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++ 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;
} |
// 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 |
# 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
|
// 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 |
<script> // JavaScript program to find the GCD of // elements which occur Fibonacci // number of times // Function to create hash table // to check Fibonacci numbers function 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 frequency function 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 code let 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> |
3
Time Complexity: O(N)
Auxiliary Space: O(N), since n extra space has been taken.