Spring 2001 CS100M  
Exercise E11: A Picture is Worth a Thousand Words
Due: online 8am, Thursday 3/15

This exercise is to give you some practice with 2-dimensional array indexing
("indexing" = "accessing elements/positions in an array").

===============================================================================
                                task
===============================================================================

Complete the "skeleton" code provided at the end of this write-up to make
function $e11(m)$ take a positive integer $m$ in the range 10..30 and 
return an $m$-by-$2m$ string matrix $s$ with:

$*$s on the border (left, right, top, and bottom edges)
$\$s on the diagonal, except for on the border
     (the *diagonal* of a matrix = all valid positions (i,i) in the matrix)
$-$s below the diagonal, except for on the border
$+$s on the edge, $@$s in the interior, and $c$ at the center of
     a disk of radius $round(m*.35)$ and center $(round(m*1.5),round(m/2))$


Note on mathematical terminology:

+ a *circle* is just the "edge"; it does not include the points inside.

+ a *disk* = the points inside a circle, possibly including the circle itself.


Hints

+ if pressed for time (e.g. studying for Prelim T2), you should still do 
  this exercise, but you might want to skip dealing with the disk.

+ examples for $m=10$, $m=20$, and $m=30$ are shown below

+ you can overwrite values: e.g. place $\$s along the entire diagonal,
  including positions $(1,1)$ and $(m,m)$, and then afterwards place $*$s
  on the border.

+ the distance between positions $(x1,y1)$ and $(x2,y2)$ is 
  $sqrt((x1-x2)^2 + (y1-y2)^2)$.

+ draw a $+$ at each position $(i,j)$ whose distance from $(xc,yc)$ is 
  in the range $]r-.5,r+.5[$.


Bonus: include the word "bonus" in a comment in your code and do either/both:

+ [1 bonus pt]  Include coordinate labels as part of $s$, as shown in the 
  examples below.  Hint: tranposition ($'$) might be useful.

+ [1 bonus pt]  Use logical arrays and other vectorization techniques 
  to write concise code: each comment in the skeleton can be implemented 
  without loops in 1 or 2 lines.  Hint: $x$, $y$ should be very useful.


===============================================================================
                                examples
===============================================================================

note: coordinates are shown for clarity
      -- you are NOT required to include coordinates as part of $s$!

e11(10):
            11111111112
   12345678901234567890
                       
 1 ************+++++***
 2 *\ooooooooo++@@@++o*
 3 *-\ooooooo++@@@@@++*
 4 *--\oooooo+@@@@@@@+*
 5 *---\ooooo+@@@c@@@+*
 6 *----\oooo+@@@@@@@+*
 7 *-----\ooo++@@@@@++*
 8 *------\ooo++@@@++o*
 9 *-------\ooo+++++oo*
10 ********************

e11(20):
            1111111111222222222233333333334
   1234567890123456789012345678901234567890
                                           
 1 ****************************************
 2 *\ooooooooooooooooooooooooooooooooooooo*
 3 *-\oooooooooooooooooooooooo+++++ooooooo*
 4 *--\ooooooooooooooooooooo++@@@@@++ooooo*
 5 *---\ooooooooooooooooooo+@@@@@@@@@+oooo*
 6 *----\ooooooooooooooooo+@@@@@@@@@@@+ooo*
 7 *-----\oooooooooooooooo+@@@@@@@@@@@+ooo*
 8 *------\oooooooooooooo+@@@@@@@@@@@@@+oo*
 9 *-------\ooooooooooooo+@@@@@@@@@@@@@+oo*
10 *--------\oooooooooooo+@@@@@@c@@@@@@+oo*
11 *---------\ooooooooooo+@@@@@@@@@@@@@+oo*
12 *----------\oooooooooo+@@@@@@@@@@@@@+oo*
13 *-----------\oooooooooo+@@@@@@@@@@@+ooo*
14 *------------\ooooooooo+@@@@@@@@@@@+ooo*
15 *-------------\ooooooooo+@@@@@@@@@+oooo*
16 *--------------\ooooooooo++@@@@@++ooooo*
17 *---------------\oooooooooo+++++ooooooo*
18 *----------------\ooooooooooooooooooooo*
19 *-----------------\oooooooooooooooooooo*
20 ****************************************

e11(30):
            111111111122222222223333333333444444444455555555556
   123456789012345678901234567890123456789012345678901234567890
                                                               
 1 ************************************************************
 2 *\ooooooooooooooooooooooooooooooooooooooooooooooooooooooooo*
 3 *-\oooooooooooooooooooooooooooooooooooooooooooooooooooooooo*
 4 *--\ooooooooooooooooooooooooooooooooooooo+++++++ooooooooooo*
 5 *---\oooooooooooooooooooooooooooooooooo++@@@@@@@++ooooooooo*
 6 *----\ooooooooooooooooooooooooooooooo++@@@@@@@@@@@++ooooooo*
 7 *-----\ooooooooooooooooooooooooooooo++@@@@@@@@@@@@@++oooooo*
 8 *------\ooooooooooooooooooooooooooo++@@@@@@@@@@@@@@@++ooooo*
 9 *-------\oooooooooooooooooooooooooo+@@@@@@@@@@@@@@@@@+ooooo*
10 *--------\oooooooooooooooooooooooo+@@@@@@@@@@@@@@@@@@@+oooo*
11 *---------\ooooooooooooooooooooooo+@@@@@@@@@@@@@@@@@@@+oooo*
12 *----------\ooooooooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
13 *-----------\oooooooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
14 *------------\ooooooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
15 *-------------\oooooooooooooooooo+@@@@@@@@@@c@@@@@@@@@@+ooo*
16 *--------------\ooooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
17 *---------------\oooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
18 *----------------\ooooooooooooooo+@@@@@@@@@@@@@@@@@@@@@+ooo*
19 *-----------------\ooooooooooooooo+@@@@@@@@@@@@@@@@@@@+oooo*
20 *------------------\oooooooooooooo+@@@@@@@@@@@@@@@@@@@+oooo*
21 *-------------------\oooooooooooooo+@@@@@@@@@@@@@@@@@+ooooo*
22 *--------------------\ooooooooooooo++@@@@@@@@@@@@@@@++ooooo*
23 *---------------------\ooooooooooooo++@@@@@@@@@@@@@++oooooo*
24 *----------------------\ooooooooooooo++@@@@@@@@@@@++ooooooo*
25 *-----------------------\oooooooooooooo++@@@@@@@++ooooooooo*
26 *------------------------\ooooooooooooooo+++++++ooooooooooo*
27 *-------------------------\oooooooooooooooooooooooooooooooo*
28 *--------------------------\ooooooooooooooooooooooooooooooo*
29 *---------------------------\oooooooooooooooooooooooooooooo*
30 ************************************************************

===============================================================================
                        skeleton code for function $e11$
===============================================================================

function s = e11(m)

% s = e11(m): return a $m$-by-$2m$ string matrix $s$ with
% + $*$s on the border (left, right, top, and bottom edges)
% + $\$s on the diagonal, except for on the border
%   (the *diagonal* of a matrix = all valid positions (i,i) in the matrix)
% + $-$s below the diagonal, except for on the border
% + $+$s on the boundary, $@$s in the interior, and $c$ at the center of
%   a disk of radius $round(m*.35)$ and center $(round(m*1.5),round(m/2))$

n = 2*m; % width of $s$             % [3/14] fixed typo below, where $xc<-->yc$
xc = round(m*1.5); yc = round(m/2); % (yc,xc) = center of disk
r = round(m*.35);                   % radius of disk

% $x$, $y$: very useful for vectorization bonus, but probably no help otherwise
    y = repmat((1:m)', 1, n);       % y(i,j) = i = the row position (i,j) is in
    x = repmat(1:n, m, 1);          % x(i,j) = j = the col position (i,j) is in

s(m,n) = ' '; % make $s$ large enough
s(:,:) = 'o'; % fill each element with $'o'$

% place $-$s below diagonal
    % ******** your code goes here ********

% place $\$s on diagonal
    % ******** your code goes here ********

% place $*$s on border
    % ******** your code goes here ********

% place $@$s inside disk
    % ******** your code goes here ********

% place $+$s on disk 
    % ******** your code goes here ********

% place $c$ at center of disk (done for you:)
    s(yc, xc) = 'c';

===============================================================================
                                submission
===============================================================================

Submit online at the Exercise Submission site by 8am of the due date.