Skip to content
Related Articles
Length of longest subsequence of Fibonacci Numbers in an Array
• Last Updated : 24 May, 2021

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:
Here, the subsequence is {3, 2, 21} and hence the answer is 3.
Input: arr[] = { 6, 4, 10, 13, 9, 25 }
Output:
Here, the subsequence is {1} and hence the answer is 1.

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`

## Javascript

 ``
Output:
`3`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up