Question

C++, data structure

An integer number’s proper divisor is any positive integer that divides the number without remainder and is less than the number. Neither zero nor any negative number is a proper divisor. Write a function returns true if its second parameter is a proper divisor of its first parameter.

The function’s prototype is

bool properDivisor(int number, int candidate)

Write a function that returns the sum of a number’s proper divisors.

The function’s prototype is

int properDivisorSum(int number);

Use the function properDivisor to write this function.

Two distinct, integer numbers, x and y are amicable numbers if the sum of x’s proper divisors equals y and the sum of y’s proper divisors equals x.

From Wikipedia

“The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.”

Write a function, amicablePair, that returns true if its two integer parameters are amicable and false otherwise. The function’s protoype is

bool amicablePair(int a, int b);

Write a program that generates pairs of random numbers until the pair of random numbers are amicable numbers.

Write the pairs of random numbers to a text file.

Answer 1

Thanks for the question.

Here is the completed code for this problem. Let me know if you have any doubts or if you need anything to change.

Thank You !!

==============================================================================================

#include<iostream>
#include<fstream>
#include<cstdlib>
using namespace std;

bool properDivisor(int number, int candidate){
   return candidate>0 && number%candidate==0;
}

int properDivisorSum(int number){
  
   int sum=0;
   for(int i=1;i<number;i++){
       if(properDivisor(number,i))
       sum+=i;
   }
   return sum;
}

bool amicablePair(int a, int b){
  
   int properDivisorSumA = properDivisorSum(a);
   int properDivisorSumB = properDivisorSum(b);
  
   return properDivisorSumA==b && properDivisorSumB==a;

}

int main(){
  
   const char * filename = "F:\\not__amicable.txt";
   ofstream outfile(filename);
  
  
   if(outfile.good()){
      
           int a = 220+rand()%2;  
           int b = 284+rand()%2;  

       while(true){
          
           if(!amicablePair(a,b)){
               outfile<<a<<", "<<b<<endl;
           }else{
               outfile<<"First Amicable Pair: "<<a<<", "<<b<<endl;
               cout<<"File updated successfully."<<endl;
               break;
           }
           a = rand()%500;  
           b = rand()%500;
          
       }
   outfile.close();
   }
  
}