We learned about big O notation, but I often see T(n) as well. For example,
public static Comparable[] mergeSort(Comparable[] A, int low, int high) {
if (low < high) { //at least 2 elements? //cost = c
int mid = (low + high)/2; //cost = d
Comparable[] A1 = mergeSort(A, low, mid); //cost = T(n/2) + e
Comparable[] A2 = mergeSort(A, mid+1, high); //cost = T(n/2) + f
return merge(A1,A2); //cost = g n + h
}
.... //cost = i
I believe c,d,e,... are meant to be arbitrarily named constants.
What does T(n/2) mean? also how is T notation related to big O?
Answer
This notation refers to the maximum amount of time (or, more specifically, steps) that a function takes to run.
T(n) may be much more specific than O(n); for example, let's say you have a program that for any input, requires n^2+n+1 steps to run:
T(n) = n^2+n+1
O(n) = n^2
More information can be found here.