table[i] = -1 # Quadratic probinghashing(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 arraystatic 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 probingstatic 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 codepublic 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; } // Quadratic probing 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> |
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).
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