Jan 31

• the textbook anagram algorithm
• run time for built-in python data structures and their methods
• timing programs (see below)

O() details

• O(n) is an upper bound (i.e. "at most", i.e. ≤ )
• Ω(n) represents lower bound (i.e. "a least", i.e. ≥ )
• Θ(n) means tight bound (i.e. "approximately", i.e. ≈ ) ;
  • f(x) = Θ(g(x)) iff f(x) = O(g(x)) and f(x) = Ω(g(x))

• worst case runtime
• average runtime (average over what?)

measuring execution speed

count program steps

• Same algorithm in a given language gives same number of steps on any computer.
• Not dependent on any other activity on the computer.

• Awkward to put into the code - can't easily feed a function f(x) into something to count steps.
• Depends on what one of code does, which depends on language features used. (Example: is "a=sorted(b)" one step?)

find elapsed time

• Can do with code outside of function being measured.
• Independent of tricky language features (i.e. "a=sorted(b)).

• Will change depending on what else computer is doing - not exactly repeatable.
• Varies substantially with computer power.

time vs space