README.md

List Exercises

Instructions

You have to implement exercises working over lists

Remember:

To enter into the REPL use:

stack ghci

There you can try the functions, like

> member 10 [1..12]

Should print:

True

---

To run all the tests use:

stack test 

1. List as Sets

Suppose that lists describe a Set of elements.

The member and union functions are defined as examples. You need to define the intersection and difference operations

> intersection [1..5] [7, 3, 1]
[1, 3]
> difference [1..5] [7, 3, 1]
[2,4,5]
> difference [7, 3, 1] [1..5]
[7]

2. Insertion Sort

Implement an operation to insert an element in the right position on an ordered list.

You should keep duplicated elements.

> insert 4 [1,2,5,7]
[1,2,4,5,7]
> insert 2 [1,2,5,7]
[1, 2, 2, 5, 7]

Based on the above implement an insertion sort.

> insertionSort [6, 3, 5]
[3,5,6]

Reimplement it using a foldr

3. Numeral Systems

First define a function that gets a list of Binary digits.

And gets the value of it as an Integer

Remember that if the number is:

x_n ... x₁ x₀

x₀ 2 ⁰ + x₁ 2 ¹ + ... + x_n 2 ⁿ

> binaryToDecimal [1, 1, 0, 1]
13

Hint: Use an auxiliary function that receives the list in reverse order.

Create an adicional function that receives the base as an argument:

> toDecimal 8 [7, 3]
59
> toDecimal 16 [1, 1]
17

Create a function that instead of receiving a list receives a string

> toDec 8 "73"
59
> toDec 16 "1F"
31

Hint use map and the function digitToInt from Data.Char

Repeat the last exercise using a List Comprehension and the zip function

> decimal 8 "73"
59
> decimal 16 "1F"
31

4. Firsts Elements of a list

Given a List, return a Nested List containing:

The first element, the first 2 elements, the first 3 elements, etc.

> firsts [1, 3, 5]
[[1],[1,3],[1,3,5]]
> firsts "Hello"
["H","He","Hel","Hell","Hello"]

5. Binary Operations -- BONUS exercise

Given two Strings that represents numbers in binary. Implement the 'binaryAdd' function.

DO NOT USE any predefined arithmetic operation

> binaryAdd "10" "1"
"3"
> binaryAdd "1111" "11"
"10010"