Feb 3

homework

2.12 : see protected for numerical experiment

 f(10) = 15
 f(100) = 127
 f(1000) = 1023
 f(10000) = 16384
 So ... what's the pattern?  What's O(f)?  Explain.

2.14 : sort O(n log(n)), then remove duplicates with O(n). Explain.

Quicksort : in place, with swaps; discuss. (See attached.)

Radix sort : describe basic ideas.

Describe the basic idea :

transform a function g(time in sec) to G(freq in Hz) by a "change of basis".
cosines and sines become complex exponentials.
inner product picks out one component
can be done as discrete series or continuous integrals
used often in both CS (compression, signal analysis) and physics (quantum is loaded with it)
very cool ... but uses some semi-formidable math

So :