Write exercises

Remember, you can test your code out on TryAPL before submitting it here! You can submit as many solutions as you like.

Since this course is still a work-in-progress, solving the write exercises will currently not lead to any credits.

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Write problem 1

Write a dfn that calculates the harmonic mean of its left and right arguments, mathematically defined as $$H(\alpha,\omega) = \frac{1}{\frac{1}{\alpha}+\frac{1}{\omega}}$$

H← Submit

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Write problem 2

Write a dfn that calculates the Heronian mean of its left and right arguments, mathematically defined as $$H(\alpha,\omega) = \frac{1}{3} \cdot (A+\sqrt{AB}+B)$$

H← Submit

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Write problem 3

Write a dfn that calculates the geometric mean of its left and right arguments, mathematically defined as $$H(\alpha,\omega) = \sqrt{AB}$$

H← Submit

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Write problem 4

Write a dfn that calculates the arithmetic geometric mean of its left and right arguments, which is defined recursively. The left argument calculating the arithmetic mean of ⍺ and ⍵, the right argument calculating the geometric mean of ⍺ and ⍵, until both means converge. Mathematically, $$ H(\alpha, \omega) = \left\{ \begin{array}{ll} \omega & \alpha=\omega \\ H(\frac{\alpha + \omega}{2}, \sqrt{\alpha \omega}) & \alpha≠\omega \\ \end{array} \right. $$

H← Submit

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Write problem 5

Write a dfn that allows the user to choose from some of the means above. The function should take in a right argument array, where the first element is an integer representing which mean to use (see table below), and that particular mean is calculated for the next two elements. \[ \begin{array}{cc} 1 & \text{Arithmetic mean} \\ 2 & \text{Geometric mean} \\ 3 & \text{Arithmetic-Geometric mean} \\ \end{array} \]

H← Submit

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Write problem 6

Write a dfn called My that displays personal information. The My function should take a string right argument and return the following

      My 'Name'
DASH
      My 'Age'
20
      My 'Profession'
Engineer
      My 'Company'
Future Gadget Lab LLC

Hint: Use the match ≡ function.

My← Submit

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Write problem 7

Recall the tape-based machine given in the Chapter 2 Write problem 12.

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

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.

Create a dfn FETCH that takes in a two element right argument vector ⍵, specifying in the first element the value of the section of tape and the second the state of the machine, and returns the corresponding instruction.

FETCH← Submit

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Write problem 8

The Caesar cipher encrypts a piece of text by shifting all its letters a fixed amount of places along the alphabet. For example, 'BUNNY' (with indices 2 21 14 14 25) under a shift of 17 places (26 | 2 21 14 14 25 + 17 -> 11 4 23 23 8) becomes 'SLEEP'.

Create a dfn that does the intermediate operation of this cipher by shifting an integer right argument vector by an integer left argument, modulo 26.

SHIFT26← Submit

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Write problem 9

Create a dfn that returns a matrix of zeroes of size ⍺ by ⍺, with a 1 in a position specified by the vector right argument ⍵.

      2 SPARSE 2 1
0 0
1 0
      10 SPARSE 5 4
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 1 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

SPARSE← Submit

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Write problem 10

Create a dfn that plots a heatmap of a matrix, that is, a * where the matrix ⍵ is above a certain value ⍺ and an underscore _ otherwise. For example,

      M ← 10 10⍴⍳9
      M
1 2 3 4 5 6 7 8 9 1
2 3 4 5 6 7 8 9 1 2
3 4 5 6 7 8 9 1 2 3
4 5 6 7 8 9 1 2 3 4
5 6 7 8 9 1 2 3 4 5
6 7 8 9 1 2 3 4 5 6
7 8 9 1 2 3 4 5 6 7
8 9 1 2 3 4 5 6 7 8
9 1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 1

      7 PLOT M
_______**_
______**__
_____**___
____**____
___**_____
__**______
_**_______
**_______*
*_______**
_______**_

Hint: Index the vector '_*' by a matrix

PLOT← Submit

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Write problem 11

Create a dfn that returns the singular form of a noun given as a vector right argument ⍵, returning 'an' with the noun when the noun begins with a vowel, and 'a' with the noun otherwise. In this case, 'Y' is not considered a vowel. The nouns will be given in UPPERCASE.

      SINGULAR "DREAM"
A DREAM
      SINGULAR "SNOOZE"
A SNOOZE
      SINGULAR "AERODROME"
AN AERODROME

SINGULAR← Submit

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Write problem 12

Create a dfn that determines an APL MOOC student's final grade. The right argument ⍵ is the number of exercises completed. For the sake of this problem, you can assume that the APL MOOC has 72 exercises. The grade boundaries and expected results are given below

      ⍝ Less than 60%
      GRADE 42
0
      ⍝ Between 60% and 70%
      GRADE 43
1
      GRADE 50
1

      ⍝ Between 70% and 80%
      GRADE 51
2
      GRADE 57
2

      ⍝ Between 80% and 90%
      GRADE 58
3
      GRADE 64
3

      ⍝ Between 90% and 99%
      GRADE 65
4
      GRADE 71
4

      ⍝ Between 99% and 100%
      Grade 72
5

      ⍝ Any higher returns nothing
      Grade 73

GRADE← Submit

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