Hashing is a technique used in computer science to quickly find, store, and manage data. It works by taking an input, like a number or a string, and converting it into a fixed-size value called a hash. This hash then points to where the data is stored in a structure called a hash table. The main goal of hashing is to make data retrieval fast, even when dealing with large amounts of information. Hashing is widely used in various applications, such as searching databases, managing passwords, and speeding up data lookups in many types of software.
Number hashing is a powerful technique employed to store data efficiently in a manner that enables quick and easy retrieval. Formally, hashing can be defined as the process of mapping data to a specific location or index in a data structure, typically an array, such that this data can be efficiently accessed at a later time. Hashing serves as the backbone for many algorithms and real-life applications where fast data retrieval is critical.
Consider a practical scenario in a food delivery application, where the use of hashing can be observed seamlessly.
On the first day, a customer places an order through the app. The application collects various details related to the order, such as the food items selected, delivery address, and payment information. All this information is stored securely in a database. The next time the customer uses the app, say on the following day, the application automatically retrieves the previously stored information, such as the delivery address, and suggests it for autofill. This convenience is achieved by fetching the data from internal memory where it was stored during the initial interaction.
From a technical perspective, this process of storing and retrieving information efficiently is an implementation of hashing. When the order details are first stored, they are hashed into specific locations in a database, where the data is associated with the customer’s profile. When the customer returns, the same hashing technique is employed to quickly locate the stored information, allowing the application to present it without requiring the user to re-enter the details.
In the context of arrays, hashing provides a highly efficient method for solving problems like counting the frequency of elements. Consider the array arr[] = {5, 6, 5, 6, 9, 6}. To determine how many times the number 6 appears in this array, there are several approaches that can be taken.
The simplest method involves traversing the entire array and counting the occurrences of the number 6. Although this method is straightforward, it is not optimal for large datasets as it requires a complete traversal of the array.
#include<bits/stdc++.h>
using namespace std;
int main() {
int arr[] = {5, 6, 5, 6, 9, 6};
int count = 0;
for(int i = 0; i < 6; i++) {
if(arr[i] == 6) {
count++;
}
}
cout << count << endl; // Output: 3
return 0;
}int[] arr = {5, 6, 5, 6, 9, 6};
int count = 0;
for (int num : arr) {
if (num == 6) {
count++;
}
}
System.out.println(count); // Output: 3arr = [5, 6, 5, 6, 9, 6]
count = 0
for num in arr:
if num == 6:
count += 1
print(count) # Output: 3const arr = [5, 6, 5, 6, 9, 6];
let count = 0;
for (let i = 0; i < arr.length; i++) {
if (arr[i] === 6) {
count++;
}
}
console.log(count); // Output: 3
A more efficient approach involves using hashing. Here, the array is hashed into another array, often called a hash table, where the index represents the element value and the content at that index represents the count of occurrences. This method allows the counting operation to be completed in a single iteration of the array, making it highly efficient.
#include<bits/stdc++.h>
using namespace std;
int main() {
int arr[] = {5, 6, 5, 6, 9, 6};
int hashTable[10] = {0};
for(int i = 0; i < 6; i++) {
hashTable[arr[i]]++;
}
cout << hashTable[6] << endl; // Output: 3
return 0;
}int[] arr = {5, 6, 5, 6, 9, 6};
int[] hashTable = new int[10];
for (int num : arr) {
hashTable[num]++;
}
System.out.println(hashTable[6]); // Output: 3
arr = [5, 6, 5, 6, 9, 6]
hash_table = [0] * 10
for num in arr:
hash_table[num] += 1
print(hash_table[6]) # Output: 3const arr = [5, 6, 5, 6, 9, 6];
const hashTable = new Array(10).fill(0);
for (let i = 0; i < arr.length; i++) {
hashTable[arr[i]]++;
}
console.log(hashTable[6]); // Output: 3
Character hashing is a specialized form of hashing used to efficiently store and retrieve data related to individual characters, particularly within a given character set such as ASCII. This technique is invaluable in various applications, from counting character frequencies to implementing efficient lookups in text processing tasks. In this editorial, the focus will be on hashing techniques for lowercase alphabets using ASCII values, with considerations for time complexity (TC) and space complexity (SC).
The American Standard Code for Information Interchange (ASCII) is a character encoding standard that assigns numerical values to characters, with lowercase letters 'a' through 'z' being assigned values from 97 to 122. This simple numerical assignment allows characters to be easily manipulated and processed in hashing operations.
For instance, if there is a need to increment a value associated with the character 'a', the corresponding operation in terms of its ASCII value would be:
hash['a']++ translates to hash[97]++
This direct mapping between characters and their ASCII values allows for the creation of a hash table where each index corresponds to a specific character. When dealing with only lowercase alphabets, this hash table can be efficiently utilized by reducing the character’s ASCII value relative to 'a'.
The efficiency of character hashing can be measured in terms of time complexity (TC) and space complexity (SC). Given a string of length N and q queries, the operations can be completed in O(N) + O(q) time. Here, O(N) accounts for the time required to initialize and populate the hash table, while O(q) refers to the time required to process each query.
As for space complexity, since the ASCII values for lowercase letters range from 97 to 122, the hash table needs to accommodate 123 possible indices. Thus, the space complexity is O(123), which is manageable and efficient for most applications.
When dealing exclusively with lowercase letters, the hash table can be further optimized by indexing relative to the character 'a'. For example:
hash['b' - 'a'] = hash[1]
In this context, 'b' - 'a' computes to 1, which allows for efficient storage and retrieval in a zero-indexed array structure. This technique not only simplifies the process but also reduces the required space since only 26 indices (0 through 25) need to be managed, rather than the full ASCII range.
The approach to character hashing can vary across different programming languages, especially in terms of the data structures used and their performance characteristics. Below are two prominent examples using C++ and Java.
In C++, one can utilize either an unordered_map or a map to implement character hashing. The choice between these structures depends on the specific use case:
unordered_map: Offers an average time complexity of O(1) for insertions, deletions, and lookups. However, in the worst-case scenario, typically due to hash collisions, the time complexity can degrade to O(N).map: Implements a balanced binary tree, offering a guaranteed time complexity of O(log N) for all operations, regardless of collisions.Java provides similar data structures for character hashing, with analogous performance characteristics:
HashMap: Like unordered_map in C++, HashMap offers an average time complexity of O(1). However, due to collisions, its worst-case performance can degrade to O(N).TreeMap: Functions similarly to map in C++, with a time complexity of O(log N), ensuring consistent performance across all operations.Hashing is a fundamental technique used to map data to specific locations in a data structure. Various methods can be employed internally to calculate hash values, each with its own unique approach and applications. In this editorial, we will delve into three widely used hashing methods: the division method, the folding method, and the mid-square method. Additionally, we will explore how the division method implements chaining internally to resolve collisions, along with common problems associated with these techniques.
The division method is one of the simplest and most commonly used hashing techniques. The fundamental idea behind this method is to divide the key by a suitable prime number and use the remainder as the hash value. The choice of the prime number is crucial as it ensures a more uniform distribution of hash values, thereby minimizing collisions.
p, which will serve as the divisor in the hashing process. Prime numbers are preferred because they tend to distribute hash values more uniformly across the available range.
k, the hash value h(k) is computed using the formula:
h(k) = k % p
%) returns the remainder when the key k is divided by the prime number p. This remainder serves as the index in the hash table where the key will be stored.
Consider a scenario where a set of keys {56, 75, 42, 88, 91} needs to be stored in a hash table. Let's choose a prime number p = 7 as the divisor.
56: h(56) = 56 % 7 = 0 (Store at index 0)75: h(75) = 75 % 7 = 5 (Store at index 5)42: h(42) = 42 % 7 = 0 (Collision occurs at index 0)88: h(88) = 88 % 7 = 4 (Store at index 4)91: h(91) = 91 % 7 = 0 (Collision occurs at index 0)In this example, multiple keys are mapped to the same index, leading to collisions at index 0. The division method alone does not address collisions, which is why additional techniques such as chaining are implemented internally to manage them.
The folding method is a hashing technique where the key is divided into equal parts, and these parts are added together to form the hash value. If the key cannot be evenly divided, the remaining digits can be handled by various strategies such as padding or wrapping around.
The mid-square method involves squaring the key and then extracting a portion of the resulting digits, typically from the middle, to use as the hash value. This method benefits from its ability to spread out similar keys more uniformly across the hash table.
Chaining is a collision resolution technique commonly used in conjunction with the division method. When two keys hash to the same index, chaining stores them in a linked list or another secondary data structure at that index, thereby allowing multiple elements to occupy the same position in the hash table.
k, compute the hash value using the division method. If a collision occurs (i.e., the computed index is already occupied), append the new key to the linked list at that index.
Using the same set of keys {56, 75, 42, 88, 91} and prime number p = 7, chaining can be implemented as follows:
56: h(56) = 0 (Insert into the list at index 0)
75: h(75) = 5 (Insert into the list at index 5)
42: h(42) = 0 (Append to the list at index 0, which now contains 56 -> 42)
88: h(88) = 4 (Insert into the list at index 4)
91: h(91) = 0 (Append to the list at index 0, which now contains 56 -> 42 -> 91)
Chaining effectively resolves collisions by allowing multiple keys to coexist at the same index without overwriting each other. This method maintains the efficiency of the division method while ensuring that all keys are accessible, even in the presence of collisions.
While these hashing techniques are powerful, they are not without challenges:
Hashing is a critical technique in computer science used for efficient data management. It simplifies data retrieval by transforming input into a fixed-size value. Number hashing utilizes methods like division to map numeric values to indices, with techniques like chaining handling collisions. Character hashing applies similar principles to characters, often using ASCII values to count occurrences or manage text efficiently. Internal hashing methods such as folding and mid-square offer alternative ways to generate hash values and handle collisions, ensuring effective data distribution. Together, these techniques enable fast and reliable data operations across various applications.