# Check if a number is Full Fibonacci or not

Given a number N, the task is to check if the given number and all its digits are Fibonacci. If so, then the given number is a Full Fibonacci Number, else not.

Examples:

Input: 13
Output: Yes
Explanation: 13 and its digits 1 and 3 are all Fibonacci numbers

Input: 34
Output: No
Explanation: 4 is not a Fibonacci number.

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

Approach:
First check if all digits of N are Fibonacci or not. If so, similarly check if N is Fibonacci or not by the principle that a number is Fibonacci if and only if one or both of (5*N2 + 4) or (5*N2 – 4) is a perfect square.

Below code is the implementation of the above approach:

## C++

 `// C++ program to check ` `// if a given number is ` `// a Full Fibonacci ` `// Number or not ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// A utility function that ` `// returns true if x is ` `// perfect square ` `bool` `isPerfectSquare(``int` `x) ` `{ ` `    ``int` `s = ``sqrt``(x); ` `    ``return` `(s * s == x); ` `} ` ` `  `// Returns true if N is a ` `// Fibonacci Number ` `// and false otherwise ` `bool` `isFibonacci(``int` `n) ` `{ ` `    ``// N is Fibonacci if one ` `    ``// of 5*N^2 + 4 or 5*N^2 - 4 ` `    ``// or both is a perferct square ` `    ``return` `isPerfectSquare(5 * n * n + 4) ` `           ``|| isPerfectSquare(5 * n * n - 4); ` `} ` ` `  `// Function to check digits ` `bool` `checkDigits(``int` `n) ` `{ ` `    ``// Check if all digits ` `    ``// are fibonacci or not ` `    ``while` `(n) { ` ` `  `        ``// Extract digit ` `        ``int` `dig = n % 10; ` ` `  `        ``// Check if the current ` `        ``// digit is not fibonacci ` `        ``if` `(dig == 4 && dig == 6 ` `            ``&& dig == 7 && dig == 9) ` `            ``return` `false``; ` ` `  `        ``n /= 10; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Function to check and ` `// return if N is a Full ` `// Fibonacci number or not ` `int` `isFullfibonacci(``int` `n) ` `{ ` `    ``return` `(checkDigits(n) ` `            ``&& isFibonacci(n)); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 13; ` `    ``if` `(isFullfibonacci(n)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to check if a given ` `// number is a full fibonacci  ` `// number or not ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `// A utility function that returns  ` `// true if x is perfect square ` `static` `boolean` `isPerfectSquare(``int` `x) ` `{ ` `    ``int` `s = (``int``) Math.sqrt(x); ` `    ``return` `(s * s == x); ` `} ` ` `  `// Returns true if N is a fibonacci ` `// number and false otherwise ` `static` `boolean` `isFibonacci(``int` `n) ` `{ ` `     `  `    ``// N is fibonacci if one of ` `    ``//  5 * N ^ 2 + 4 or 5 * N ^ 2 - 4 ` `    ``// or both is a perferct square ` `    ``return` `isPerfectSquare(``5` `* n * n + ``4``) ||  ` `           ``isPerfectSquare(``5` `* n * n - ``4``); ` `} ` ` `  `// Function to check digits ` `static` `boolean` `checkDigits(``int` `n) ` `{ ` `     `  `    ``// Check if all digits ` `    ``// are fibonacci or not ` `    ``while` `(n != ``0``) ` `    ``{ ` ` `  `        ``// Extract digit ` `        ``int` `dig = n % ``10``; ` ` `  `        ``// Check if the current ` `        ``// digit is not fibonacci ` `        ``if` `(dig == ``4` `&& dig == ``6` `&&  ` `            ``dig == ``7` `&& dig == ``9``) ` `            ``return` `false``; ` ` `  `        ``n /= ``10``; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Function to check and return if N  ` `// is a full fibonacci number or not ` `static` `boolean` `isFullfibonacci(``int` `n) ` `{ ` `    ``return` `(checkDigits(n) && ` `            ``isFibonacci(n)); ` `} ` ` `  ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``13``; ` `     `  `    ``if` `(isFullfibonacci(n)) ` `        ``System.out.println(``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `} ` ` `  `// This code is contributed by offbeat `

## Python3

 `# Python3 program to check ` `# if a given number is ` `# a Full Fibonacci ` `# Number or not ` `from` `math ``import` `*` ` `  `# A utility function that ` `# returns true if x is ` `# perfect square ` `def` `isPerfectSquare(x): ` `     `  `    ``s ``=` `sqrt(x) ` `    ``return` `(s ``*` `s ``=``=` `x) ` ` `  `# Returns true if N is a ` `# Fibonacci Number ` `# and false otherwise ` `def` `isFibonacci(n): ` `     `  `    ``# N is Fibonacci if one ` `    ``# of 5 * N ^ 2 + 4 or 5 * N ^ 2 - 4 ` `    ``# or both is a perferct square ` `    ``return` `(isPerfectSquare(``5` `*` `n ``*` `n ``+` `4``) ``or`  `            ``isPerfectSquare(``5` `*` `n ``*` `n ``-` `4``)) ` ` `  `# Function to check digits ` `def` `checkDigits(n): ` `     `  `    ``# Check if all digits ` `    ``# are fibonacci or not ` `    ``while` `(n): ` `         `  `        ``# Extract digit ` `        ``dig ``=` `n ``%` `10` ` `  `        ``# Check if the current ` `        ``# digit is not fibonacci ` `        ``if` `(dig ``=``=` `4` `and` `dig ``=``=` `6` `and` `            ``dig ``=``=` `7` `and` `dig ``=``=` `9``): ` `            ``return` `False` ` `  `        ``n ``/``=` `10` `    ``return` `True` ` `  `# Function to check and ` `# return if N is a Full ` `# Fibonacci number or not ` `def` `isFullfibonacci(n): ` `     `  `    ``return` `(checkDigits(n) ``and` `isFibonacci(n)) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``n ``=` `13` `     `  `    ``if` `(isFullfibonacci(n)): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# This code is contributed by Samarth `

Output:

```Yes
```

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Improved By : ipg2016107, offbeat