Check if a number is Full Fibonacci or not

0 0 5 minutes read

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.

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*N^{2 + 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 <bits/stdc++.h>
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 perfect 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 perfect 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 perfect 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

C#

// C# program to check if a given
// number is a full fibonacci 
// number or not
using System;
 
class GFG{
 
// A utility function that returns 
// true if x is perfect square
static bool 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 bool isFibonacci(int n)
{
     
    // N is fibonacci if one of
    // 5 * N ^ 2 + 4 or 5 * N ^ 2 - 4
    // or both is a perfect square
    return isPerfectSquare(5 * n * n + 4) || 
           isPerfectSquare(5 * n * n - 4);
}
 
// Function to check digits
static bool 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 bool isFullfibonacci(int n)
{
    return (checkDigits(n) &&
            isFibonacci(n));
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 13;
     
    if (isFullfibonacci(n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by SoumikMondal

Javascript

<script>
 
// Javascript program to check if a given
// number is a full fibonacci 
// number or not
 
    // A utility function that returns
    // true if x is perfect square
    function isPerfectSquare(x) {
        var s = parseInt( Math.sqrt(x));
        return (s * s == x);
    }
 
    // Returns true if N is a fibonacci
    // number and false otherwise
    function isFibonacci(n) {
 
        // N is fibonacci if one of
        // 5 * N ^ 2 + 4 or 5 * N ^ 2 - 4
        // or both is a perfect square
        return isPerfectSquare(5 * n * n + 4) ||
        isPerfectSquare(5 * n * n - 4);
    }
 
    // Function to check digits
    function checkDigits(n) {
 
        // Check if all digits
        // are fibonacci or not
        while (n != 0) {
 
            // Extract digit
            var 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
    function isFullfibonacci(n) {
        return (checkDigits(n) && isFibonacci(n));
    }
 
    // Driver code
     
        var n = 13;
 
        if (isFullfibonacci(n))
            document.write("Yes");
        else
            document.write("No");
 
// This code contributed by Rajput-Ji 
 
</script>

Output:

Yes

Time Complexity: O(logn)
Auxiliary Space: O(1)

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!