Task 1: Toeplitz Matrix

You are given an m x n matrix.  Write a script to find out if the given
matrix is a Toeplitz Matrix - a matrix is Toeplitz if every diagonal
from top-left to bottom-right has the same elements.

Example 1

  Input: @matrix = [ [4, 3, 2, 1],
                     [5, 4, 3, 2],
                     [6, 5, 4, 3],
                   ]
  Output: true

Example 2

  Input: @matrix = [ [1, 2, 3],
                     [3, 2, 1],
                   ]
  Output: false

MY NOTES: sounds very easy.

GUEST LANGUAGE: As a bonus, I also had a go at translating ch-1.pl into C
(look in the C directory for that).


Task 2: Split Same Average

You are given an array of integers.  Write a script to find out if the
given can be split into two separate arrays whose average are the same.

Example 1:

  Input: @nums = (1, 2, 3, 4, 5, 6, 7, 8)
  Output: true

  We can split the given array into (1, 4, 5, 8) and (2, 3, 6, 7).
  The average of the two arrays are the same i.e. 4.5.

Example 2:

  Input: @list = (1, 3)
  Output: false

MY NOTES: sounds easy enough as a brute force search.
First observation: the "average of each sub-array" (our goal) must be
the overall average, as that's the only way the sub-array averages can be
the same value.
Second observation: each element is either in the first subarray or in the
second subarray, a binary counting approach is the obvious brute force method.
(Note: I last did this in challenge 136, task 2, when we were summing subsets
of Fibonacci numbers, so I've reused a little code from there).
Third observation: we need only check one of the two sub-arrays (eg the first)
as having the right sub-array average - the overall average.

GUEST LANGUAGE: As a bonus, I also had a go at translating ch-2.pl into C
(look in the C directory for that)