programs

Logic Games

Challenges to programming which can be “circumvented” using logic commands

Thinking about the program

Working around the problem

Lateral Thinking Example: Cake Cut

Can easily cut cake in to 8 even pieces (4 cuts) …

How can we get 8 even pieces with 3 cuts?

ahem …

Lots of ways to get around things

Projectile Motion – tend issue

Goal was to have the projectile plot STOP when the object reaches the ground again (y = 0)

Calculate tend from quadratic equation and limit the range of the time vector (t = 0: step: tend)

• do while • for + if • calculate to t = 1,000 and then “cut” the vector • calculate to t = 1,000 and then plot only to y = 0

while • variant on do-loop • condition is “while this is satisfied”

n = 10 ; f = n ; while n > 1

n = n-1 ; f = f*n ;

end disp(['n! = ’, num2str(f)])

factorials. 6! = 6 * 5* 4* 3* 2 * 1

apply the while construct here to avoid using the quadratic

equation to find tend

Compare some Approaches

tend from quadratic equation is probably the

most “elegant” of the options

(but they all work)

Logic Commands

Reduce things to TRUE vs. NOT-TRUE

= = (exactly equal to) ~= (not equal to) <= (less than or equal to)

Can we use these in a subtle manner? – capitalizing on the output (1 for true, 0 for false)

Recall ….

• <, >, ==, ~=

• Command window: x = 5; y = 1; x<y

logical 0

derp.

how is this useful?

Challenge Problem

Code to plot [ sin(x)/x ] from -4pi to + 4pi

This function shows up in a lot of engineering projects

• radar systems • filtering of signals • probability theory • Fourier transforms

what problems does this code have?

the old “divide by zero” issue …

classic

OK – fix it. (i.e. how can we use a logic structure to repair it?)

Ran “fine” without – but we couldn’t operate on y at all because of NaN

Now is good

-15 -10 -5 0 5 10 15 -0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Challenge Problem

• Plot [ tan(x) ] from -3/2 pi to + 3/2 pi

• Seems simple enough.

I love San Francisco

Looks really easy to write …

Looks like poo ….

-5 -4 -3 -2 -1 0 1 2 3 4 5 -6

-4

-2

0

2

4

6 10 15

We “know” tan(x) and this isnt’ it

-5 -4 -3 -2 -1 0 1 2 3 4 5 -6

-4

-2

0

2

4

6 10 15

What is the problem with this code and how can we fix it?

-5 -4 -3 -2 -1 0 1 2 3 4 5 -6

-4

-2

0

2

4

6 10 15

goal is to use logic structures ”inline” with the code

Share out ….

Education is a crucible for your transformation

as a result … you should see world differently

scribbles evolve

• keep at it