查找此方法的时间复杂度

Question

I am trying to figure out the time complexity of this code.

My last conclusions about the sections is that the 'while' section the O(logn) the outer for loop must be under 100 so its O(1) and the inner for loop is O(logn) so i think that the time complexity here is O(logn) in the worst case but i am not sure.

public void foo (int n, int m) {
    int i = m;

    while (i > 100) {
        i = i/3;
    }

    for (int k=i ; k>=0; k--) {
        for (int j=1; j<n; j*=2) {
            System.out.print(k + "\t" + j);
        }

        System.out.println();
    }
}

Answer 1

Lets break your code step by step :

The first loop ie,

 while (i > 100)  
     i = i/3;

runs O(logm) times.

for (int k=i ; k>=0; k--) { 
        for (int j=1; j<n; j*=2) {
            System.out.print(k + "\t" + j); 
        } //end inner for loop
        System.out.println(); 
    }

The outer loop can run atmost 100 times, and the inner loop ie

for (int j=1; j<n; j*=2) {
      System.out.print(k + "\t" + j); 
} //end inner for loop

executes logn times.

total time complexity of for loops = 100logn - > ignoring constants - > logn

Therefore, the complexity is O(log(m)) + O(log(n))