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Count of consecutive Fibonacci pairs in the given Array
• Last Updated : 08 Apr, 2021

Given an array arr[], the task is to count the number of consecutive Fibonacci pairs in this array.
Examples:

Input: arr[] = { 3, 5, 6, 11 }
Output:
The only pair is (3, 5) which is consecutive fibonacci pair in the array
Input: arr[] = { 3, 5, 8, 11 }
Output:
There are two pairs (3, 5) and (5, 8) in the array, which is consecutive Fibonacci pair.

Approach:

• Find out all the pairs of the array.
• For each pair,
• Find the minimum and maximum of the pair
• Find the next consective fibonacci number after minimum_element and check that it is equal to the maximum of the pair.
• If the next consecutive fibonacci number is equal to the maximum element of the pair, then increment the count by 1.
• Return the total count as the required number of pairs.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to count the``// consecutive fibonacci pairs in the array` `#include ``using` `namespace` `std;` `// Function to find the previous``// fibonacci for the number N``int` `previousFibonacci(``int` `n)``{``    ``double` `a = n / ((1 + ``sqrt``(5)) / 2.0);``    ``return` `round(a);``}` `// Function to find the next``// fibonacci number for the number N``int` `nextFibonacci(``int` `n)``{``    ``double` `a = n * (1 + ``sqrt``(5)) / 2.0;``    ``return` `round(a);``}` `// Function to check that a Number``// is a perfect square or not``bool` `isPerfectSquare(``int` `x)``{``    ``int` `s = ``sqrt``(x);``    ``return` `(s * s == x);``}` `// Function to check that a number``// is fibonacci number or not``bool` `isFibonacci(``int` `n)``{``    ``// N is Fibinacci if one of``    ``// (5*n*n + 4) or (5*n*n - 4)``    ``// is a perferct square``    ``return` `(isPerfectSquare(5 * n * n + 4)``            ``|| isPerfectSquare(5 * n * n - 4));``}` `// Function to count the fibonacci``// pairs in the array``int` `countFibonacciPairs(``int` `arr[], ``int` `n)``{``    ``int` `res = 0;` `    ``// Loop to iterate over the array``    ``// to choose all pairs of the array``    ``for` `(``int` `i = 0; i < n; i++)``        ``for` `(``int` `j = i + 1; j < n; j++)` `            ``// Condition to check if both``            ``// the number of pair is a``            ``// fibonacci number``            ``if` `(isFibonacci(arr[i])``                ``&& isFibonacci(arr[j])) {` `                ``int` `prevFib = previousFibonacci(arr[i]);``                ``int` `nextFib = nextFibonacci(arr[i]);` `                ``// Condition to check if both``                ``// the number form consecutive``                ``// fibonacci numbers``                ``if` `(prevFib == arr[j]``                    ``|| nextFib == arr[j]) {``                    ``res++;``                ``}``            ``}` `    ``return` `res;``}` `// Driver Code``int` `main()``{``    ``int` `a[] = { 3, 5, 8, 11 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);``    ``cout << countFibonacciPairs(a, n);``    ``return` `0;``}`

## Java

 `// Java implementation to count the``// consecutive fibonacci pairs in the array``import` `java.util.*;``import` `java.lang.*;` `class` `GFG``{`` ` `// Function to find the previous``// fibonacci for the number N``static` `int` `previousFibonacci(``int` `n)``{``    ``double` `a = n / ((``1` `+ (``int``)Math.sqrt(``5``)) / ``2.0``);``    ``return` `(``int``)Math.round(a);``}`` ` `// Function to find the next``// fibonacci number for the number N``static` `int` `nextFibonacci(``int` `n)``{``    ``double` `a = n * (``1` `+ (``int``)Math.sqrt(``5``)) / ``2.0``;``    ``return` `(``int``)Math.round(a);``}`` ` `// Function to check that a Number``// is a perfect square or not``static` `boolean` `isPerfectSquare(``int` `x)``{``    ``int` `s = (``int``)Math.sqrt(x);``    ``return` `(s * s == x);``}`` ` `// Function to check that a number``// is fibonacci number or not``static` `boolean` `isFibonacci(``int` `n)``{``    ``// N is Fibinacci if one of``    ``// (5*n*n + 4) or (5*n*n - 4)``    ``// is a perferct square``    ``return` `(isPerfectSquare(``5` `* n * n + ``4``)``            ``|| isPerfectSquare(``5` `* n * n - ``4``));``}`` ` `// Function to count the fibonacci``// pairs in the array``static` `int` `countFibonacciPairs(``int` `arr[], ``int` `n)``{``    ``int` `res = ``0``;`` ` `    ``// Loop to iterate over the array``    ``// to choose all pairs of the array``    ``for` `(``int` `i = ``0``; i < n; i++)``        ``for` `(``int` `j = i + ``1``; j < n; j++)`` ` `            ``// Condition to check if both``            ``// the number of pair is a``            ``// fibonacci number``            ``if` `(isFibonacci(arr[i])``                ``&& isFibonacci(arr[j])) {`` ` `                ``int` `prevFib = previousFibonacci(arr[i]);``                ``int` `nextFib = nextFibonacci(arr[i]);`` ` `                ``// Condition to check if both``                ``// the number form consecutive``                ``// fibonacci numbers``                ``if` `(prevFib == arr[j]``                    ``|| nextFib == arr[j]) {``                    ``res++;``                ``}``            ``}`` ` `    ``return` `res;``}`` ` `// Driver Code``public` `static` `void` `main(String []args)``{``    ``int` `[]a = { ``3``, ``5``, ``8``, ``11` `};``    ``int` `n = a.length;``    ``System.out.print(countFibonacciPairs(a, n));   ``}``}` `// This code is contributed by chitranayal`

## Python3

 `# Python3 implementation to count the``# consecutive fibonacci pairs in the array``from` `math ``import` `sqrt` `# Function to find the previous``# fibonacci for the number N``def` `previousFibonacci(n):` `    ``a ``=` `n ``/` `((``1` `+` `sqrt(``5``)) ``/` `2.0``)``    ``return` `round``(a)` `# Function to find the next``# fibonacci number for the number N``def` `nextFibonacci(n):` `    ``a ``=` `n ``*` `(``1` `+` `sqrt(``5``)) ``/` `2.0``    ``return` `round``(a)` `# Function to check that a Number``# is a perfect square or not``def` `isPerfectSquare(x):` `    ``s ``=` `sqrt(x)``    ``return` `(s ``*` `s ``=``=` `x)` `# Function to check that a number``# is fibonacci number or not``def` `isFibonacci(n):` `    ``# N is Fibinacci if one of``    ``# (5*n*n + 4) or (5*n*n - 4)``    ``# is a perferct square``    ``return` `(isPerfectSquare(``5` `*` `n ``*` `n ``+` `4``)``            ``or` `isPerfectSquare(``5` `*` `n ``*` `n ``-` `4``))` `# Function to count the fibonacci``# pairs in the array``def` `countFibonacciPairs(arr, n):` `    ``res ``=` `0` `    ``# Loop to iterate over the array``    ``# to choose all pairs of the array``    ``for` `i ``in` `range``(n):``        ``for` `j ``in` `range``(i``+``1``,n):` `            ``# Condition to check if both``            ``# the number of pair is a``            ``# fibonacci number``            ``if` `(isFibonacci(arr[i])``                ``and` `isFibonacci(arr[j])):` `                ``prevFib ``=` `previousFibonacci(arr[i])``                ``nextFib ``=` `nextFibonacci(arr[i])` `                ``# Condition to check if both``                ``# the number form consecutive``                ``# fibonacci numbers``                ``if` `(prevFib ``=``=` `arr[j]``                    ``or` `nextFib ``=``=` `arr[j]):``                    ``res ``+``=` `1` `    ``return` `res` `# Driver Code``a ``=` `[``3``, ``5``, ``8``, ``11``]``n ``=` `len``(a)``print``(countFibonacciPairs(a, n))` `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation to count the``// consecutive fibonacci pairs in the array``using` `System;` `class` `GFG``{``  ` `// Function to find the previous``// fibonacci for the number N``static` `int` `previousFibonacci(``int` `n)``{``    ``double` `a = n / ((1 + (``int``)Math.Sqrt(5)) / 2.0);``    ``return` `(``int``)Math.Round(a);``}``  ` `// Function to find the next``// fibonacci number for the number N``static` `int` `nextFibonacci(``int` `n)``{``    ``double` `a = n * (1 + Math.Sqrt(5)) / 2.0;``    ``return` `(``int``)Math.Round(a);``}``  ` `// Function to check that a Number``// is a perfect square or not``static` `bool` `isPerfectSquare(``int` `x)``{``    ``int` `s = (``int``)Math.Sqrt(x);``    ``return` `(s * s == x);``}``  ` `// Function to check that a number``// is fibonacci number or not``static` `bool` `isFibonacci(``int` `n)``{``    ``// N is Fibinacci if one of``    ``// (5*n*n + 4) or (5*n*n - 4)``    ``// is a perferct square``    ``return` `(isPerfectSquare(5 * n * n + 4)``            ``|| isPerfectSquare(5 * n * n - 4));``}``  ` `// Function to count the fibonacci``// pairs in the array``static` `int` `countFibonacciPairs(``int` `[]arr, ``int` `n)``{``    ``int` `res = 0;``  ` `    ``// Loop to iterate over the array``    ``// to choose all pairs of the array``    ``for` `(``int` `i = 0; i < n; i++)``        ``for` `(``int` `j = i + 1; j < n; j++)``  ` `            ``// Condition to check if both``            ``// the number of pair is a``            ``// fibonacci number``            ``if` `(isFibonacci(arr[i])``                ``&& isFibonacci(arr[j])) {``  ` `                ``int` `prevFib = previousFibonacci(arr[i]);``                ``int` `nextFib = nextFibonacci(arr[i]);``  ` `                ``// Condition to check if both``                ``// the number form consecutive``                ``// fibonacci numbers``                ``if` `(prevFib == arr[j]``                    ``|| nextFib == arr[j]) {``                    ``res++;``                ``}``            ``}``  ` `    ``return` `res;``}``  ` `// Driver Code``public` `static` `void` `Main(String []args)``{``    ``int` `[]a = { 3, 5, 8, 11 };``    ``int` `n = a.Length;``    ``Console.Write(countFibonacciPairs(a, n));   ``}``}` `// This code is contributed by sapnasingh4991`

## Javascript

 ``
Output:
`2`

Performance Analysis:

• Time Complexity: As in the above approach, there are two nested loops which takes O(N2) time, Hence the Time Complexity will be O(N2).
• Space Complexity: As in the above approach, there is no extra space used, Hence the space complexity will be O(1).

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