Calculating Big O

Suppose we have the following function

func(x):
	if cond1 
		O(n^2)
	elif cond2
		O(n)
	else 
		O(1)

How do we define the average time complexity:

any input which isn't setup to be special
1. linear search which always finds the first elementO(1)
2. linear search that doen't find anything/last elementO(n)

With linear searches: finding an average item in the middle(somwhere) we have to cover: * x% of the n size list

Since we drop the constants in time complexity expressions we thus end up with O(n).

Heap Sort

Time Complexity Exercise

Time Complexity Exercise

Best:
- Already sorted meaning we go through the whole list once
- O(n) - because we'll do the check into our left sub-list but we don't go into it leaving us as constant time spent per item ie c*n
Average:
- Pretty close to n^2 just for the sake of
- O(n^2)
Worst:
- Going through the whole list sorting everything(backwards)
- O(n^2)
  - must go through N items for each item
Space:

Time Complexity: O(n)

Space Complexity: OMEGA(n)

Both Complexity: THETA(n) * such a complexity only exists if O(n) == OMEGA(n)