Spring 2001 CS100M    Solutions to Exercise E7

notes
+ answers are below
+ you were not required to draw code inside the scopes,
  but we do so for clarity:
  + to show what code is run where
  + to keep track of what is being executed
+ code appears in multiple scopes: 
  only the code in the rightmost scope is actively running;
  other code is waiting for code to the right to finish
+ for an animated trace, download the following code from the Examples page:
  + $strhcat.m$
  + $boxscope.m$ -- upgraded since it was previously posted
  + $boxe7.m$ <-- run this function for the animation
  note: you might need to resize the Matlab Command Window
+ you can also download and run $boxfib.m$ to see an animated trace of calls
  to $fib$ (from the 2/27 lecture)

  note: $fib$ is renamed $f$ to save space, but you still might 
        need to resize the Matlab Command Window
_______________________________________________________________________________

Picture #1

+------------------------+
|command                 |
|+---------------------+ |
||     a = 10;         | |
||     b = 20;         | |
||     x = 30;         | |
|| --> % draw pic!     | |
||                     | |
||     x = g(15, 6);   | |
||     % draw pic!     | |
||   +----+            | |
|| a | 10 |            | |
||   +----+            | |
||   +----+            | |
|| b | 20 |            | |
||   +----+            | |
||   +----+            | |
|| x | 30 |            | |
||   +----+            | |
|+---------------------+ |
+------------------------+
_______________________________________________________________________________

Picture #2

+------------------------------------------------+
|command                 g                       |
|+---------------------+ +---------------------+ |
||     a = 10;         | | run function body   | |
||     b = 20;         | |                     | |
||     x = 30;         | |                     | |
||     % draw pic!     | | function x = g(a,b) | |
|| -->     ????????    | | --> % draw pic!     | |
||     x = g(15, 6);   | |     a = 2*a;        | |
||     % draw pic!     | |     b = 2*b;        | |
||   +----+            | |                     | |
|| a | 10 |            | |     [a,b] = f(b,a); | |
||   +----+            | |     a = 2*a;        | |
||   +----+            | |     b = 3*b;        | |
|| b | 20 |            | |     x = a-b;        | |
||   +----+            | |     % draw pic!     | |
||   +----+            | |   +----+            | |
|| x | 30 |            | | a | 15 |            | |
||   +----+            | |   +----+            | |
|+---------------------+ |   +---+             | |
|                        | b | 6 |             | |
|                        |   +---+             | |
|                        +---------------------+ |
+------------------------------------------------+
_______________________________________________________________________________

Picture #3

+----------------------------------------------------------------------------+
|command                 g                       f                           |
|+---------------------+ +---------------------+ +-------------------------+ |
||     a = 10;         | | run function body   | | run function body       | |
||     b = 20;         | |                     | |                         | |
||     x = 30;         | |                     | |                         | |
||     % draw pic!     | | function x = g(a,b) | | function [x,y] = f(a,b) | |
|| -->     ????????    | |     % draw pic!     | | --> % draw pic!         | |
||     x = g(15, 6);   | |     a = 2*a;        | |     x = b-a;            | |
||     % draw pic!     | |     b = 2*b;        | |     y = a;              | |
||   +----+            | | -->         ??????  | |     % draw pic!         | |
|| a | 10 |            | |     [a,b] = f(b,a); | |   +----+                | |
||   +----+            | |     a = 2*a;        | | a | 12 |                | |
||   +----+            | |     b = 3*b;        | |   +----+                | |
|| b | 20 |            | |     x = a-b;        | |   +----+                | |
||   +----+            | |     % draw pic!     | | b | 30 |                | |
||   +----+            | |   +----+            | |   +----+                | |
|| x | 30 |            | | a | 30 |            | +-------------------------+ |
||   +----+            | |   +----+            |                             |
|+---------------------+ |   +----+            |                             |
|                        | b | 12 |            |                             |
|                        |   +----+            |                             |
|                        +---------------------+                             |
+----------------------------------------------------------------------------+
_______________________________________________________________________________

Picture #4

+----------------------------------------------------------------------------+
|command                 g                       f                           |
|+---------------------+ +---------------------+ +-------------------------+ |
||     a = 10;         | | run function body   | | run function body       | |
||     b = 20;         | |                     | |                         | |
||     x = 30;         | |                     | |                         | |
||     % draw pic!     | | function x = g(a,b) | | function [x,y] = f(a,b) | |
|| -->     ????????    | |     % draw pic!     | |     % draw pic!         | |
||     x = g(15, 6);   | |     a = 2*a;        | |     x = b-a;            | |
||     % draw pic!     | |     b = 2*b;        | |     y = a;              | |
||   +----+            | | -->         ??????  | | --> % draw pic!         | |
|| a | 10 |            | |     [a,b] = f(b,a); | |   +----+                | |
||   +----+            | |     a = 2*a;        | | a | 12 |                | |
||   +----+            | |     b = 3*b;        | |   +----+                | |
|| b | 20 |            | |     x = a-b;        | |   +----+                | |
||   +----+            | |     % draw pic!     | | b | 30 |                | |
||   +----+            | |   +----+            | |   +----+                | |
|| x | 30 |            | | a | 30 |            | |   +----+                | |
||   +----+            | |   +----+            | | x | 18 |                | |
|+---------------------+ |   +----+            | |   +----+                | |
|                        | b | 12 |            | |   +----+                | |
|                        |   +----+            | | y | 12 |                | |
|                        +---------------------+ |   +----+                | |
|                                                +-------------------------+ |
+----------------------------------------------------------------------------+
_______________________________________________________________________________

Picture #5

+----------------------------------------------------------------------------+
|command                 g                       f                           |
|+---------------------+ +---------------------+ +----------------------/--+ |
||     a = 10;         | | run function body   | | kill activation reco/d  | |
||     b = 20;         | |                     | |                    /    | |
||     x = 30;         | |                     | |                   /     | |
||     % draw pic!     | | function x = g(a,b) | | function [x,y] = /(a,b) | |
|| -->     ????????    | |     % draw pic!     | |     % draw pic! /       | |
||     x = g(15, 6);   | |     a = 2*a;        | |     x = b-a;   /        | |
||     % draw pic!     | |     b = 2*b;        | |     y = a;    /         | |
||   +----+            | |                     | | --> % draw pi/!         | |
|| a | 10 |            | |     [a,b] = f(b,a); | |   +----+    /           | |
||   +----+            | |     a = 2*a;        | | a | 12 |   /            | |
||   +----+            | |     b = 3*b;        | |   +----+  /             | |
|| b | 20 |            | |     x = a-b;        | |   +----+ /              | |
||   +----+            | | --> % draw pic!     | | b | 30 |/               | |
||   +----+            | |   +----+            | |   +----/                | |
|| x | 30 |            | | a | 36 |            | |   +---/+                | |
||   +----+            | |   +----+            | | x | 1/ |                | |
|+---------------------+ |   +----+            | |   +-/--+                | |
|                        | b | 36 |            | |   +/---+                | |
|                        |   +----+            | | y / 12 |                | |
|                        |   +---+             | |  /+----+                | |
|                        | x | 0 |             | +-/-----------------------+ |
|                        |   +---+             |                             |
|                        +---------------------+                             |
+----------------------------------------------------------------------------+
_______________________________________________________________________________

Picture #6

+----------------------------------------------------------------------------+
|command                 g                       f                           |
|+---------------------+ +---------------------+ +----------------------/--+ |
||     a = 10;         | | kill activation rec.| | kill activation reco/d  | |
||     b = 20;         | |                     | |                    /    | |
||     x = 30;         | |                     | |                   /     | |
||     % draw pic!     | | function x = g(a,b) / | function [x,y] = /(a,b) | |
||                     | |     % draw pic!    /| |     % draw pic! /       | |
||     x = g(15, 6);   | |     a = 2*a;      / | |     x = b-a;   /        | |
|| --> % draw pic!     | |     b = 2*b;     /  | |     y = a;    /         | |
||   +----+            | |                 /   | | --> % draw pi/!         | |
|| a | 10 |            | |     [a,b] = f(b/a); | |   +----+    /           | |
||   +----+            | |     a = 2*a;  /     | | a | 12 |   /            | |
||   +----+            | |     b = 3*b; /      | |   +----+  /             | |
|| b | 20 |            | |     x = a-b;/       | |   +----+ /              | |
||   +----+            | | --> % draw /ic!     | | b | 30 |/               | |
||   +---+             | |   +----+  /         | |   +----/                | |
|| x | 0 |             | | a | 36 | /          | |   +---/+                | |
||   +---+             | |   +----+/           | | x | 1/ |                | |
|+---------------------+ |   +----/            | |   +-/--+                | |
|                        | b | 36/|            | |   +/---+                | |
|			 |   +--/-+            | | y / 12 |                | |
|			 |   +-/-+             | |  /+----+                | |
|			 | x |/0 |             | +-/-----------------------+ |
|			 |   /---+             |                             |
|			 +--/------------------+                             |
+----------------------------------------------------------------------------+