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:
- traverse the array and store the frequencies of all the elements in a map.
- 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++
// 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 numbersvoid 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 frequencyint 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 codeint main(){ int arr[] = { 5, 3, 6, 5, 6, 6, 5, 5 }; int n = sizeof(arr) / sizeof(arr[0]); cout << gcdFibonacciFreq(arr, n); return 0;} |
Java
// Java program to find the GCD of// elements which occur Fibonacci// number of timesimport java.util.*;class GFG{ // Function to create hash table// to check Fibonacci numbersstatic 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 frequencystatic 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 codepublic 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 |
Python3
# Python 3 program to find the GCD of# elements which occur Fibonacci# number of timesfrom collections import defaultdict import math # Function to create hash table# to check Fibonacci numbersdef 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 frequencydef 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 codeif __name__ == "__main__": arr = [ 5, 3, 6, 5, 6, 6, 5, 5 ] n = len(arr) print(gcdFibonacciFreq(arr, n)) # This code is contributed by chitranayal |
C#
// C# program to find the GCD of// elements which occur Fibonacci// number of timesusing System;using System.Linq;using System.Collections.Generic;class GFG{ // Function to create hash table// to check Fibonacci numbersstatic 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 frequencystatic 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 codepublic 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 |
Javascript
<script>// JavaScript program to find the GCD of// elements which occur Fibonacci// number of times// Function to create hash table// to check Fibonacci numbersfunction createHash(hash, maxElement){ // Inserting the first two // numbers into the hash let prev = 0, curr = 1; hash.add(prev); hash.add(curr); // Adding the remaining Fibonacci // numbers using the previously // added elements while (curr <= maxElement) { let temp = curr + prev; hash.add(temp); prev = curr; curr = temp; }}// Function to return the GCD of elements// in an array having fibonacci frequencyfunction gcdFibonacciFreq(arr, n){ let hash = new Set(); // Creating the hash createHash(hash, arr.sort((a, b) => b - a)[0]); let i, j; // Map is used to store the // frequencies of the elements let m = new Map(); // Iterating through the array for (i = 0; i < n; i++){ if(m.has(arr[i])){ m.set(arr[i], m.get(arr[i]) + 1) }else{ m.set(arr[i], 1) } } let gcd = 0; // Traverse the map using iterators for (let it of m) { // Calculate the gcd of elements // having fibonacci frequencies if (hash.has(it[1])) { gcd = __gcd(gcd, it[0]); } } return gcd;}function __gcd(a, b) { return (b == 0? a:__gcd(b, a % b)); } // Driver codelet arr = [ 5, 3, 6, 5, 6, 6, 5, 5 ];let n = arr.length;document.write(gcdFibonacciFreq(arr, n));// This code is contributed by gfgking</script> |
Output:
3
Time Complexity: O(N)
Auxiliary Space: O(N), since n extra space has been taken.
