Please help for Big O analysis

[fung915]

Hi I have written a piece of code for this problem:

5. Given an input set S containing n real numbers and a real number x. Design an algorithm that determines whether there are two numbers in S whose sum is exactly x. Submit your algorithm and its time complexity analysis in terms of the big O.

Here is my code
for (i = 0 ; i < length; i ++)
for (j = i +1; j < length; j++)
if (array.i + array.j = x)
cout << i << j ;

My question is, I don't know if my code is O(n^2) or O(n log n)
Can someone please tell me which one it is....
Thank you very much

[Peter87]

For an iteration of the outer loop, what is the average number of comparisons that you are doing?

[fung915]

for (i = 0 ; i < length; i ++)
{
for (j = i +1; j < length; j++)
if (array.i + array.j = x)
{cout << i << j ; }
}

the whole thing should be like this.
So for outer loop, say i have an array of 5, array [1,2,3,4,5]
outer loop to put i point to array[0], and examine second loop
which it add array[0] and [1], [0] and [2], [0] and [3], and [0] and [4]
after that, i is incremented, and examine again
[1] and [2] , [1] and [3], [1] and [4], and so on

but I am confused about whether this algorithm is in O(n^2) or in O(n log n)

[fung915]

I guess the average number of comparison I am doing is depended on the amount of input n the algorithm is dealing with

[ne555]

> I am confused about whether this algorithm is in O(n^2) or in O(n log n)
don't guess, explain the rationale behind each of your answers.


Count the operations, if it's too hard to do, simulate.