Note: In this problem, you’re asked to enter some APL code, including an APL symbol and the data (text or numbers) given to it. Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

1: Easy as 1-2-3

It is easy to count in APL. Just write the symbol ⍳ (iota, a Greek letter), to the left of a number; this will give you all the whole numbers from 1 to the number that you wrote. (Iota is like an i for integers, which means whole numbers.) For example, ⍳ 7 gives 1 2 3 4 5 6 7

Write some APL code that uses ⍳ to get the numbers from 1 to 12. The result should be 1 2 3 4 5 6 7 8 9 10 11 12

In this problem, you’re asked to enter some APL code, including an APL symbol and the data (text or numbers) given to it. Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

2: I’m Larger than You

In APL, we use the symbol ⌈ (up-stile) to find which of two numbers is the largest. The symbol looks like a vertical line with a mark at the highest value. This is because it compares the number on its left with the number on its right, and gives the one that is highest. For example, 5 ⌈ 2 gives 5 because 5 is a higher value than 2.

APL users usually call ⌈ Maximum. Maximum – and all other basic mathematical symbols of APL – can work on multiple numbers at once. For example, 5 ⌈ 2 7 1 8 gives 5 7 5 8 because:

• 5 ⌈ 2 is 5 as 5 is larger than 2
• 5 ⌈ 7 is 7 as 7 is larger than 5
• 5 ⌈ 1 is 5 as 5 is larger than 1
• 5 ⌈ 8 is 8 as 8 is larger than 5

Write some APL code that uses a single ⌈ to change the numbers 31 41 59 26 into 50 50 59 50.

In this problem, you’re asked to enter some APL code, including an APL symbol and the data (text or numbers) given to it. Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

3: Where Are You?

In APL, text must appear between single quotes ('). For example, 'ABC' will give a result that looks like ABC.

Equal To (=) can be used to check whether letters are the same. It gives 1 when letters are the same and 0 when letters are different. For example, 'B' = 'C' will give 0 and 'D' = 'D' will give 1.

As well as comparing single letters, APL can also compare lists of letters (also called as texts). For example, 'HELLO' = 'WORLD' gives 0 0 0 1 0 because:

You can also compare a single letter with a whole text. APL will compare the single letter to each letter of the text.

Write some APL code using Equal To that shows where the Rs are in 'RASPBERRY'. The answer should be 1 0 0 0 0 0 1 1 0.

Note: In this problem, you’re asked to enter an APL expression (some APL code), including arguments (data given to APL symbols). Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

4: The Greatest Number

The APL symbols you’ve met so far take either one data argument on the right or a data argument on each side. These symbols are called functions. APL also has operators. These are similar to functions, but, on the left, they take a function instead of data. Each operator uses the given function with the given data in a specific way.

Insert (/) is such an operator. It takes a list on its right, and a function on its left. The function could be a common mathematical function (like + or ×) or, for example, = (Equal To) from problem 3. Insert inserts the symbol between the items of the list. For example, you can use Insert to add up all the numbers in a list: +/ 1 2 3 4 gives 10 because it is the same as 1 + 2 + 3 + 4.

Using Maximum (⌈) from problem 2, find the largest number in the list 2 7 1 8 2 8 1 8 2 8 4 6. The result should be 8.

In this problem, you’re asked to enter an APL expression (some APL code), including arguments (data given to APL symbols). Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

5: Cards on the Table

If you put ∘. (jot dot, but sometimes called Table) immediately to left of a function, then it produces a table for that function. It does this by inserting the function between all the combinations of numbers from the arguments. If the resulting table had row and column headings, the left argument would be used as the headings for the rows (down the left side) and the right argument would be used as the headings for the columns (across the top). Here’s a multiplication table (times table) in APL form – and as you might see it in a book (showing the row and column headings, even though they are not table data):

      2 3 4 ∘.× 2 3 4 5
4  6  8 10
6  9 12 15
8 12 16 20

As in the above example, when we write APL code and its result together, we often write the code above the result, with six spaces to the left of the code.

Using Table (∘.), create an addition table (plus table) for the numbers 3, 1, and 4. The result should look like this:

6 4 7
4 2 5
7 5 8

In this problem, you’re asked to enter an APL expression (some APL code), including arguments (data given to APL symbols). Your code will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described below.

6: Identity Matrix

An APL function takes the answer of all the code to its right as its right argument. For example, 2×3+4 gives 14, rather than the 10 that you might expect. This is because the × takes the answer of 3+4 as its right argument. However, you can use round brackets to change the order in which things are calculated, limiting any right argument so it only goes as far as the nearest closing bracket …) on its right: (2×3)+4 gives 10.

When you used Equal To (=) in problem 3, you were using it to compare letters in a text. However, it also works on numbers. For example:

      1 = 3 1 4 1 5 9
0 1 0 1 0 0

Using round brackets, ⍳ (iota from problem 1), =, and ∘. (Table from problem 5), create a 5-by-5 table that has 1s on the diagonal from the top left to the bottom right, with all other numbers being 0s. This is known as an identity matrix of size 5 and looks like this:

1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

Note: In this problem, you’re asked to enter your own APL function, without giving it any arguments. Your code will be checked by the APL Challenge system using several tests to see whether it is correct.

7: More Identity Matrices

You can create your own function by putting an expression (for example, ⍳10) in curly brackets (for example, {⍳10}). Within this expression (in our example, ⍳10), any ⍵ (omega, the right-most letter of the Greek alphabet) is replaced by the argument to the right of the closing curly bracket ( } ).

For example, a function that multiplies its argument by two could be written {2×⍵}, so {2×⍵} 5 gives 10.

Using what you learnt in problem 6, write a function that gives an identity matrix of the given size. For example:

      {answer} 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

      {answer} 2
1 0
0 1

      {answer} 6
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

In this problem, you’re asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

8: Spell it Out

You can select specific letters from a text by putting square brackets ( [] ) to the right of the text. Inside the square brackets, you put numbers that say which letters you want to get from the text. For example, 'ABCDE'[1] gives you the letter A because that’s the 1st letter of 'ABCDE'. Similarly, 'ABCDE'[5 2 2] gives you EBB, because:

• The 5^th letter of 'ABCDE' is E
• The 2^nd letter of 'ABCDE' is B
• The 2^nd letter of 'ABCDE' is B

Write a function that takes a list of numbers and returns a text that consists of the corresponding uppercase letters from the English alphabet. For example:

      {answer} 1 2 3 2 1
ABCBA

      {answer} 1 16 12
APL

      {answer} 4 25 1 12 15 7
DYALOG

In this problem, you’re asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

9: How Many of Each?

When using a function with Insert (/ from problem 4) on a table, it inserts the function between the items in each row in the table. For example, take the multiplication table from problem 5:

      2 3 4 ∘.× 2 3 4 5
4  6  8 10
6  9 12 15
8 12 16 20

Now we put +/ in front of the table:

      +/ 2 3 4 ∘.× 2 3 4 5
28 42 56

This tells us that:

• the first row had a sum of 28 (from +/ 4 6 8 10 which is 4 + 6 + 8 + 10)
• the second row had a sum of 42 (from +/ 6 9 12 15) which is 6 + 9 + 12 + 15)
• the third row had a sum of 56 (from +/ 8 12 16 20 which is 8 + 12 + 16 + 20)

Using + with / and ∘. with = (Equal To from problem 3), write a function that takes an uppercase text and, for each of the three letters A, P, and L, counts how many there are in the text. For example:

      {answer} 'DYALOG APL'
2 1 2

This tells us that 'DYALOG APL' has 2 As, 1 P, and 2 Ls.

      {answer} 'MISSISSIPPI'
0 2 0

      {answer} 'THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG!'
1 1 1

In this problem, you’re asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

10: Histogram

You have used = in several earlier questions, but APL has additional comparison functions, such as Less Than (<), Less Than Or Equal To (≤), Greater Than Or Equal To (≥), Greater Than (>), and Not Equal To (≠). All these functions give 1 for yes and 0 for no.

Using everything that you’ve learnt so far, write a function that takes a list of numbers between 1 and 6 (representing dice throws) and draws a histogram (bar chart) showing how many times each number was thrown. Use dashes (-) to show how many times each number was thrown, with the number of 1s shown on the first line, the number of 2s shown on the second line, and so on. Use spaces ( ) to fill out the table so it becomes rectangular. For example:

      {answer} 6 2 1 3 5 6 6 4 1 2
-- 
-- 
-  
-  
-  
---

      {answer} 3 4 3 4 6
  
  
--
--
  
- 

      {answer} 5 3 6 6 3 5 5 4 1 6 1 6 4 6 3 2 3 2 6 3 1 4 4 3 5
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