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

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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