# 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.

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.

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.

## 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  `

Output:

```2 8 5 1 13
```

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