Write exercises

Submit APL code for the following exercises. Your submissions are graded using TMC.

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You can submit as many solutions as you like. If you submit a correct solution at least once, you will receive points on the TMC server and be able to see the model solution.

If the write problem is red, it is unsolved. If it it green, you have solved it and received points for it on the server.

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Write problem 1

Create a vector consisting of the first ten prime numbers called PRIMES

⎕← Submit

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Write problem 2

Create a vector called POWER of value 2 to the power of PRIMES, minus two

⎕← Submit

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Write problem 3

Divide the vector POWER by PRIMES

⎕← Submit

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Write problem 4

Create the word "BUNNY" by indexing the alphabet vector ⎕A

⎕← ⎕A[ Submit

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Write problem 5

The following matrix CIPHER consists of shifted versions of the alphabet for every row.

      CIPHER
  ABCDEFGHIJKLMNOPQRSTUVWXYZ
  BCDEFGHIJKLMNOPQRSTUVWXYZA
  CDEFGHIJKLMNOPQRSTUVWXYZAB
  DEFGHIJKLMNOPQRSTUVWXYZABC
  EFGHIJKLMNOPQRSTUVWXYZABCD
  FGHIJKLMNOPQRSTUVWXYZABCDE
  GHIJKLMNOPQRSTUVWXYZABCDEF
  HIJKLMNOPQRSTUVWXYZABCDEFG
  IJKLMNOPQRSTUVWXYZABCDEFGH
  JKLMNOPQRSTUVWXYZABCDEFGHI
  KLMNOPQRSTUVWXYZABCDEFGHIJ
  LMNOPQRSTUVWXYZABCDEFGHIJK
  MNOPQRSTUVWXYZABCDEFGHIJKL
  NOPQRSTUVWXYZABCDEFGHIJKLM
  OPQRSTUVWXYZABCDEFGHIJKLMN
  PQRSTUVWXYZABCDEFGHIJKLMNO
  QRSTUVWXYZABCDEFGHIJKLMNOP
  RSTUVWXYZABCDEFGHIJKLMNOPQ
  STUVWXYZABCDEFGHIJKLMNOPQR
  TUVWXYZABCDEFGHIJKLMNOPQRS
  UVWXYZABCDEFGHIJKLMNOPQRST
  VWXYZABCDEFGHIJKLMNOPQRSTU
  WXYZABCDEFGHIJKLMNOPQRSTUV
  XYZABCDEFGHIJKLMNOPQRSTUVW
  YZABCDEFGHIJKLMNOPQRSTUVWX
  ZABCDEFGHIJKLMNOPQRSTUVWXY

The Caesar cipher encrypts a phrase by shifting all its letters by a specific amount along the alphabet. For example, "ARENA" becomes "RIVER" under a shift of 9 places. Use indexing of the above matrix to encipher the word "BUNNY" by shifting its letters 17 places.

⎕← CIPHER[ Submit

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Write problem 6

Consider the following ASCII art stored in a matrix called ART

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

Create a matrix called APL which consists of the following subarray obtained by indexing ART

  __  ____ __ 
 / _\(  _ (  )  
/    \) __/ (_/ 
\_/\_(__) \____        

⎕← ART[ Submit

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Write problem 7

Create a 3 by 3 grid of 'X's and 'O's called BOARD

⎕← 'XO' Submit

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Write problem 8

Considering the above array as a game of noughts and crosses, change a single element to make the O player win.

⎕← BOARD[ Submit

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Write problem 9

Given the coefficients list C of a quadratic $P(x) = C[1] x^2 + C[2] x + C[3]$, evaluate the polynomial for a value X. For example, for C ← 1 2 3, and X ← 10, this should evaluate to $ 1 \cdot 10^2 + 2 \cdot 10 + 3 = 123 $.

⎕← Submit

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Write problem 10

Consider the following list of GAMES

      GAMES
CHESS                   
CHECKERS                
BACKGAMMON              
POKER                   
GLOBAL THERMONUCLEAR WAR

Get the first letter of each of the games listed using indexing

⎕← GAMES[ Submit

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Write problem 11

Get the first three letters of the second and fifth game listed above using indexing

⎕← GAMES[ Submit

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Write problem 12

Consider a tape-controlled computer which operates by reading a certain section of a tape, changing its internal state based on the value of that section, writing a certain value to that section, then possibly moving the tape along to the next or previous section. For this specific machine, the value of the tape sections is either a 1 or a 2, the internal state of the machine is either 1 2 or 3, and the matrix which specifies the actions to be taken is the following

      INSTRUCTIONS
┌─────┬─────┬─────┐
│1 R 2│1 L 1│1 L 2│
├─────┼─────┼─────┤
│1 L 3│1 R 2│1 N H│
└─────┴─────┴─────┘

The first value in each element is what to write to the section of tape, the second whether to move right 'R' left 'L' or stay in place 'N', and the last value is the next state of the machine 1, 2, 3, or 'H' for halting the machine.

The first (second) row of the matrix specifies the possible instructions when the value of the section of tape is a 1 (2). The columns similarly specify the possible instructions depending on the state of the machine.

Using indexing, find the instruction for the tape section having value 1 when the machine is in state 3.

⎕← INSTRUCTIONS[ Submit

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