Comprobar si un número es Full Fibonacci o no

Dado un número N , la tarea es verificar si el número dado y todos sus dígitos son Fibonacci. Si es así, entonces el número dado es un número completo de Fibonacci, de lo contrario no lo es.
Ejemplos:

Entrada: 13
Salida: Sí
Explicación: 13 y sus dígitos 1 y 3 son todos números de Fibonacci

Entrada: 34
Salida: No
Explicación: 4 no es un número de Fibonacci.

Enfoque:
primero verifique si todos los dígitos de N son Fibonacci o no. Si es así, verifique de manera similar si N es Fibonacci o no por el principio de que un número es Fibonacci si y solo si uno o ambos (5*N ^{2 + 4)} o (5*N ² – 4) es un cuadrado perfecto.
El siguiente código es la implementación del enfoque anterior:

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>

Producción:

Yes

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)

Publicación traducida automáticamente

Artículo escrito por spp____ y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

C++

Java

Python3

C#

Javascript

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