feynmanium - 1 year ago 87

Java Question

I am having trouble figuring out the time complexity of this code:

`public static void myfun1 (int n) {`

System.out.println("n = " + n);

for (int k = 1; k <= n / 2; k++){

System.out.println(k);

for(int m = 1; m <= k; m++){

System.out.println(k + ", " + m);

}

}

}

public static void main(String[] args){

myfun1(8);

}

When i ran it for n=8, the following was the output:

Output

I am thinking that the first loop will run (n/2) and that I have to multiply it by the inner loop. What I am having trouble with, is the inner loop. Normally I would assume two nested loops are (n^2) but I feel that n/2 in the first loop is correct but I am not sure how the inner loop relates to it. I see that from the output for every k there are k number of loops done my m. For some reason my brain can't translate this relationship in terms of n. Can someone offer me some guidance on this?

Thanks in advance.

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Answer Source

Your inner loop runs 1 time the first time
2 times the second time... up to `n/2`

so it runs like the sum of integers from 1 to `n/2`

= `((n/2+1)*n)/4`

(For 8, it runs 10 times, add a counter to make sure)

So complexity is O(n**2) here.

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