My code stops at a certain condition - c++

Question

In this code I input a test case number t and then input t numbers (n). Then my code prints the nth prime number. In the 1st line of the function, prime(), if I write if(a > 43000) return; Then the code works perfectly. But if I write if(a >= 165000) return; in the same place, codeblocks says the program has stopped working. But I can't understand why.
#include <iostream>
#include <cmath>
using namespace std;
int p[15000];
void prime(int a, int i)
{
if(a >= 165000) return;
else {
int q = 0;
int s=sqrt(a), d=3;
while(d<=s){
if(a % d == 0) {
q = 1;
}
d += 2;
}
if(q == 0) {
p[i] = a;
i++;
a += 2;
prime(a, i);
}
else {
a += 2;
prime(a, i);
}
}
}
int main()
{
p[0]=2;
prime(3, 1);
int k, T;
cin >> T;
for(int i = 1; i <= T; i++){
cin >> k;
cout << p[k - 1] << endl;
}
return 0;
}

Answer 1

First, I'll point out that your array p has only 15000 elements and that the 15001-th prime number is 163,847. This means that if you do a check for a >= 165000 before quiting you'll end up trying to fill indices of your array that are outside the bounds of your array.
Second, everyone is quite right that you should be careful when doing recursion. With each run of prime() you're allocating space for 5 new integer variables a, i, q, s, and d. This means you're allocating memory for tens of thousands of integers when (from the looks of your method) all you really need is 5.
Since it looks like these values are independent of all other iterations, you can employ a couple tricks. First, for q, s, and d by declaring them as globals they will only be allocated once. Secondly, by changing prime(int a, int i) to prime(int &a, int &i) you wont be allocating memory for a and i with each loop. This changes your code to look like the following:
#include <iostream>
#include <cmath>
using namespace std;
const int max_size = 15000 ;
int p[max_size];
int q ;
int s ;
int d ;
void prime(int &a, int &i)
{
if (i>=max_size) return ;
q = 0;
s=sqrt(a) ;
d=3;
while(d<=s){
if(a % d == 0) {
q = 1;
}
d += 2;
}
if(q == 0) {
p[i] = a;
i++;
a += 2;
prime(a, i);
}
else {
a += 2;
prime(a, i);
}
}
int main()
{
p[0]=2;
int a(3), i(1) ;
prime(a, i);
int k, T;
cin >> T;
for(int i = 1; i <= T; i++){
cin >> k;
// You should do a check of whether k is larger than
// the size of your array, otherwise the check on p[k-1]
// will cause a seg fault.
if (k>max_size) {
std::cout << "That value is too large, try a number <= " << max_size << "." << std::endl;
} else {
cout << p[k - 1] << endl;
}
}
return 0;
}
A couple of other changes:
instead of filling the array until you reach a specific prime number, I've changed your check so that it will fill the array until it hits the maximum number of entries.
I've also included a check as to whether the user has passed an index number outside the range of the "p" array. Otherwise it will produce a segmentation fault.
Now compiling this and running gives:
$ g++ prime_calc.cpp -o prime_calc
$ ./prime_calc
3
1500
12553
15000
163841
15001
That value is too large, try a number <= 15000.