GCD of elements occurring Fibonacci number of times in an Array

Given an array arr[] containing N elements, the task is to find the GCD of the elements which have frequency count which is a Fibonacci number in the array.

Examples:

Input: arr[] = { 5, 3, 6, 5, 6, 6, 5, 5 }
Output: 3
Explanation :
Elements 5, 3, 6 appears 4, 1, 3 times respectively.
Hence, 3 and 6 have Fibonacci frequencies.
So, gcd(3, 6) = 1

Input: arr[] = {4, 2, 3, 3, 3, 3}
Output: 2
Explanation :
Elements 4, 2, 3 appears 1, 1, 4 times respectively.
Hence, 4 and 2 have Fibonacci frequencies.
So, gcd(4, 2) = 2

Approach: The idea is to use hashing to precompute and store the Fibonacci nodes up to the maximum value to make checking easy and efficient (in O(1) time).



After precomputing the hash:

  1. traverse the array and store the frequencies of all the elements in a map.
  2. Using the map and hash, calculate the gcd of elements having fibonacci frequency using the precomputed hash.

Below is the implementation of the above approach:

C++

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// C++ program to find the GCD of
// elements which occur Fibonacci
// number of times
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to create hash table
// to check Fibonacci numbers
void createHash(set<int>& hash,
                int maxElement)
{
    // Inserting the first two
    // numbers into the hash
    int prev = 0, curr = 1;
    hash.insert(prev);
    hash.insert(curr);
  
    // Adding the remaining Fibonacci
    // numbers using the previously
    // added elements
    while (curr <= maxElement) {
        int temp = curr + prev;
        hash.insert(temp);
        prev = curr;
        curr = temp;
    }
}
  
// Function to return the GCD of elements
// in an array having fibonacci frequency
int gcdFibonacciFreq(int arr[], int n)
{
    set<int> hash;
  
    // Creating the hash
    createHash(hash,
               *max_element(arr,
                            arr + n));
  
    int i, j;
  
    // Map is used to store the
    // frequencies of the elements
    unordered_map<int, int> m;
  
    // Iterating through the array
    for (i = 0; i < n; i++)
        m[arr[i]]++;
  
    int gcd = 0;
  
    // Traverse the map using iterators
    for (auto it = m.begin();
         it != m.end(); it++) {
  
        // Calculate the gcd of elements
        // having fibonacci frequencies
        if (hash.find(it->second)
            != hash.end()) {
            gcd = __gcd(gcd,
                        it->first);
        }
    }
  
    return gcd;
}
  
// Driver code
int main()
{
    int arr[] = { 5, 3, 6, 5,
                  6, 6, 5, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << gcdFibonacciFreq(arr, n);
  
    return 0;
}

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Java

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// Java program to find the GCD of
// elements which occur Fibonacci
// number of times
import java.util.*;
  
class GFG{
   
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet<Integer> hash,
                int maxElement)
{
    // Inserting the first two
    // numbers into the hash
    int prev = 0, curr = 1;
    hash.add(prev);
    hash.add(curr);
   
    // Adding the remaining Fibonacci
    // numbers using the previously
    // added elements
    while (curr <= maxElement) {
        int temp = curr + prev;
        hash.add(temp);
        prev = curr;
        curr = temp;
    }
}
   
// Function to return the GCD of elements
// in an array having fibonacci frequency
static int gcdFibonacciFreq(int arr[], int n)
{
    HashSet<Integer> hash = new HashSet<Integer>();
   
    // Creating the hash
    createHash(hash,Arrays.stream(arr).max().getAsInt());
   
    int i;
   
    // Map is used to store the
    // frequencies of the elements
    HashMap<Integer,Integer> m = new HashMap<Integer,Integer>();
   
    // Iterating through the array
    for (i = 0; i < n; i++) {
        if(m.containsKey(arr[i])){
            m.put(arr[i], m.get(arr[i])+1);
        }
        else{
            m.put(arr[i], 1);
        }
    }
   
    int gcd = 0;
   
    // Traverse the map using iterators
    for (Map.Entry<Integer, Integer> it : m.entrySet()) {
   
        // Calculate the gcd of elements
        // having fibonacci frequencies
        if (hash.contains(it.getValue())) {
            gcd = __gcd(gcd,
                        it.getKey());
        }
    }
   
    return gcd;
}
static int __gcd(int a, int b)  
{  
    return b == 0? a:__gcd(b, a % b);     
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 5, 3, 6, 5,
                  6, 6, 5, 5 };
    int n = arr.length;
   
    System.out.print(gcdFibonacciFreq(arr, n));
}
}
  
// This code is contributed by Princi Singh

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Python3

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# Python 3 program to find the GCD of
# elements which occur Fibonacci
# number of times
from collections import defaultdict 
import math 
   
# Function to create hash table
# to check Fibonacci numbers
def createHash(hash1,maxElement):
  
    # Inserting the first two
    # numbers into the hash
    prev , curr = 0, 1
    hash1.add(prev)
    hash1.add(curr)
   
    # Adding the remaining Fibonacci
    # numbers using the previously
    # added elements
    while (curr <= maxElement):
        temp = curr + prev
        if temp <= maxElement:
            hash1.add(temp)
        prev = curr
        curr = temp
   
# Function to return the GCD of elements
# in an array having fibonacci frequency
def gcdFibonacciFreq(arr, n):
  
    hash1 = set()
   
    # Creating the hash
    createHash(hash1,max(arr))
   
    # Map is used to store the
    # frequencies of the elements
    m = defaultdict(int)
   
    # Iterating through the array
    for i in range(n):
        m[arr[i]] += 1
   
    gcd = 0
   
    # Traverse the map using iterators
    for it in m.keys():
   
        # Calculate the gcd of elements
        # having fibonacci frequencies
        if (m[it] in hash1):
            gcd = math.gcd(gcd,it)
    return gcd
   
# Driver code
if __name__ == "__main__":
      
    arr = [ 5, 3, 6, 5,
                  6, 6, 5, 5 ]
    n = len(arr)
   
    print(gcdFibonacciFreq(arr, n))
   
 # This code is contributed by chitranayal

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C#

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// C# program to find the GCD of
// elements which occur Fibonacci
// number of times
using System;
using System.Linq;
using System.Collections.Generic;
  
class GFG{
    
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet<int> hash,
                int maxElement)
{
    // Inserting the first two
    // numbers into the hash
    int prev = 0, curr = 1;
    hash.Add(prev);
    hash.Add(curr);
    
    // Adding the remaining Fibonacci
    // numbers using the previously
    // added elements
    while (curr <= maxElement) {
        int temp = curr + prev;
        hash.Add(temp);
        prev = curr;
        curr = temp;
    }
}
    
// Function to return the GCD of elements
// in an array having fibonacci frequency
static int gcdFibonacciFreq(int []arr, int n)
{
    HashSet<int> hash = new HashSet<int>();
    
    // Creating the hash
    createHash(hash, hash.Count > 0 ? hash.Max():0);
    
    int i;
    
    // Map is used to store the
    // frequencies of the elements
    Dictionary<int,int> m = new Dictionary<int,int>();
    
    // Iterating through the array
    for (i = 0; i < n; i++) {
        if(m.ContainsKey(arr[i])){
            m[arr[i]] = m[arr[i]] + 1;
        }
        else{
            m.Add(arr[i], 1);
        }
    }
    
    int gcd = 0;
    
    // Traverse the map using iterators
    foreach(KeyValuePair<int, int> it in m) {
    
        // Calculate the gcd of elements
        // having fibonacci frequencies
        if (hash.Contains(it.Value)) {
            gcd = __gcd(gcd,
                        it.Key);
        }
    }
    
    return gcd;
}
static int __gcd(int a, int b)  
{  
    return b == 0? a:__gcd(b, a % b);     
   
// Driver code
public static void Main(String[] args)
{
    int []arr = { 5, 3, 6, 5,
                  6, 6, 5, 5 };
    int n = arr.Length;
    
    Console.Write(gcdFibonacciFreq(arr, n));
}
}
  
// This code is contributed by 29AjayKumar

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Output:

3

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