Length of longest Fibonacci subarray formed by removing only one element

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: 5
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: 3
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

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// C++ program to find length of the longest
// subarray with all fibonacci numbers
  
#include <bits/stdc++.h>
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 fibnonacci 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;
}

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Java

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// 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<Integer> hash,
                int maxElement)
{
   
    // Insert first two fibnonacci 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<Integer> hash = new HashSet<Integer>();
   
    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

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Python3

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# 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 fibnonacci 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

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C#

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// 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 fibnonacci 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

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Output:

5

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