Read exercises

For each of the following exercises, try to figure out what the input will produce in the TryAPL terminal. Check your answers by opening the "Output" tab.

If you think an error will occur, try to predict which error it will be and where the arrow will point to.

The exercises are not checked or graded: use them to check your knowledge!

Read problem 1

InputOutput

      5 ? 52

      5 ? 52
38 47 28 43 41

      ⍝ Dealing 5 random numbers without repetition from 1 and 52

Read problem 2

InputOutput

      CARDS
┌──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┐
│♠2│♠3│♠4│♠5│♠6│♠7│♠8│♠9│♠10│♠J│♠Q│♠K│♠A│♥2│♥3│♥4│♥5│♥6│♥7│♥8│♥9│♥10│♥J│♥Q│♥K│♥A│♦2│♦3│♦4│♦5│♦6│♦7│♦8│♦9│♦10│♦J│♦Q│♦K│♦A│♣2│♣3│♣4│♣5│♣6│♣7│♣8│♣9│♣10│♣J│♣Q│♣K│♣A│
└──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┘

      CARDS[5 ? 52]

      CARDS
┌──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬───┬──┬──┬──┬──┐
│♠2│♠3│♠4│♠5│♠6│♠7│♠8│♠9│♠10│♠J│♠Q│♠K│♠A│♥2│♥3│♥4│♥5│♥6│♥7│♥8│♥9│♥10│♥J│♥Q│♥K│♥A│♦2│♦3│♦4│♦5│♦6│♦7│♦8│♦9│♦10│♦J│♦Q│♦K│♦A│♣2│♣3│♣4│♣5│♣6│♣7│♣8│♣9│♣10│♣J│♣Q│♣K│♣A│
└──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴───┴──┴──┴──┴──┘

      CARDS[5 ? 52]
┌──┬──┬───┬───┬──┐
│♥K│♦3│♠10│♥10│♠7│
└──┴──┴───┴───┴──┘
      ⍝ Dealing a hand of five cards

Read problem 3

InputOutput

      APL
     ._________________.    
     |.---------------.|    
     ||  __  ____ __  ||    
     || / _\(  _ (  ) ||    
     ||/    \) __/ (_/||    
     ||\_/\_(__) \____||    
     ||_______________||    
     /.-.-.-.-.-.-.-.-.\    
    /.-.-.-.-.-.-.-.-.-.\   
   /.-.-.-.-.-.-.-.-.-.-.\  
  /______/__________\_____\ 
  \_______________________/ 
      2/APL

      APL
     ._________________.    
     |.---------------.|    
     ||  __  ____ __  ||    
     || / _\(  _ (  ) ||    
     ||/    \) __/ (_/||    
     ||\_/\_(__) \____||    
     ||_______________||    
     /.-.-.-.-.-.-.-.-.\    
    /.-.-.-.-.-.-.-.-.-.\   
   /.-.-.-.-.-.-.-.-.-.-.\  
  /______/__________\_____\ 
  \_______________________/ 
      2/APL
      ..__________________________________..        
      ||..------------------------------..||        
      ||||    ____    ________  ____    ||||        
      ||||  //  __\\((    __  ((    ))  ||||        
      ||||//        \\))  ____//  ((__//||||        
      ||||\\__//\\__((____))  \\________||||        
      ||||______________________________||||        
      //..--..--..--..--..--..--..--..--..\\        
    //..--..--..--..--..--..--..--..--..--..\\      
  //..--..--..--..--..--..--..--..--..--..--..\\    
//____________//____________________\\__________\\  
\\______________________________________________//

Read problem 4

InputOutput

      DICTIONARY
AA  
AAHED  
AAHING  
AAHS  
AALII  
AALIIS  
AALS  
AARDVARK 
. . .
      DICTIONARY[1;]
AA
      DICTIONARY[;1]
A
A
A
A
. . .
      DICTIONARY[⍸DICTIONARY[;1]='X';]

      DICTIONARY
AA  
AAHED  
AAHING  
AAHS  
AALII  
AALIIS  
AALS  
AARDVARK 
. . .
      DICTIONARY[1;]
AA
      DICTIONARY[;1]
A
A
A
A
. . .
      DICTIONARY[⍸DICTIONARY[;1]='X';]
XANTHAM        
XANTHAMS       
XANTHAN        
XANTHANS       
XANTHATE       
XANTHATES      
. . .

All words starting with 'X'

Read problem 5

InputOutput

      'TELE' ⍷ DICTIONARY
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . .
      ⍸ 'TELE' ⍷ DICTIONARY
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬─
│14061 2│14062 2│14063 2│14064 2│14065 2│18946 3│18947 3│18948 3│19107 4│19108 4│19109 4│23447 4│23448 4│23449 4│35280 4│4
└───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴─
      1 1⊃(⍸ 'TELE' ⍷ DICTIONARY)

      'TELE' ⍷ DICTIONARY
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . .
      ⍸ 'TELE' ⍷ DICTIONARY
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬─
│14061 2│14062 2│14063 2│14064 2│14065 2│18946 3│18947 3│18948 3│19107 4│19108 4│19109 4│23447 4│23448 4│23449 4│35280 4│4
└───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴─
      1 1⊃(⍸ 'TELE' ⍷ DICTIONARY)
14061

Read problem 6

InputOutput

      DICTIONARY[1 1⊃(⍸ 'TELE' ⍷ DICTIONARY);]

      DICTIONARY[1 1⊃(⍸ 'TELE' ⍷ DICTIONARY);]
ATELECTASES

First word with 'TELE'

Read problem 7

ProblemSolution

$$ \sum_{n=1}^{100} \frac{1}{n^2} $$

can be written in APL using reduce / as...

$$ \sum_{n=1}^{100} \frac{1}{n^2} $$

can be written in APL using reduce / as...

      +/ 1÷2*⍨⍳100

Read problem 8

ProblemSolution

$$ \frac{1}{\frac{2}{\frac{3}{\frac{\dots}{10}}}} $$

can be written in APL using reduce / as

$$ \frac{1}{\frac{2}{\frac{3}{\frac{\dots}{10}}}} $$

can be written in APL using reduce / as

      ÷/⍳10

Read problem 9

InputOutput

$$ \frac{F_1}{F_2},\frac{F_2}{F_3},\ldots,\frac{F_9}{F_{10}} $$

where $F_n$ is the nth Fibonacci number, can be written in APL (given an array FIBB of the first 10 Fibonacci numbers) as

$$ \frac{F_1}{F_2},\frac{F_2}{F_3},\ldots,\frac{F_9}{F_{10}} $$

where $F_n$ is the nth Fibonacci number, can be written in APL (given an array FIBB of the first 10 Fibonacci numbers) as

      2÷/FIBB

This is a sequence of approximations to the golden ratio

Read problem 10

InputOutput

      VOTES ← 'HAUNTED HOUSE' 'CAFE' 'CAFE' 'CAFE' 'HAUNTED HOUSE' 'HAUNTED HOUSE' 'CAFE' 'HAUNTED HOUSE' 'ANIMAL CAFE' 'CAFE' 'CAFE'
      {⍺,⍴⍵}⌸VOTES

      VOTES ← 'HAUNTED HOUSE' 'CAFE' 'CAFE' 'CAFE' 'HAUNTED HOUSE' 'HAUNTED HOUSE' 'CAFE' 'HAUNTED HOUSE' 'ANIMAL CAFE' 'CAFE' 'CAFE'
      {⍺,⍴⍵}⌸VOTES
┌─────────────┬─┐
│HAUNTED HOUSE│4│
├─────────────┼─┤
│CAFE         │6│
├─────────────┼─┤
│ANIMAL CAFE  │1│
└─────────────┴─┘

Read problem 11

InputOutput

      ({⍺}⌸VOTES)[⍒{⍴⍵}⌸VOTES]

      ({⍺}⌸VOTES)[⍒{⍴⍵}⌸VOTES]
┌────┬─────────────┬───────────┐
│CAFE│HAUNTED HOUSE│ANIMAL CAFE│
└────┴─────────────┴───────────┘

Read problem 12

InputOutput

      ⍝ Hours spent on homework per day
      HOMEWORK ← 1 1 2 2 4 0 1
      +/HOMEWORK

      +\HOMEWORK

      2-/HOMEWORK

      -2-/HOMEWORK

      +\-2-/HOMEWORK

      +\HOMEWORK[1],-2-/HOMEWORK

      ⍝ Hours spent on homework per day
      HOMEWORK ← 1 1 2 2 4 0 1
      +/HOMEWORK
11
      +\HOMEWORK
1 2 4 6 10 10 11
      2-/HOMEWORK
0 ¯1 0 ¯2 4 ¯1
      -2-/HOMEWORK
0 1 0 2 ¯4 1
      +\-2-/HOMEWORK
0 1 1 3 ¯1 0
      +\HOMEWORK[1],-2-/HOMEWORK
1 1 2 2 4 0 1

The first number is the total number of hours spent on homework, the second is the cumulative number of hours, the third the difference in number of hours between the days.

Notice that the cumulative sum of the first element of HOMEWORK with the first differences of HOMEWORK is the same as HOMEWORK itself. If you know a little calculus, this might look familiar as the integral of the derivative being the same function up to a constant C.