Issues with Sieve of Eratosthenes - c++

Question

I picked up "Programming Principles and Practice using C++", and was doing an early problem involving the Sieve of Eratosthenes, and I'm having unexpected output, but I cannot pin down exactly what the problem is. Here is my code:
#include <iostream>
#include <vector>
int main()
{
std::vector<int> prime;
std::vector<int> nonPrime;
int multiple = 0;
for(int i = 2; i < 101; i++) //initialized to first prime number, i will
// be the variable that should contain prime numbers
{
for(int j = 0; j < nonPrime.size(); j++) //checks i against
// vector to see if
// marked as nonPrime
{
if(i == nonPrime[j])
{
goto outer;//jumps to next iteration if number
// is on the list
}
}
prime.push_back(i); //adds value of i to Prime vector if it
//passes test
for(int j = i; multiple < 101; j++) //This loop is where the
// sieve bit comes in
{
multiple = i * j;
nonPrime.push_back(multiple);
}
outer:
;
}
for(int i = 0; i < prime.size(); i++)
{
std::cout << prime[i] << std::endl;
}
return 0;
}
The question only currently asks me to find prime numbers up to 100 utilizing this method. I also tried using this current 'goto' method of skipping out of a double loop under certain conditions, and I also tried using a Boolean flag with an if statement right after the check loop and simply used the "continue;" statement and neither had any effect.
(Honestly I figured since people say goto was evil perhaps it had consequences that I hadn't foreseen, which is why I tried to switch it out) but the problem doesn't call for me to use modular functions, so I assume it wants me to solve it all in main, ergo my problem of utilizing nested loops in main. Oh, and to further specify my output issues, it seems like it only adds multiples of 2 to the nonPrime vector, but everything else checks out as passing the test (e.g 9).
Can someone help me understand where I went wrong?

Answer 1

Given that this is not a good way to implement a Sieve of Eratosthenes, I'll point out some changes to your code to make it at least output the correct sequence.
Please also note that the indentation you choose is a bit misleading, after the first inner loop.
#include <iostream>
#include <vector>
int main()
{
std::vector<int> prime;
std::vector<int> nonPrime;
int multiple = 0;
for(int i = 2; i < 101; i++)
{
// you can use a flag, but note that usually it could be more
// efficiently implemented with a vector of bools. Try it yourself
bool is_prime = true;
for(int j = 0; j < nonPrime.size(); j++)
{
if(i == nonPrime[j])
{
is_prime = false;
break;
}
}
if ( is_prime )
{
prime.push_back(i);
// You tested 'multiple' before initializing it for every
// new prime value
for(multiple = i; multiple < 101; multiple += i)
{
nonPrime.push_back(multiple);
}
}
}
for(int i = 0; i < prime.size(); i++)
{
std::cout << prime[i] << std::endl;
}
return 0;
}