Task 1: "Coins Sum

You are given a set of coins @C, assuming you have infinite amount of each coin in the set.

Write a script to find how many ways you make sum $S using the coins from the set @C.
Example:

Input:
    @C = (1, 2, 4)
    $S = 6

Output: 6
There are 6 possible ways to make sum 6.
a) (1, 1, 1, 1, 1, 1)
b) (1, 1, 1, 1, 2)
c) (1, 1, 2, 2)
d) (1, 1, 4)
e) (2, 2, 2)
f) (2, 4)
"

My notes: ok.  Reasonably easy: bag of coins shows what coins we've used,
at every stage explore 2 paths: 1). add another instance of each possible coin,
2). don't add another instance..

Task 2: "Largest Rectangle Histogram

You are given an array of positive numbers @A.

Write a script to find the largest rectangle histogram created by the given array.
BONUS: Try to print the histogram as shown in the example, if possible.

Example 1:

Input: @A = (2, 1, 4, 5, 3, 7)

     7           #
     6           #
     5       #   #
     4     # #   #
     3     # # # #
     2 #   # # # #
     1 # # # # # #
     _ _ _ _ _ _ _
       2 1 4 5 3 7

Looking at the above histogram, the largest rectangle (4 x 3) is formed by columns (4, 5, 3 and 7).
Output: 12

Example 2:

Input: @A = (3, 2, 3, 5, 7, 5)

     7         #
     6         #
     5       # # #
     4       # # #
     3 #   # # # #
     2 # # # # # #
     1 # # # # # #
     _ _ _ _ _ _ _
       3 2 3 5 7 5

Looking at the above histogram, the largest rectangle (3 x 5) is formed by columns (5, 7 and 5).
Output: 15"

My notes: hmm.. so max(area of all rectangles "in" a histogram).  But what does that mean?
Hang on: the "graphs" are NOT actually histograms: each is simply the array of values itself.
So forgot frequency hashes.  The simplest way that I can see is to calculate the area of all
possible rectangles (where 1 or more adjacent values are at least some minimum height) and
then to find the maximum of all those.