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 whether it gives the correct answer and uses the methods described below.

1: Are You There?

It is easy to look for things in APL. Think of it as looking for some pencils in a drawer. We use the symbol ∊ which looks like the E in Exists In. If we use a pencils and drawer example, the symbol tells you which pencils are in the drawer. The pencils (what you are looking for) are on the left of the symbol and the drawer (what you are looking in) is to the right of the symbol. This will give you a 1 for each pencil that was found in the drawer and a 0 for each pencil that was not found in the drawer. For example, 1 16 12 ∊ 12 25 1 12 15 7 gives 1 0 1 as follows:

1. 1 because 1 was found in 12 25 1 12 15 7
2. 0 because 16 was not found in 12 25 1 12 15 7
3. 1 because 12 was found in 12 25 1 12 15 7

In APL, a text is a list of letters and must be between single quotes ( ' ). For example, 'ABC' will give a result that looks like ABC.

Write some APL code that uses ∊ to check which letters of 'DYALOG IN USE' appear in the list of vowels ('AEIOU'). The result should be 0 0 1 0 1 0 0 1 0 0 1 0 1 as follows:

1. 0 because 'D' is not a vowel
2. 0 because 'Y' is not a vowel
3. 1 because 'A' is a vowel
4. 0 because 'L' is not a vowel
5. 1 because 'O' is a vowel
6. 0 because 'G' is not a vowel
7. 0 because ' ' is not a vowel
8. 1 because 'I' is a vowel
9. 0 because 'N' is not a vowel
10. 0 because ' ' is not a vowel
11. 1 because 'U' is a vowel
12. 0 because 'S' is not a vowel
13. 1 because 'E' is a vowel

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 whether it gives the correct answer and uses the methods described below.

2: Are They There?

In problem 1 you saw a list created by putting numbers next to each other with a space between them. You can also have a list of multiple texts. For example, 'here' 'we' 'are' is a list of three texts; 'here', 'we', and 'are'. Since a text is a letter list, a list of texts is a list of letter lists.

∊ works with any sort of list and list of lists, for example, a list of number lists. You can create a list of number lists by writing each inner list in round brackets. For example, (10 1) (222 200 2) (30 30) is a list of these three number lists:

1. 10 1
2. 22 200 2
3. 30 30

Write some APL code that uses ∊ to find out which of the texts 'TO' 'BE' 'OR' 'NOT' 'TO' 'BE' appear among the texts 'HERE' 'BE' 'DRAGONS'. The result should be 0 1 0 0 0 1.

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 whether it gives the correct answer and uses the methods described below.

3: Summation

Finding the product of a list of numbers means using × to multiply them together. You write this as ×/ (times slash) to the left of the numbers. For example, the product of 3 1 4 1 5 can be found with ×/ 3 1 4 1 5 (the product is 60).

Whatever mathematical operation symbol is to the left of the / will be inserted between the numbers.

Write some APL code that uses / to find the sum of 3 1 4 1 5 by adding the numbers together. The result should be 14.

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 whether it gives the correct answer and uses the methods described below.

4: How Many Are There?

Symbols that are used to change data are called functions.

An APL function takes the result of all code to its right as its right argument (the data on the right of the symbol). For example, 2×3+4 gives 14 (rather than the 10 you might expect) because the × takes the result of 3+4 as its right argument. Similarly, -2-6 gives 4 because the left - negates the result of 2-6.

Write an expression that uses what you learnt in problem 3 and ∊ from problem 1 to count how many of the texts 'TO' 'BE' 'OR' 'NOT' 'TO' 'BE' appear among the texts 'HERE' 'BE' 'DRAGONS'. The result should be 2.

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 whether it gives the correct answer and uses the methods described below.

5: Windows

In problem 3 you saw how ×/ multiplies all the numbers in a list (giving the product) and how any mathematical operation symbol can be used instead of times. Sometimes, you only want to multiply a limited number of adjacent elements. For example, you might want to find the product of each number and its neighbour. We can tell / (slash) to apply its function over each “window” of a given size by putting the size on the left of the function. Since a number and its neighbour together are 2 numbers, 2 ×/ 3 2 5 4 4 3 finds the product of each number in 3 2 5 4 4 3 and its neighbour, which gives 6 10 20 16 12, because:

1. 3×2 is 6
2. 2×5 is 10
3. 5×4 is 20
4. 4×4 is 16
5. 4×3 is 12

Similarly, we can find the product of every window of size 4 with 4 ×/ 3 2 5 4 4 3 which gives 120 160 240, because:

• 3×2×5×4 is 120
• 2×5×4×4 is 160
• 5×4×4×3 is 240

Use / to find the sum of every window of size 5 in the list 1 0 1 2 2 0 1 2. The result should be 6 5 6 7.

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 whether it gives the correct answer and uses the methods described below.

6: Tag Along

You can join things (letters, numbers, lists, and so on) together by putting a , (comma) between them. For example, 1 , 2 gives 1 2 and 1 2 , 3 4 gives 1 2 3 4.

Websites are written in a language called HTML using tags. A tag consists of a less-than symbol, a tag name, and a greater-than symbol. For example, the HTML tag for an image is <img>.

Using , create an HTML image tag by joining together the three texts '<' and 'img' and '>'. The result should be <img>.

Note: 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.

7: Tag me

You can create your own function by putting an expression in curly brackets. For example, the expression 2+3 becomes the function {2+3}. Within this function, 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 takes an HTML tag name and creates the HTML tag. For example:

      {answer} 'img'
<img>

      {answer} 'button'
<button>

      {answer} 'input'
<input>

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: Play Tag

In problem 7, you saw how to write a function that takes a right argument using ⍵. If you want to create a function that also takes a left argument, use ⍺ (alpha; the left-most letter of the Greek alphabet). For example, a function that sums its left and right arguments and then multiplies by 2 could be written {2×⍺+⍵}.

HTML content is usually between a regular tag and its corresponding closing tag. A closing tag is just like a normal tag, except that it has a slash before its name. For example, the closing tag for a button is </button>.

Using what you’ve learnt so far, write a function that takes an HTML tag name as its right argument and content as its left argument. It must join a tag (see problem 6) with the content and a corresponding closing tag. For example:

      'use it wisely' {answer} 'head'
<head>use it wisely</head>

      'heavy lifting' {answer} 'strong'
<strong>heavy lifting</strong>

      'a bridge too far' {answer} 'span'
<span>a bridge too far</span>

Note: 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: DNA

Using / doesn't always give a single value. If the function used returns a list, then you get a list result. If you give a window size, as in problem 5, you get a list of lists (remember that a text is just a list of letters).

Genes are grouped into codons which are three DNA letters in a row. Reading can begin at any point in the DNA code, so to find all possible codons, you need to read three letters starting from every base, except the last two. For example, the DNA string 'ACCTGGCCT' has the following possible codons:

1. 'ACC'
2. 'CCT'
3. 'CTG'
4. 'TGG'
5. 'GGC'
6. 'GCC'
7. 'CCT'

Note that there can be duplicate codons, and the number of codons is smaller than the number of given DNA letters.

From the functions you’ve learnt in the earlier problems, find one to use with / so that you can write a function that takes a DNA string and gives all the possible codons. For example:

      {answer} 'GTTTCGGTG'
┌───┬───┬───┬───┬───┬───┬───┐
│GTT│TTT│TTC│TCG│CGG│GGT│GTG│
└───┴───┴───┴───┴───┴───┴───┘

      {answer} 'CCCACT'
┌───┬───┬───┬───┐
│CCC│CCA│CAC│ACT│
└───┴───┴───┴───┘

      {answer} 'GATTACA'
┌───┬───┬───┬───┬───┐
│GAT│ATT│TTA│TAC│ACA│
└───┴───┴───┴───┴───┘

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: Wolfram Rules

Remember from problem 2 that round brackets are used to make a list of number lists.

You can also use round brackets to change the order in which things are calculated. In problem 4 you learnt that an APL function takes the result of all code to its right as its right argument. This was a simplification; the right argument only goes as far as the nearest closing bracket …) on its right:

• 2×3+4 gives 14 because × takes the result of all code to its right, 3+4, as its right argument.
• 2×(3+4) gives 14 because × takes the result of all code to its right, (3+4), as its right argument.
• (2×3)+4 gives 10 because the right argument of × only goes as far as the nearest closing bracket.

You will be writing the code for rules invented by Stephen Wolfram. Each set of rules shows how to change a list of 0s and 1s into a new list of the same length, again only with 0s and 1s. For every number in the given list, you need to look at it together with its neighbours to the left and right, then check whether this triplet of numbers exists in a given list of triplets. If found, that number becomes a 1. Otherwise it becomes a 0. Consider the first number to have an invisible 0 on its left and the last number to have an invisible 0 on its right.

Everything taught in the previous problems is sufficient to solve this one: Write a function that takes a rule set and an initial list, and then calculates a new list based on those. The rule set will be the left argument, and is a list of lists of 0s and 1s. The initial list is the right argument, and is a simple list of 0s and 1s. For example:

      (1 1 0) (1 0 0) (0 1 1) (0 0 1) {answer} 0 1 1 0 1
1 1 1 0 0

Here are the reasons for the numbers in the result:

1. 1 because 0 has the triplet 0 0 1 (invisible 0 on the left) which is found in the rule set
2. 1 because 1 has the triplet 0 1 1 which is found in the rule set
3. 1 because 1 has the triplet 1 1 0 which is found in the rule set
4. 0 because 0 has the triplet 1 0 1 which is not found in the rule set
5. 0 because 0 has the triplet 0 1 0 (invisible 0 on the right) which is not found in the rule set

      (1 0 0) (0 1 1) (0 1 0) (0 0 1) {answer} 0 1 0 0 1 0 1 0
1 1 1 1 1 0 1 1

      (1 1 0) (1 0 1) (0 1 1) (0 1 0) (0 0 1) {answer} 0 0 0 0 1
0 0 0 1 1

      (1 1 0) (1 0 1) (0 1 1) (0 1 0) (0 0 1) {answer} 0 0 0 1 1
0 0 1 1 1

      (1 1 0) (1 0 1) (0 1 1) (0 1 0) (0 0 1) {answer} 0 0 1 1 1
0 1 1 0 1

      (1 1 0) (1 0 1) (0 1 1) (0 1 0) (0 0 1) {answer} 0 1 1 0 1
1 1 1 1 1