What does “in constant time” imply?

Question

I work as a programmer, but have no computer science background, so recently I\'ve been following along with the excellent MIT OpenCourseWare intro to Computer Science and Progr

Answer 1

"Constant time" means that the operation will execute in an amount of time (or memory space - that's another thing often measured) independent of the input size. Usually you pick a variable (let's use n) to indicate the input size.

O(1) - constant time - running time does not depend on n

O(n) - linear time - running time is linearly proportional to n

O(n^2) - quadratic time - running time is proportional to the square of n

These are just a few examples; the possibilities are endless. See the wiki article on complexity

Here's a few specific ways that a program composed of only the operations you mention could take various amounts of time:

int n = // some value
doSomething
doSomething
doSomething

Note how it is three somethings in length, independent of what n is. O(1)

int n = // some value
def f(n):
    if n == 0 return
    doSomething
    f(n-1)
f(n)

Now we run a something for each value 0..n (linear time, O(n))

And we can have a bit of fun -

int n = //some value
def f(n):
    if n == 0 return
    doSomething
    f(n-1)
    f(n-1)

What's the running time here? (i.e. how many somethings do we execute?) :)