Un número es una Repunit en base B si se puede representar como una string de tres o más unos en base >= 2.
Comprobar si N es un número de Repunit
Dado un número entero N, la tarea es comprobar si N es un número de Repunit en base B.
Ejemplos:
Entrada: N = 31, B = 5
Salida: Sí
31 se puede escribir como 111 en base 5
Entrada: N = 5, B = 2
Salida: No
5 es 101 en base 2
Enfoque: Contaremos el número de unos en la base B de un número N dado y también contaremos el número de dígitos en la base B de un número N dado . Si son iguales, escriba «SÍ», de lo contrario, escriba «NO».
Por ejemplo:
N = 31, B = 5
31 se puede escribir como 111 en base 5, por lo que el número de unos en base B de un número dado N = 3 y el número de dígitos en la base B de un número dado N = 3
Dado que ambos son iguales por lo tanto, 31 es un número Repunit en base 5 .
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation to check
// if a number is Repunit Number
#include <iostream>
#include <math.h>
using namespace std;
// Function to check if a number
// contains all the digits 0, 1, .., (b-1)
// an equal number of times
bool isRepunitNum(int n, int b)
{
// to store number of digits of n
// in base B
int length = 0;
// to count frequency of digit 1
int countOne = 0;
while (n != 0) {
int r = n % b;
length++;
if (r == 1)
countOne++;
n = n / b;
}
// condition to check three or more 1's
// and number of ones is equal to number
// of digits of n in base B
return countOne >= 3 && countOne == length;
}
// Driver Code
int main()
{
// taking inputs
int n = 31;
int base = 2;
// function to check
if (isRepunitNum(n, base))
cout << "Yes";
else
cout << "NO";
return 0;
}
Java
// Java implementation to check
// if a number is Repunit Number
class GFG{
// Function to check if a number
// contains all the digits 0, 1, .., (b-1)
// an equal number of times
static boolean isRepunitNum(int n, int b)
{
// to store number of digits of n
// in base B
int length = 0;
// to count frequency of digit 1
int countOne = 0;
while (n != 0)
{
int r = n % b;
length++;
if (r == 1)
countOne++;
n = n / b;
}
// condition to check three or more 1's
// and number of ones is equal to number
// of digits of n in base B
return countOne >= 3 &&
countOne == length;
}
// Driver Code
public static void main(String[] args)
{
// taking inputs
int n = 31;
int base = 2;
// function to check
if (isRepunitNum(n, base))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by rock_cool
Python3
# Python3 implementation to check
# if a number is Repunit Number
# Function to check if a number
# contains all the digits 0, 1, .., (b-1)
# an equal number of times
def isRepunitNum(n, b):
# to store number of digits of n
# in base B
length = 0;
# to count frequency of digit 1
countOne = 0;
while (n != 0):
r = n % b;
length += 1;
if (r == 1):
countOne += 1;
n = n // b;
# condition to check three or more 1's
# and number of ones is equal to number
# of digits of n in base B
return countOne >= 3 and countOne == length;
# Driver Code
if __name__ == '__main__':
# taking inputs
n = 31;
base = 2;
# function to check
if (isRepunitNum(n, base)):
print("Yes");
else:
print("No");
# This code is contributed by 29AjayKumar
C#
// C# implementation to check
// if a number is Repunit Number
using System;
class GFG{
// Function to check if a number
// contains all the digits 0, 1, .., (b-1)
// an equal number of times
static bool isRepunitNum(int n, int b)
{
// to store number of digits of n
// in base B
int length = 0;
// to count frequency of digit 1
int countOne = 0;
while (n != 0)
{
int r = n % b;
length++;
if (r == 1)
countOne++;
n = n / b;
}
// condition to check three or more 1's
// and number of ones is equal to number
// of digits of n in base B
return countOne >= 3 &&
countOne == length;
}
// Driver Code
public static void Main()
{
// taking inputs
int n = 31;
int base1 = 2;
// function to check
if (isRepunitNum(n, base1))
Console.Write("Yes");
else
Console.Write("No");
}
}
// This code is contributed by Code_Mech
Javascript
<script>
// Javascript implementation to check
// if a number is Repunit Number
// Function to check if a number
// contains all the digits 0, 1, .., (b-1)
// an equal number of times
function isRepunitNum( n ,b) {
// to store number of digits of n
// in base B
let length = 0;
// to count frequency of digit 1
let countOne = 0;
while (n != 0) {
let r = n % b;
length++;
if (r == 1)
countOne++;
n = parseInt(n / b);
}
// condition to check three or more 1's
// and number of ones is equal to number
// of digits of n in base B
return countOne >= 3 && countOne == length;
}
// Driver Code
// taking inputs
let n = 31;
let base = 2;
// function to check
if (isRepunitNum(n, base))
document.write("Yes");
else
document.write("No");
// This code contributed by gauravrajput1
</script>
Yes
Complejidad del tiempo: O(log b n)
Espacio Auxiliar: O(1)
Referencia : http://www.numbersaplenty.com/set/repunit/