Largest subset whose all elements are Fibonacci numbers

Given an array with positive number the task is that we find largest subset from array that contain elements which are Fibonacci numbers.

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Examples :

Input : arr[] = {1, 4, 3, 9, 10, 13, 7};
Output : subset[] = {1, 3, 13}
The output three numbers are Fibonacci
numbers.

Input  : arr[] = {0, 2, 8, 5, 2, 1, 4, 
                  13, 23};
Output : subset[] = {0, 2, 8, 5, 2, 1, 
                    13, 23}

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution is to iterate through all elements of given array. For every number, check if it is Fibonacci or not. If yes, add it to the result.

Below is an efficient solution based on hashing.

Find max in the array
Generate Fibonacci numbers till the max and store it in hash table.
Traverse array again if the number is present in hash table then add it to the result.

C++

// C++ program to find largest Fibonacci subset 
#include<bits/stdc++.h> 
using namespace std; 
  
// Prints largest subset of an array whose 
// all elements are fibonacci numbers 
void findFibSubset(int arr[], int n) 
{ 
    // Find maximum element in arr[] 
    int max = *std::max_element(arr, arr+n); 
  
    // Generate all Fibonacci numbers till 
    // max and store them in hash. 
    int a = 0, b = 1; 
    unordered_set<int> hash; 
    hash.insert(a); 
    hash.insert(b); 
    while (b < max) 
    { 
        int c = a + b; 
        a = b; 
        b = c; 
        hash.insert(b); 
    } 
  
    // Npw iterate through all numbers and 
    // quickly check for Fibonacci using 
    // hash. 
    for (int i=0; i<n; i++) 
        if (hash.find(arr[i]) != hash.end()) 
            printf("%d ", arr[i]); 
} 
  
// Driver code 
int main() 
{ 
    int arr[] = {4, 2, 8, 5, 20, 1, 40, 13, 23}; 
    int n = sizeof(arr)/sizeof(arr[0]); 
    findFibSubset(arr, n); 
    return 0; 
} 

Java

// Java program to find  
// largest Fibonacci subset 
import java.util.*; 
  
class GFG 
{ 
    // Prints largest subset of an array whose 
    // all elements are fibonacci numbers 
    public static void findFibSubset(Integer[] x) 
    { 
        Integer max = Collections.max(Arrays.asList(x)); 
        List<Integer> fib = new ArrayList<Integer>();  
        List<Integer> result = new ArrayList<Integer>(); 
          
        // Generate all Fibonacci numbers  
        // till max and store them 
        Integer a = 0; 
        Integer b = 1; 
        while (b < max){ 
            Integer c = a + b; 
            a=b; 
            b=c; 
            fib.add(c); 
        } 
      
        // Now iterate through all numbers and 
        // quickly check for Fibonacci 
        for (Integer i = 0; i < x.length; i++){ 
        if(fib.contains(x[i])){ 
            result.add(x[i]);  
        }      
        } 
        System.out.println(result); 
    } 
  
    // Driver code 
    public static void main(String args[]) 
    { 
        Integer[] a = {4, 2, 8, 5, 20, 1, 40, 13, 23}; 
        findFibSubset(a); 
    } 
} 
  
// This code is contributed by prag93 

Python3

# python3 program to find largest Fibonacci subset 
   
# Prints largest subset of an array whose 
# all elements are fibonacci numbers 
def findFibSubset(arr, n): 
  
    # Find maximum element in arr[] 
    m= max(arr) 
   
    # Generate all Fibonacci numbers till 
    # max and store them in hash. 
    a = 0
    b = 1
    hash = [] 
    hash.append(a) 
    hash.append(b) 
    while (b < m): 
      
        c = a + b 
        a = b 
        b = c 
        hash.append(b) 
      
   
    # Npw iterate through all numbers and 
    # quickly check for Fibonacci using 
    # hash. 
    for i in range (n): 
        if arr[i] in hash : 
            print( arr[i],end=" ") 
   
# Driver code 
if __name__ == "__main__": 
  
    arr = [4, 2, 8, 5, 20, 1, 40, 13, 23] 
    n = len(arr) 
    findFibSubset(arr, n) 

C#

// C# program to find  
// largest Fibonacci subset 
using System; 
using System.Linq; 
using System.Collections.Generic;  
      
class GFG 
{ 
    // Prints largest subset of an array whose 
    // all elements are fibonacci numbers 
    public static void findFibSubset(int[] x) 
    { 
        int max = x.Max(); 
        List<int> fib = new List<int>();  
        List<int> result = new List<int>(); 
          
        // Generate all Fibonacci numbers  
        // till max and store them 
        int a = 0; 
        int b = 1; 
        while (b < max) 
        { 
            int c = a + b; 
            a = b; 
            b = c; 
            fib.Add(c); 
        } 
      
        // Now iterate through all numbers and 
        // quickly check for Fibonacci 
        for (int i = 0; i < x.Length; i++) 
        { 
            if(fib.Contains(x[i])) 
            { 
                result.Add(x[i]);  
            }      
        } 
        foreach(int i in result) 
            Console.Write(i + " "); 
    } 
  
    // Driver code 
    public static void Main(String []args) 
    { 
        int[] a = {4, 2, 8, 5, 20, 1, 40, 13, 23}; 
        findFibSubset(a); 
    } 
} 
  
// This code is contributed by PrinciRaj1992  

Output:

2 8 5 1 13

Reference :
https://www.careercup.com/question?id=5154130839470080

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My Personal Notes

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python3

C#

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