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Question

I'm having a bit of a hard time creating a function, using iteration and recursion to find the sum of all even integers between 1 and the number the user inputs. The program guidelines require a function to solve this three ways:

1. a formula
2. iteration
3. recursion

This is what I have so far:

#include <iostream>
#include <iomanip>
#include <cstdlib>
using namespace std;
void formulaEvenSum(int num, int& evenSum)
{
    evenSum = num / 2 * (num / 2 + 1);
    return;
}
void loopEvenSum(int num, int& evenSum2)
{
}
int main()
{
    int num, evenSum, evenSum2;
     cout << "Program to compute sum of even integers from 1 to num.";
     cout << endl << endl;
     cout << "Enter a positive integer (or 0 to exit): ";
     cin >> num;
     formulaEvenSum(num, evenSum);
     loopEvenSum(num, evenSum2);
     cout << "Formula result = " << evenSum << endl;
     cout << "Iterative result = " << evenSum2 << endl;
   
     system("PAUSE");
     return 0;
}

Answer

You should be able to build an iterative solution using a for loop without too much problem.

A recursive solution might take the form:

f(a)
  if(a>0)
    return a+f(a-1)
  else
    return 0
f(user_input)

You have to differentiate between a case where you "dive deeper" and one wherein you provide an answer which doesn't affect the total, but begins the climb out of the recursion (though there are other ways to end it).

An alternative solution is a form:

f(a,sum,total)
  if(a<=total)
    return f(a+1,sum+a,total)
  else
    return sum
f(0,0,user_input)

The advantage of this second method is that some languages are able to recognise and optimize for what's known as "tail recursion". You'll see in the first recursive form that it's necessary to store an intermediate result for each level of recursion, but this is not necessary in the second form as all the information needed to return the final answer is passed along each time.

Hope this helps!