Question

According to my analysis, the running time of this algorithm should be N², because each of the loops goes once through all the elements. I am not sure whether the presence of the if statement changes the time complexity?

for(int i=0; i<N; i++){
    for(int j=1; j<N; j++){

        System.out.println("Yayyyy");
        if(i<=j){
            System.out.println("Yayyy not");
        }
    }
}

Answer 1

• Tp: time it takes to print a constant text to standard output.
• Ti: time it takes for all other operations inside the inner loop (predicate evaluation etc.).
• To: time it takes for all operations inside the outer loop except the execution of inner loop (initializing counters etc.).
• Tc: time it takes for setting up the process and every other bookkeeping

Total running time will be Tc + N x (To + NxTi + N/2xTp).

This is equal to Tc + NxTo + (Nx(N/2)) x (2Ti + Tp) which is bounded by K x (N^2) for values of K > Ti + Tp/2 as N goes to infinity. This boundary makes the time complexity still O(N^2).

No, the if statement does not change the time complexity in this example.