Discussion 4 - Black

1. Answered HW questions (mostly just clarifications)

2. Did coin-changing problem with coin denominations 1, 3, 8, and 17

Question: what is the min # coins with which we can make T cents?

Let v_i be the value of coin i.  Let C(t, i) be the min number of coins
required to make t cents using only coins 1 thru i.

C(t,i) = min{C(t, i-1), C(t-v_i,i)+1}

Or (Rogaway's method):

C(t) = 1 + min{C(t-1), C(t-3), C(t-8), C(t-17)}

(these are roughly equivalent methods)

Now we build a table:

    0  1  2  3  4  5  6  7  8  9     <--- cents from 0 to 9
    --------------------------------
 1  0  1  2  3  4  5  6  7  8  9
 3  0  1  2  1  2  3  2  3  4  3
 8  0  1  2  1  2  3  2  3  1  2
17  0  1  2  1  2  3  2  3  1  2