In this guide, we will explore methods to identify an index with a hash collision in C++, accompanied by multiple illustrations.
Problem Statement:
Assume there is a value denoted as a along with an array P, which consists of n elements. In a hash table with 'a' buckets numbered from 0 to (a-1), the goal is to insert n numbers from the array P. The assignment of each number from the array P to a specific bucket is determined by the hash function h(P[i]), where P(k) = k mod a. It is important to note that each bucket is limited to holding only one element at a time.
A "collision" happens when attempting to add a new number to a full bucket, requiring the return of the index where the collision happened. If no collision occurs, the return value will be -1.
Algorithm 1:
1. Import vectors, unordered sets, and IO libraries as needed.
2. Function findCollisionIndex (a, P):
a. Create a blank set called buckets.
b. For every item in the array P[k]:
i. Use the modulo operation to calculate the bucket for P[k]: bucket = P[k] % a.
ii. Return I as the collision index if the bucket is located within the set buckets.
iii. If not, place the bucket into the designated buckets.
c. Return -1 if, after processing every element, no collision is discovered.
3. Main function:
a. Declare the variables a and n;
b. Read the input for a and n;
c. Make an array P that is empty and has size n;
d. Read the input for the P elements.
e. Make use of findCollisionIndex(a, P) and assign collisionIndex to the outcome.
f. If the collisionIndex is not equal to -1:
print- "Collision is found at index no: " + collisionIndex.
g.otherwise,
print- "No collision found".
4. End of Algorithm
Example 1:
Let's consider a C++ program that identifies an index where a hash collision occurs:
#include<iostream>
#include<vector>
#include<unordered_set>
int findColl (int a, const std::vector<int>& P) {
std::unordered_set<int> buckets;
for (int i = 0; i < P.size(); ++i)
{
int bucket = P[i] % a;
if (buckets.find(bucket) != buckets.end())
{
return i;
}
buckets.insert(bucket);
}
return -1; // No collision
}
int main() {
int a;
std::cout << "Enter the number of buckets (a): ";
std::cin >> a;
int n;
std::cout << "Enter the number of elements in the array (n): ";
std::cin >> n;
// Input the elements of the array (P)
std::vector<int> P(n);
std::cout << "Enter the elements of the array:" << std::endl;
for (int i = 0; i < n; ++i) {
std::cin >> P[i];
}
int collisionIndex = findColl(a, P);
if (collisionIndex != -1) {
std::cout << "Collision found at index: " << collisionIndex << std::endl;
} else {
std::cout << "No collision found." << std::endl;
}
return 0;
}
Output:
Algorithm 2:
a:= size of P
Create an array called Arr with the size n, then fill it with ?0?
initialize: i = 0; when i < n, update (increase I value by 1), do:
z = P[i]
If Arr[z mod n] is not equal to zero,
then
return i
increase Arr[z mod n] by 1
return i
Example 2:
Let's consider a different C++ program to identify an index where a hash collision occurs:
#include<iostream>
#include<vector>
#include<unordered_set>
int findCollisionIndex(int n, const std::vector<int>& P)
{
std::vector<int> arr(n, 0);
for (int i = 0; i < P.size(); ++i)
{
int z = P[i];
int bucket = z % n;
if (arr[bucket] != 0) {
return i;
}
arr[bucket]++;
}
return -1;
}
int main() {
int n, x;
// Input the number of buckets (n)
std::cout << "Enter the number of buckets (n): ";
std::cin >> n;
// Input the number of elements in the array (x)
std::cout << "Enter the number of elements in the array (x): ";
std::cin >> x;
// Input the elements of the array (P)
std::vector<int> P(n);
std::cout << "Enter the elements of the array:" << std::endl;
for (int i = 0; i < x; ++i) {
std::cin >> P[i];
}
// Find the collision index and print the result
int collisionIndex = findCollisionIndex(n, P);
if (collisionIndex != -1) {
std::cout << "Collision found at index: " << collisionIndex << std::endl;
} else {
std::cout << "No collision found." << std::endl;
}
return 0;
}
Output:
Conclusion:
In summary, it is evident that by employing the aforementioned methods to detect collisions, we can prevent data loss or ambiguity. Hash tables are capable of effectively and securely handling data, thanks to their proficient collision detection mechanisms, thus establishing them as dependable assets for managing data in extensive applications.
