Given a fraction Convert into a decimal.

Given a fraction. Convert it into a decimal. So simple :P

eg.
10/2 = 5
3/5 = 0.6

(The Question Begins Now)  :D
If the decimals are repeating recursively, then enclose them inside  ().

eg.
8/3 = 2.(6)

as 8/3 = 2.66666666.......  infinitly.   

Let us simulate the process of converting fraction to decimal. Let us look at the part where we have already figured out the integer part which is floor(numerator/denominator). Now we are left with      ( remainder = numerator%denominator ) / denominator.
If you remember the process of converting to decimal, at each step we do the following :

1. Multiply the remainder by 10.
2. Append remainder / denominator to result.
3. Remainder = remainder % denominator.

At any moment, if remainder becomes 0, we are done.

However, when there is a recurring sequence, remainder never becomes 0. For example if you look at 1/3, the remainder never becomes 0.

Below is one important observation :
If we start with remainder ‘rem’ and if the remainder repeats at any point of time, the digits between the two occurrence of ‘rem’ keep repeating.

  

#include <bits/stdc++.h> 

using namespace std; 

void fractionToDecimal(int numr, int denr) 

{ 

    string res; 

  

    // Create a map to store already seen remainders 

    // remainder is used as key and its position in 

    // result is stored as value. Note that we need 

    // position for cases like 1/6.  In this case, 

    // the recurring sequence doesn't start from first 

    // remainder. 

    map <int, int> mp; 

    mp.clear(); 

  

    // Find first remainder 

    int rem = numr%denr; 

  

    // Keep finding remainder until either remainder 

    // becomes 0 or repeats 

    while ( (rem!=0) && (mp.find(rem) == mp.end()) ) 

    { 

        // Store this remainder 

        mp[rem] = res.length(); 

  

        // Multiply remainder with 10 

        rem = rem*10; 

  

        // Append rem / denr to result 

        int res_part = rem / denr; 

        res += to_string(res_part); 

  

        // Update remainder 

        rem = rem % denr; 

    } 

  

     (rem == 0)? cout<<(double)numr/denr<<endl : cout<<(numr/denr)<<"." <<(res.substr(0,mp[rem]))<<"("<<res.substr(mp[rem])<<")"<<endl; 

} 

  

int main() { 
    int t;

cin>>t;

while(t--){

    int numr, denr; 

    cin>>numr;

    cin>>denr;

    fractionToDecimal(numr, denr); 

            }

    return 0; 

}