c++ - What is the correct Big O of this code -

i'm trying learn big o notation , i'm little confused c++ code:

void enterelements(int *s1, int s1size) {     for(int x = 0;x < s1size;++x)     {     retry:         cout<<"element "<<x + 1<<": ";         cin>>s1[x];         int valid = validation();         if(valid == 1)         {             cout<<"the input must numbers."<<endl;             goto retry;         }     } } 

because don't know how got 3 results:

1. 9n + 1 -> o(n)
2. 7nm + 2m + 2n + 1 -> o(nm)
3. 7n^2 + 4n + 1 -> o(n^2)

is of correct? if not, can me find correct answer?

int validation() { int validation = 0; if(cin.fail()) {     validation = 1;     cin.clear();     cin.ignore(std::numeric_limits<std::streamsize>::max(),'\n'); } else     validation = 0; return validation; } 

big-oh notation isn't applicable here. have lower bound, there absolutely no gurantees on validation(), big-oh designation o(inf), that's quite unhelpful.

your code (should validations go properly), be:

Ω(s1size) 

because executed s1size times, not less. big-oh notation not lower bounds. since have no guarantee on how many times goto statement used, , therefore no upper bound, no applicable big-oh derivation.

your runtime, in simple terms: greater or equal s1size iterations (barring error causes loop exit).

thus best case above, , worst case, well, forever!

edit: Ω correct here, not ω, Ω implies runtime greater or equal s1size