Count number of digits after decimal on dividing a 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++

// CPP program to count digits after dot when a
// number is divided by another.
#include <bits/stdc++.h>
using namespace std;

int count(int x, int y)
{
    int ans = 0;  // Initialize result

    unordered_map<int, int> m;

    // 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.find(x) != m.end())
            return -1;

        m[x] = 1;
        x = x * 10;
    }
    return ans;
}

// Driver code
int main()
{
    int res = count(1, 2);
    (res == -1)? cout << "INF" : cout << res;

    cout << endl;
    res = count(5, 3);
    (res == -1)? cout << "INF" : cout << res;

    cout << endl;
    res = count(3, 5);
    (res == -1)? cout << "INF" : cout << res;
    return 0;
}

Java

// Java program to count digits after dot when a
// number is divided by another.
import java.util.*;

class GFG
{

static int count(int x, int y)
{
    int ans = 0; // Initialize result

    Map<Integer,Integer> m = new HashMap<>();

    // 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.put(x, 1);
        x = x * 10;
    }
    return ans;
}

// Driver code
public static void main(String[] args)
{
    int res = count(1, 2);
    if((res == -1))
        System.out.println("INF");
    else
        System.out.println(res);

    res = count(5, 3);
    if((res == -1))
        System.out.println("INF");
    else
        System.out.println(res);

    res = count(3, 5);
    if((res == -1))
        System.out.println("INF");
    else
        System.out.println(res);
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 program to count digits after dot
# when a number is divided by another.
def count(x, y):
    ans = 0 # Initialize result

    m = dict()

    # calculating remainder
    while x % y != 0:
        x %= y

        ans += 1

        # 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 x in m:
            return -1

        m[x] = 1
        x *= 10

    return ans

# Driver Code
if __name__ == "__main__":
    res = count(1, 2)

    print("INF") if res == -1 else print(res)

    res = count(5, 3)
    print("INF") if res == -1 else print(res)

    res = count(3, 5)
    print("INF") if res == -1 else print(res)

# This code is contributed by
# sanjeev2552

C#

// 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

    Dictionary<int,int> 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

Javascript

<script>

// JavaScript program to count digits after dot when a
// number is divided by another.

function count(x,y)
{
    let ans = 0; // Initialize result
    let m = new Map();
    // 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.has(x))
            return -1;

        m.set(x, 1);
        x = x * 10;
    }
    return ans;
}

// Driver code
let res = count(1, 2);
    if((res == -1))
        document.write("INF"+"<br>");
    else
        document.write(res+"<br>");

    res = count(5, 3);
    if((res == -1))
        document.write("INF"+"<br>");
    else
        document.write(res+"<br>");

    res = count(3, 5);
    if((res == -1))
        document.write("INF"+"<br>");
    else
        document.write(res+"<br>");


// This code is contributed by rag2127

</script>

Output:

1
INF
1

Time Complexity: O(N * log(N) )

Auxiliary Space: O(N)