What's complexity of this algorithm?

Question

I'm learning how to find algorithm complexity and I can't figure out what's the complexity of this algorithm. Could someone explain to me how to get the answer?

void algorithm(int a, int b) {
    while (a >= b) {
        int x = a - b;
        for (int i = 0; i <= x; i++) {
            std::cout << "complexity of this algorithm?";
        }
        a = x;
    }
}

Please any input is welcome. This is what I have so far:

Answer 1

The complexity is (a^2/b)

As I described in the image, you need to sum up all "x", then you will get the complexity.

in summation part for (-b -2b -3b - ... -nb) you can write :
[![enter image description here][1]][1]-b (1+2+...)
so this is -b*(n(n+1)/2)

summation_part_definition_link

So in the end, if "a" and "b" were for the same order then the result is :

O(c) = 0 (c is numeric)

this means complexity is in numeric order. but if "a" was for upper order then the result is :

O((a^2)/b)

Answer 2

As a is modified, you should have it in parameters of the sum:

(1) x = a - b  // first iteration
(2) x = a - 2b // second iteration
(3) x = a - 3b
...

if a = k * b, the outer loop iterates k times. Hence, the final complexity is:

(a - b) + (a - 2b) + ... + (a - (k-1) b) = 
(k-1) b + (k-2) b + ... + b = k * (k-1) * b/2

As you have mentioned , time complexity is .