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# Largest subset whose all elements are Fibonacci numbers

• Difficulty Level : Easy
• Last Updated : 16 Nov, 2022

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

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:

## C++

 `#include ``using` `namespace` `std;``void` `findFibSubset(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `fact1 = 5 * ``pow``(arr[i], 2) + 4;``        ``int` `fact2 = 5 * ``pow``(arr[i], 2) - 4;``        ``if` `((``int``)``pow``((``int``)``pow``(fact1, 0.5), 2) == fact1``            ``|| (``int``)``pow``((``int``)``pow``(fact2, 0.5), 2) == fact2)``            ``cout << arr[i] << ``" "``;``    ``}``}` `int` `main()``{``    ``int` `arr[] = { 4, 2, 8, 5, 20, 1, 40, 13, 23 };``    ``int` `n = 9;``    ``findFibSubset(arr, n);``}` `// This code is contributed by garg28harsh.`

## Java

 `/*package whatever //do not write package name here */``import` `java.util.*;``class` `GFG {` `  ``static` `void` `findFibSubset(``int` `arr[], ``int` `n)``  ``{``    ``for``(``int` `i = ``0``; i < n; i++){``      ``int` `fact1 = ``5` `* (``int``)Math.pow(arr[i], ``2``) + ``4``;``      ``int` `fact2 = ``5` `* (``int``)Math.pow(arr[i], ``2``) - ``4``;``      ``if``((``int``)Math.pow((``int``)Math.pow(fact1, ``0.5``), ``2``) == fact1 || (``int``)Math.pow((``int``)Math.pow(fact2, ``0.5``), ``2``) == fact2)``        ``System.out.print(arr[i] + ``" "``);``    ``}``  ``}` `  ``public` `static` `void` `main (String[] args) {``    ``int` `[]arr = {``4``, ``2``, ``8``, ``5``, ``20``, ``1``, ``40``, ``13``, ``23``};``    ``int` `n = arr.length;``    ``findFibSubset(arr, n);``  ``}``}` `// This code is contributed by aadityaburujwale.`

## 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)`

## C#

 `using` `System;``class` `GFG {``  ``static` `void` `findFibSubset(``int``[] arr, ``int` `n)``  ``{``    ``for` `(``int` `i = 0; i < n; i++) {``      ``int` `fact1 = 5 * (``int``)Math.Pow(arr[i], 2) + 4;``      ``int` `fact2 = 5 * (``int``)Math.Pow(arr[i], 2) - 4;``      ``if` `((``int``)Math.Pow((``int``)Math.Pow(fact1, 0.5), 2)``          ``== fact1``          ``|| (``int``)Math.Pow((``int``)Math.Pow(fact2, 0.5),``                           ``2)``          ``== fact2)``        ``Console.Write(arr[i] + ``" "``);``    ``}``  ``}``  ``static` `void` `Main()``  ``{``    ``int``[] arr = { 4, 2, 8, 5, 20, 1, 40, 13, 23 };``    ``int` `n = 9;``    ``findFibSubset(arr, n);``  ``}``}` `// This code is contributed by garg28harsh.`

## Javascript

 `function` `findFibSubset( arr,  n)``{``    ``let ans=[];``    ``for` `(let i = 0; i < n; i++) {``        ``let fact1 = 5 * Math.pow(arr[i], 2) + 4;``        ``let fact2 = 5 * Math.pow(arr[i], 2) - 4;``        ``if` `(Math.pow(Math.round(Math.pow(fact1, 0.5)), 2) == fact1  || Math.pow(Math.round(Math.pow(fact2, 0.5)), 2) == fact2)``            ``ans.push(arr[i]);``    ``}``    ``console.log(ans);``}` `    ``let arr = [ 4, 2, 8, 5, 20, 1, 40, 13, 23 ];``    ``let n = 9;``    ``findFibSubset(arr, n);``    ` `    ``// This code is contributed by garg28harsh.`

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``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

## 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 fib = ``new` `ArrayList();``        ``List result = ``new` `ArrayList();``        ` `        ``// 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

 ``

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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