Extended Midy's theorem in C++

Midy’s Theorem is a statement used for decimal expansion of numbers denoted by n/p, where n is any number and p is a prime number and a/p has a repeating decimal with even period.

In Extended Midy’s Theorem, the repeating portion is divided into m digits, then their sum is a multiple of 10m - 1. 

Program to illustrate Extended Midy’s Theorem: 

Example

Live Demo

#include <bits/stdc++.h> using namespace std; string findDecimalValue(int num, int den) {        string res;    unordered_map<int, int> mp;    int rem = num % den;    while ((rem != 0) && (mp.find(rem) == mp.end())) {       mp[rem] = res.length();       rem = rem * 10;       int part = rem / den;       res += to_string(part);       rem = rem % den;    }    return (rem == 0) ? "-1" : res.substr(mp[rem]); } bool isPrime(int n) {        for (int i = 2; i <= n / 2; i++)       if (n % i == 0)          return false;    return true; } void ExtendedMidysAlgo(string str, int n, int m) {        if (!isPrime(n)) {       cout<<"Denominator is not prime, thus Extended Midy's theorem is not applicable";       return;      }    int l = str.length();    int part1 = 0, part2 = 0;    if (l % 2 == 0 && l % m == 0) {       int part[m] = { 0 }, sum = 0, res = 0;       for (int i = 0; i < l; i++) {          int var = i / m;          part[var] = part[var] * 10 + (str[i] - '0');       }       for (int i = 0; i < m; i++) {          sum = sum + part[i];          cout << part[i] << " ";       }       cout << endl;       res = pow(10, m) - 1;       if (sum % res == 0)          cout << "Extended Midy's theorem holds!";             else          cout << "Extended Midy's theorem doesn't hold!";          }    else if (l % 2 != 0) {       cout << "The repeating decimal is of odd length thus Extended Midy's theorem is not applicable";    }    else if (l % m != 0) {       cout<<" The repeating decimal can not be divided into m digits";    } } // Driver code int main() {    int numr = 1, denr = 17, m = 4;    string res = findDecimalValue(numr, denr);    if (res == "-1")       cout << "The fraction does not have repeating decimal";    else {       cout << "Repeating decimal = " << res << endl;       ExtendedMidysAlgo(res, denr, m);    }    return 0; }

Output −

Repeating decimal = 0588235294117647 588 2352 9411 7647 Extended Midy's theorem holds!