Đếm số chữ số thập phân khi chia 2 số

 Link: https://www.geeksforgeeks.org/count-number-digits-decimal-dividing-number/

We are given two numbers A and B. We need to calculate the number of digits after decimal. If in case the numbers are irrational then print “INF”.

Examples: 

Input  : x = 5, y = 3
Output : INF
5/3 = 1.666....

Input :  x = 3, y = 6
Output : 1
3/6 = 0.5

The idea is simple we follow school division and keep track of remainders while dividing one by one. If remainder becomes 0, we return count of digits seen after decimal. If remainder repeats, we return INF.

// C# program to count digits after dot when a
// number is divided by another.
using System;
using System.Collections.Generic;
     
class GFG
{
 
static int count(int x, int y)
{
    int ans = 0; // Initialize result
     
    var m = new Dictionary<int,int>();
     
    // calculating remainder
    while (x % y != 0)
    {
 
        x = x % y;
 
        ans++;
 
        // if this remainder appeared before then
        // the numbers are irrational and would not
        // converge to a solution the digits after
        // decimal will be infinite
        if (m.ContainsKey(x))
            return -1;
 
        m.Add(x, 1);
        x = x * 10;
    }
    return ans;
}
 
// Driver code
public static void Main(String[] args)
{
    int res = count(1, 2);
    if((res == -1))
        Console.WriteLine("INF");
    else
        Console.WriteLine(res);
 
    res = count(5, 3);
    if((res == -1))
        Console.WriteLine("INF");
    else
        Console.WriteLine(res);
     
    res = count(3, 5);
    if((res == -1))
        Console.WriteLine("INF");
    else
        Console.WriteLine(res);
}
}
 
// This code is contributed by 29AjayKumar

Output:

1
INF
1

Time Complexity: O(N * log(N) ) 

Auxiliary Space: O(N)