# Length of longest Fibonacci subarray formed by removing only one element

Last Updated : 04 Jan, 2023

Given an array A containing integers, the task is to find the length of longest Fibonacci subarray formed by removing only one element from the array.
Examples:

Input: arr[] = { 2, 8, 5, 7, 3, 5, 7 }
Output:
Explanation:
If we remove the number 7 at index 3, then the remaining array contains a Fibonacci subarray {2, 8, 5, 3, 5} of length 5, which is maximum.
Input: arr[] = { 2, 3, 6, 1 }
Output:
Explanation:
If we remove the number 6 at index 2, then the remaining array contains a Fibonacci subarray {2, 3, 1} of length 3, which is maximum.

Approach: The above-mentioned problem can be solved by counting the contiguous Fibonacci numbers just before every index and just after every index.

1. Now traverse the array again and find an index for which counts of Fibonacci numbers after and before is maximum.
2. In order to check for Fibonacci numbers, we will build a hash table containing all the Fibonacci numbers less than or equal to the maximum value in the array to test a number in O(1) time.

Below is the implementation of the above approach:

## CPP

 `// C++ program to find length of the longest` `// subarray with all fibonacci numbers`   `#include ` `using` `namespace` `std;` `#define N 100000`   `// Function to create hash table` `// to check for Fibonacci numbers` `void` `createHash(set<``int``>& hash,` `                ``int` `maxElement)` `{`   `    ``// Insert first two fibonacci numbers` `    ``int` `prev = 0, curr = 1;`   `    ``hash.insert(prev);` `    ``hash.insert(curr);`   `    ``while` `(curr <= maxElement) {`   `        ``// Summation of last two numbers` `        ``int` `temp = curr + prev;`   `        ``hash.insert(temp);`   `        ``// Update the variable each time` `        ``prev = curr;` `        ``curr = temp;` `    ``}` `}`   `// Function to find the` `// longest fibonacci subarray` `int` `longestFibSubarray(` `    ``int` `arr[], ``int` `n)` `{`   `    ``// Find maximum value in the array` `    ``int` `max_val` `        ``= *max_element(arr, arr + n);`   `    ``// Creating a set` `    ``// containing Fibonacci numbers` `    ``set<``int``> hash;`   `    ``createHash(hash, max_val);`   `    ``int` `left[n], right[n];` `    ``int` `fibcount = 0, res = -1;`   `    ``// Left array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from left of current element` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``left[i] = fibcount;`   `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.find(arr[i])` `            ``!= hash.end()) {` `            ``fibcount++;` `        ``}`   `        ``else` `            ``fibcount = 0;` `    ``}`   `    ``// Right array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from right of current element` `    ``fibcount = 0;`   `    ``for` `(``int` `i = n - 1; i >= 0; i--) {`   `        ``right[i] = fibcount;`   `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.find(arr[i])` `            ``!= hash.end()) {` `            ``fibcount++;` `        ``}` `        ``else` `            ``fibcount = 0;` `    ``}`   `    ``for` `(``int` `i = 0; i < n; i++)` `        ``res = max(` `            ``res,` `            ``left[i] + right[i]);`   `    ``return` `res;` `}`   `// Driver code` `int` `main()` `{`   `    ``int` `arr[] = { 2, 8, 5, 7, 3, 5, 7 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``cout << longestFibSubarray(arr, n)` `         ``<< endl;`   `    ``return` `0;` `}`

## Java

 `// Java program to find length of the longest` `// subarray with all fibonacci numbers` `import` `java.util.*;`   `class` `GFG{` `static` `final` `int` `N = ``100000``;` ` `  `// Function to create hash table` `// to check for Fibonacci numbers` `static` `void` `createHash(HashSet hash,` `                ``int` `maxElement)` `{` ` `  `    ``// Insert first two fibonacci numbers` `    ``int` `prev = ``0``, curr = ``1``;` ` `  `    ``hash.add(prev);` `    ``hash.add(curr);` ` `  `    ``while` `(curr <= maxElement) {` ` `  `        ``// Summation of last two numbers` `        ``int` `temp = curr + prev;` ` `  `        ``hash.add(temp);` ` `  `        ``// Update the variable each time` `        ``prev = curr;` `        ``curr = temp;` `    ``}` `}` ` `  `// Function to find the` `// longest fibonacci subarray` `static` `int` `longestFibSubarray(` `    ``int` `arr[], ``int` `n)` `{` ` `  `    ``// Find maximum value in the array` `    ``int` `max_val = Arrays.stream(arr).max().getAsInt();` ` `  `    ``// Creating a set` `    ``// containing Fibonacci numbers` `    ``HashSet hash = ``new` `HashSet();` ` `  `    ``createHash(hash, max_val);` ` `  `    ``int` `[]left = ``new` `int``[n];` `    ``int` `[]right = ``new` `int``[n];` `    ``int` `fibcount = ``0``, res = -``1``;` ` `  `    ``// Left array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from left of current element` `    ``for` `(``int` `i = ``0``; i < n; i++) {` ` `  `        ``left[i] = fibcount;` ` `  `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.contains(arr[i])) {` `            ``fibcount++;` `        ``}` ` `  `        ``else` `            ``fibcount = ``0``;` `    ``}` ` `  `    ``// Right array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from right of current element` `    ``fibcount = ``0``;` ` `  `    ``for` `(``int` `i = n - ``1``; i >= ``0``; i--) {` ` `  `        ``right[i] = fibcount;` ` `  `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.contains(arr[i])) {` `            ``fibcount++;` `        ``}` `        ``else` `            ``fibcount = ``0``;` `    ``}` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++)` `        ``res = Math.max(` `            ``res,` `            ``left[i] + right[i]);` ` `  `    ``return` `res;` `}` ` `  `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` `  `    ``int` `arr[] = { ``2``, ``8``, ``5``, ``7``, ``3``, ``5``, ``7` `};` `    ``int` `n = arr.length;` ` `  `    ``System.out.print(longestFibSubarray(arr, n)` `         ``+``"\n"``);` ` `  `}` `}`   `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 program to find length of the longest ` `# subarray with all fibonacci numbers `   `N ``=` `100000`   `# Function to create hash table ` `# to check for Fibonacci numbers ` `def` `createHash(``hash``, maxElement) :`   `    ``# Insert first two fibonacci numbers ` `    ``prev ``=` `0` `    ``curr ``=` `1`   `    ``hash``.add(prev) ` `    ``hash``.add(curr) `   `    ``while` `(curr <``=` `maxElement) :`   `        ``# Summation of last two numbers ` `        ``temp ``=` `curr ``+` `prev `   `        ``hash``.add(temp) `   `        ``# Update the variable each time ` `        ``prev ``=` `curr ` `        ``curr ``=` `temp `   `# Function to find the ` `# longest fibonacci subarray  ` `def` `longestFibSubarray(arr, n) :`   `    ``# Find maximum value in the array ` `    ``max_val ``=` `max``(arr)`   `    ``# Creating a set ` `    ``# containing Fibonacci numbers ` `    ``hash` `=` `{``int``}`   `    ``createHash(``hash``, max_val) `   `    ``left ``=` `[ ``0` `for` `i ``in` `range``(n)]`   `    ``right ``=` `[ ``0` `for` `i ``in` `range``(n)]`   `    ``fibcount ``=` `0` `    ``res ``=` `-``1`   `    ``# Left array is used to count number of ` `    ``# continuous fibonacci numbers starting ` `    ``# from left of current element ` `    ``for` `i ``in` `range``(n) :`   `        ``left[i] ``=` `fibcount `   `        ``# Check if current element ` `        ``# is a fibonacci number ` `        ``if` `(arr[i] ``in` `hash``) :` `            ``fibcount ``+``=` `1` `        ``else``:` `            ``fibcount ``=` `0`   `    ``# Right array is used to count number of ` `    ``# continuous fibonacci numbers starting ` `    ``# from right of current element ` `    ``fibcount ``=` `0`   `    ``for` `i ``in` `range``(n``-``1``,``-``1``,``-``1``) :`   `        ``right[i] ``=` `fibcount `   `        ``# Check if current element ` `        ``# is a fibonacci number ` `        ``if` `(arr[i] ``in` `hash``) :` `            ``fibcount ``+``=` `1` `        ``else``:` `            ``fibcount ``=` `0`   `    ``for` `i ``in` `range``(``0``,n) : ` `        ``res ``=` `max``(res, left[i] ``+` `right[i]) `   `    ``return` `res`   `# Driver code ` `arr ``=` `[ ``2``, ``8``, ``5``, ``7``, ``3``, ``5``, ``7` `] ` `n ``=` `len``(arr)` `print``(longestFibSubarray(arr, n))`   `# This code is contributed by Sanjit_Prasad`

## C#

 `// C# program to find length of the longest` `// subarray with all fibonacci numbers` `using` `System;` `using` `System.Linq;` `using` `System.Collections.Generic;`   `class` `GFG{` `static` `readonly` `int` `N = 100000;` `  `  `// Function to create hash table` `// to check for Fibonacci numbers` `static` `void` `createHash(HashSet<``int``> hash,` `                ``int` `maxElement)` `{` `  `  `    ``// Insert first two fibonacci numbers` `    ``int` `prev = 0, curr = 1;` `  `  `    ``hash.Add(prev);` `    ``hash.Add(curr);` `  `  `    ``while` `(curr <= maxElement) {` `  `  `        ``// Summation of last two numbers` `        ``int` `temp = curr + prev;` `  `  `        ``hash.Add(temp);` `  `  `        ``// Update the variable each time` `        ``prev = curr;` `        ``curr = temp;` `    ``}` `}` `  `  `// Function to find the` `// longest fibonacci subarray` `static` `int` `longestFibSubarray(` `    ``int` `[]arr, ``int` `n)` `{` `  `  `    ``// Find maximum value in the array` `    ``int` `max_val = arr.Max();` `  `  `    ``// Creating a set` `    ``// containing Fibonacci numbers` `    ``HashSet<``int``> hash = ``new` `HashSet<``int``>();` `  `  `    ``createHash(hash, max_val);` `  `  `    ``int` `[]left = ``new` `int``[n];` `    ``int` `[]right = ``new` `int``[n];` `    ``int` `fibcount = 0, res = -1;` `  `  `    ``// Left array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from left of current element` `    ``for` `(``int` `i = 0; i < n; i++) {` `  `  `        ``left[i] = fibcount;` `  `  `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.Contains(arr[i])) {` `            ``fibcount++;` `        ``}` `  `  `        ``else` `            ``fibcount = 0;` `    ``}` `  `  `    ``// Right array is used to count number of` `    ``// continuous fibonacci numbers starting` `    ``// from right of current element` `    ``fibcount = 0;` `  `  `    ``for` `(``int` `i = n - 1; i >= 0; i--) {` `  `  `        ``right[i] = fibcount;` `  `  `        ``// Check if current element` `        ``// is a fibonacci number` `        ``if` `(hash.Contains(arr[i])) {` `            ``fibcount++;` `        ``}` `        ``else` `            ``fibcount = 0;` `    ``}` `  `  `    ``for` `(``int` `i = 0; i < n; i++)` `        ``res = Math.Max(` `            ``res,` `            ``left[i] + right[i]);` `  `  `    ``return` `res;` `}` `  `  `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `  `  `    ``int` `[]arr = { 2, 8, 5, 7, 3, 5, 7 };` `    ``int` `n = arr.Length;` `  `  `    ``Console.Write(longestFibSubarray(arr, n)` `         ``+``"\n"``);  ` `}` `}`   `// This code is contributed by sapnasingh4991`

## Javascript

 ``

Output

```5
```

Time Complexity: O(n + log(m)), where n is the size of the given array and m is the maximum element in the array.
Auxiliary Space: O(n)

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