Question

here is code, which fills two dimensional array with random genarated numbers in range [1 19] without duplication, my question is: how to determine it’s complexity?

For example, I see that its running time is at least O(n^2), because of its inner and outer cycles, but that about the goto statement?

Here is my code:

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

int main()
{
    int min=1;
    int max=19;
    int  a[3][3];
    set<int>b;

    for (int i=0; i<3; i++)
    {
        for (int j=0; j<3; j++)
        {
loop:
            int m=min+rand()%(max-min);

            if (b.find(m)==b.end())
            {
                a[i][j]=m;
                b.insert(m);
            }
            else
                goto loop;
        }
    }

    for (int i=0; i<3; i++)
    {
        for (int j=0; j<3; j++)
            cout<< a[i][j]<<"  ";
        cout<<endl;
    }
    return 0;
}

I would say that complexity of algorithm is c*O(n^2) where c is some constant, it is because if it finds duplicated element inside cycles it repeats generation of random numbers and takes some constant time, am I right?

Answer 1

As the likelihood of getting a working number decreases, the number of goto-loops increases.
For a uniform random number generator, the behavior is linear with respect to the number of.. numbers. It definitely doesn’t add a constant to your complexity.

If n is the number of elements in a, then it’ll on average scale with O(n²). (or if n is the number of rows in the square matrix a; O(n⁴)).

A much simpler implementation would be using Fisher-Yates shuffle