Encuentra el enésimo dígito en la fracción propia de dos números

Dados tres enteros P , Q y N donde P < Q , la tarea es calcular el valor de la fracción de P / Q y encontrar el ^dígito N después del decimal.
Ejemplo 
 

Entrada: P = 1, Q = 2, N = 1 
Salida: 5 
(1/2) = 0,5 y 5 es el primer dígito después del decimal.
Entrada: P = 5, Q = 6, N = 5 
Salida: 3 
(5 / 6) = 0,833333333… 
 

Enfoque: inicialice una variable entera res que almacene el enésimo dígito resultante. Ahora, mientras N > 0 haga lo siguiente: 
 

1. Disminuya N en 1 .
2. Para calcular el dígito, actualice el valor P = P * 10 .
3. Calcule res = P / Q y actualice P = P % Q .

Finalmente, imprima el res.
A continuación se muestra la implementación del enfoque anterior: 
 

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to print the Nth digit
// in the fraction (p / q)
int findNthDigit(int p, int q, int N)
{
    // To store the resultant digit
    int res;
 
    // While N > 0 compute the Nth digit
    // by dividing p and q and store the
    // result into variable res
    // and go to next digit
    while (N > 0) {
        N--;
        p *= 10;
        res = p / q;
        p %= q;
    }
    return res;
}
 
// Driver code
int main()
{
    int p = 1, q = 2, N = 1;
 
    cout << findNthDigit(p, q, N);
 
    return 0;
}

// Java implementation of the approach
class GFG
{
 
    // Function to print the Nth digit
    // in the fraction (p / q)
    static int findNthDigit(int p,
                            int q, int N)
    {
        // To store the resultant digit
        int res = 0;
     
        // While N > 0 compute the Nth digit
        // by dividing p and q and store the
        // result into variable res
        // and go to next digit
        while (N > 0)
        {
            N--;
            p *= 10;
            res = p / q;
            p %= q;
        }
        return res;
    }
     
    // Driver code
    public static void main(String args[])
    {
        int p = 1, q = 2, N = 1;
     
        System.out.println(findNthDigit(p, q, N));
    }
}
 
// This code is contributed by AnkitRai01

# Python3 implementation of the approach
 
# Function to print the Nth digit
# in the fraction (p / q)
def findNthDigit(p, q, N) :
 
    # While N > 0 compute the Nth digit
    # by dividing p and q and store the
    # result into variable res
    # and go to next digit
    while (N > 0) :
        N -= 1;
        p *= 10;
        res = p // q;
        p %= q;
 
    return res;
 
# Driver code
if __name__ == "__main__" :
     
    p = 1; q = 2; N = 1;
    print(findNthDigit(p, q, N));
 
# This code is contributed by kanugargng

// C# implementation of the approach
using System;
 
class GFG
{
 
    // Function to print the Nth digit
    // in the fraction (p / q)
    static int findNthDigit(int p, int q, int N)
    {
        // To store the resultant digit
        int res = 0;
     
        // While N > 0 compute the Nth digit
        // by dividing p and q and store the
        // result into variable res
        // and go to next digit
        while (N > 0)
        {
            N--;
            p *= 10;
            res = p / q;
            p %= q;
        }
        return res;
    }
     
    // Driver code
    public static void Main()
    {
        int p = 1, q = 2, N = 1;
     
        Console.WriteLine(findNthDigit(p, q, N));
    }
}
 
// This code is contributed by AnkitRai01

<script>
      // JavaScript implementation of the approach
 
      // Function to print the Nth digit
      // in the fraction (p / q)
      function findNthDigit(p, q, N)
      {
       
        // To store the resultant digit
        var res;
 
        // While N > 0 compute the Nth digit
        // by dividing p and q and store the
        // result into variable res
        // and go to next digit
        while (N > 0)
        {
          N--;
          p *= 10;
          res = parseInt(p / q);
          p %= q;
        }
        return res;
      }
 
      // Driver code
      var p = 1,
        q = 2,
        N = 1;
      document.write(findNthDigit(p, q, N));
       
      // This code is contributed by rdtank.
    </script>

5

Complejidad de tiempo: O(N)

Espacio Auxiliar : O(1)