# Length of longest subsequence of Fibonacci Numbers in an Array

Given an array arr containing non-negative integers, the task is to print the length of the longest subsequence of Fibonacci numbers in this array.

Examples:

Input: arr[] = { 3, 4, 11, 2, 9, 21 }
Output: 3
Here, the subsequence is {3, 2, 21} and hence the answer is 3.

Input: arr[] = { 6, 4, 10, 13, 9, 25 }
Output: 1
Here, the subsequence is {1} and hence the answer is 1.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Build hash table containing all the Fibonacci numbers which will be used to test a number in O(1) time.
• Now, we will traverse through the given array.
• We will include all the Fibonacci numbers that we encounter during our traversal into the longest subsequence and hence increase the answer by 1 for every encounter of a Fibonacci number.
• Once the entire initial array has been encountered, we have the length of the longest subsequence containing only Fibonacci numbers with us.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the length ` `// of longest subsequence of ` `// Fibonacci Numbers in an Array ` ` `  `#include ` `using` `namespace` `std; ` `#define N 100005 ` ` `  `// Function to create hash table ` `// to check Fibonacci numbers ` `void` `createHash(set<``int``>& hash, ` `                ``int` `maxElement) ` `{ ` `    ``int` `prev = 0, curr = 1; ` `    ``hash.insert(prev); ` `    ``hash.insert(curr); ` ` `  `    ``while` `(curr <= maxElement) { ` `        ``int` `temp = curr + prev; ` `        ``hash.insert(temp); ` `        ``prev = curr; ` `        ``curr = temp; ` `    ``} ` `} ` ` `  `// Function to find the longest ` `// subsequence containing ` `// all Fibonacci numbers ` `int` `longestFibonacciSubsequence( ` `    ``int` `arr[], ``int` `n) ` `{ ` `    ``set<``int``> hash; ` `    ``createHash( ` `        ``hash, ` `        ``*max_element(arr, arr + n)); ` ` `  `    ``int` `answer = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(hash.find(arr[i]) ` `            ``!= hash.end()) { ` `            ``answer++; ` `        ``} ` `    ``} ` ` `  `    ``return` `answer; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 3, 4, 11, 2, 9, 21 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``// Function call ` `    ``cout << longestFibonacciSubsequence(arr, n) ` `         ``<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the length ` `// of longest subsequence of ` `// Fibonacci Numbers in an Array ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `static` `final` `int` `N = ``100005``; ` `  `  `// Function to create hash table ` `// to check Fibonacci numbers ` `static` `void` `createHash(HashSet hash, ` `                ``int` `maxElement) ` `{ ` `    ``int` `prev = ``0``, curr = ``1``; ` `    ``hash.add(prev); ` `    ``hash.add(curr); ` `  `  `    ``while` `(curr <= maxElement) { ` `        ``int` `temp = curr + prev; ` `        ``hash.add(temp); ` `        ``prev = curr; ` `        ``curr = temp; ` `    ``} ` `} ` `  `  `// Function to find the longest ` `// subsequence containing ` `// all Fibonacci numbers ` `static` `int` `longestFibonacciSubsequence( ` `    ``int` `arr[], ``int` `n) ` `{ ` `    ``HashSet hash = ``new` `HashSet(); ` `    ``createHash( ` `        ``hash,Arrays.stream(arr).max().getAsInt()); ` `  `  `    ``int` `answer = ``0``; ` `  `  `    ``for` `(``int` `i = ``0``; i < n; i++) { ` `        ``if` `(hash.contains(arr[i])) { ` `            ``answer++; ` `        ``} ` `    ``} ` `  `  `    ``return` `answer; ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``3``, ``4``, ``11``, ``2``, ``9``, ``21` `}; ` `    ``int` `n = arr.length; ` `  `  `    ``// Function call ` `    ``System.out.print(longestFibonacciSubsequence(arr, n) ` `         ``+``"\n"``); ` `  `  `} ` `} ` ` `  `// This code contributed by Princi Singh `

## Python 3

 `# Python 3 program to find the length ` `# of longest subsequence of ` `# Fibonacci Numbers in an Array ` ` `  `N ``=` `100005` ` `  `# Function to create hash table ` `# to check Fibonacci numbers ` `def` `createHash(``hash``,maxElement): ` `    ``prev ``=` `0` `    ``curr ``=` `1` `    ``hash``.add(prev) ` `    ``hash``.add(curr) ` ` `  `    ``while` `(curr <``=` `maxElement): ` `        ``temp ``=` `curr ``+` `prev ` `        ``hash``.add(temp) ` `        ``prev ``=` `curr ` `        ``curr ``=` `temp ` `     `  `# Function to find the longest ` `# subsequence containing ` `# all Fibonacci numbers ` `def` `longestFibonacciSubsequence(arr, n): ` `    ``hash` `=` `set``() ` `    ``createHash(``hash``,``max``(arr)) ` ` `  `    ``answer ``=` `0` ` `  `    ``for` `i ``in` `range``(n): ` `        ``if` `(arr[i] ``in` `hash``): ` `            ``answer ``+``=` `1` ` `  `    ``return` `answer ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``3``, ``4``, ``11``, ``2``, ``9``, ``21``] ` `    ``n ``=` `len``(arr) ` ` `  `    ``# Function call ` `    ``print``(longestFibonacciSubsequence(arr, n)) ` ` `  `# This code is contributed by Surendra_Gangwar `

## C#

 `// C# program to find the length ` `// of longest subsequence of ` `// Fibonacci Numbers in an Array ` `using` `System; ` `using` `System.Linq; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` `static` `readonly` `int` `N = 100005; ` `   `  `// Function to create hash table ` `// to check Fibonacci numbers ` `static` `void` `createHash(HashSet<``int``> hash, ` `                ``int` `maxElement) ` `{ ` `    ``int` `prev = 0, curr = 1; ` `    ``hash.Add(prev); ` `    ``hash.Add(curr); ` `   `  `    ``while` `(curr <= maxElement) { ` `        ``int` `temp = curr + prev; ` `        ``hash.Add(temp); ` `        ``prev = curr; ` `        ``curr = temp; ` `    ``} ` `} ` `   `  `// Function to find the longest ` `// subsequence containing ` `// all Fibonacci numbers ` `static` `int` `longestFibonacciSubsequence( ` `    ``int` `[]arr, ``int` `n) ` `{ ` `    ``HashSet<``int``> hash = ``new` `HashSet<``int``>(); ` `    ``createHash(hash,arr.Max()); ` `   `  `    ``int` `answer = 0; ` `   `  `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(hash.Contains(arr[i])) { ` `            ``answer++; ` `        ``} ` `    ``} ` `   `  `    ``return` `answer; ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]arr = { 3, 4, 11, 2, 9, 21 }; ` `    ``int` `n = arr.Length; ` `   `  `    ``// Function call ` `    ``Console.Write(longestFibonacciSubsequence(arr, n) ` `         ``+``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

Output:

```3
```

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