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}

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.

Implementation:

Python3

# python3 program to find largest Fibonacci subset
# Prints largest subset of an array whose
# all elements are fibonacci numbers
def findFibSubset(arr, n):
  #Now iterate through all elements of the array..
  for i in range(n):
    #we are using the property of fibonacci series to check arr[i] is a
    # fib number or not by checking whether any one out of 5(n^2)+4 and 5(n^2)-4
    # is a perfect square or not.
    fact1=5*(arr[i]**2)+4
    fact2=5*(arr[i]**2)-4
    if int(fact1**(.5))**2==fact1 or int(fact2**(.5))**2==fact2:
      print(arr[i],end=" ")
  return None


 # Driver code
if __name__ == "__main__":

    arr = [4, 2, 8, 5, 20, 1, 40, 13, 23]
    n = len(arr)
    findFibSubset(arr, n)
 # This code is contributed by Rajat Kumar (GLA University)

Output

2 8 5 1 13 

Time complexity: Time complexity of the above solution is O(n) and space complexity is O(1).

Below is an another solution based on hashing. 

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

Implementation:

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

Javascript

<script>

// Javascript program to find largest Fibonacci subset

// Prints largest subset of an array whose
// all elements are fibonacci numbers
function findFibSubset(arr, n)
{
    // Find maximum element in arr[]
    var max = arr.reduce((a,b)=>Math.max(a,b))

    // Generate all Fibonacci numbers till
    // max and store them in hash.
    var a = 0, b = 1;
    var hash = new Set();
    hash.add(a);
    hash.add(b);
    while (b < max)
    {
        var c = a + b;
        a = b;
        b = c;
        hash.add(b);
    }

    // Npw iterate through all numbers and
    // quickly check for Fibonacci using
    // hash.
    for (var i=0; i<n; i++)
        if (hash.has(arr[i]))
            document.write( arr[i]
            + " ");
}

// Driver code
var arr = [4, 2, 8, 5, 20, 1, 40, 13, 23];
var n = arr.length;
findFibSubset(arr, n);

// This code is contributed by famously.
</script>

Output

2 8 5 1 13 

Time Complexity: Time complexity of above code is O(n) and space complexity will also be O(n) as we are storing it in hash map each fibonacci number in hashmap….

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