一个简单的 while 循环的时间复杂度

Question

I am confused as to the time complexity of this code.

int a = 1;

while ( a < n ) {
  a = a * 2;
}

I am new to time complexities

Answer 1

It's log(n). If n is 4, the loop executes 2 times. If n is 8, the loop executes 3 times. If n is 16, the loop executes 4 times.

That's a logarithmic relationship, not a linear one.

Answer 2

If you check for the values a can get you will see:

1, 2, 4, 8, 16, 32, ..., 

and the iterations will continue until a is smaller than n , which means that the number of iterations is bounded by ⌈log2(n)⌉ .

You can thus conclude that the time complexity is logarithmic in n .