Difference between revisions of "FP Laboratory 3"
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− | == | + | <translate> |
+ | == Usage of lists == <!--T:1--> | ||
+ | Find out the results of the following operations: | ||
+ | </translate> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | [3,2,1] > [2,1,0] | ||
+ | [3,2,1] > [2,10,100] | ||
+ | [3,4,2] > [3,4] | ||
+ | [3,4,2] > [2,4] | ||
+ | [3,4,2] == [3,4,2] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | == Simple functions working with list == <!--T:2--> | ||
Implement following functions: | Implement following functions: | ||
* Create a function that computes length of a list. | * Create a function that computes length of a list. | ||
− | <syntaxhighlight lang="Haskell">length :: [a] -> Int</syntaxhighlight> | + | </translate> |
+ | |||
+ | <syntaxhighlight lang="Haskell">length' :: [a] -> Int</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> length' "ABCD" | ||
+ | 4 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | length' :: [a] -> Int | ||
+ | length' [] = 0 | ||
+ | length' (_:xs) = 1 + length' xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:3--> | ||
* Create a function that sums the list of integers. | * Create a function that sums the list of integers. | ||
+ | </translate> | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/Yuz8lpKZiJs]]</div> | ||
<syntaxhighlight lang="Haskell">sumIt :: [Int] -> Int</syntaxhighlight> | <syntaxhighlight lang="Haskell">sumIt :: [Int] -> Int</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> sumIt [1,2,3] | ||
+ | 6 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | sumIt :: [Int] -> Int | ||
+ | sumIt [] = 0 | ||
+ | sumIt (x:xs) = x + sumIt xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:4--> | ||
* Create a function that returns the first element in the list. | * Create a function that returns the first element in the list. | ||
+ | </translate> | ||
+ | |||
<syntaxhighlight lang="Haskell">getHead :: [a] -> a</syntaxhighlight> | <syntaxhighlight lang="Haskell">getHead :: [a] -> a</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> getHead [1,2,3] | ||
+ | 1 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | getHead :: [a] -> a | ||
+ | getHead (x:_) = x | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:5--> | ||
* Create a function that returns the last element in the list. | * Create a function that returns the last element in the list. | ||
+ | </translate> | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/I5AZu8_G8pQ]]</div> | ||
<syntaxhighlight lang="Haskell">getLast :: [a] -> a</syntaxhighlight> | <syntaxhighlight lang="Haskell">getLast :: [a] -> a</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> getLast [1,2,3] | ||
+ | 3 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | getLast :: [a] -> a | ||
+ | getLast [x] = x | ||
+ | getLast (x:xs) = getLast xs | ||
+ | |||
+ | getLast' :: [a] -> a | ||
+ | getLast' (x:xs) | length xs == 0 = x | ||
+ | | otherwise = getLast' xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:6--> | ||
+ | * Create a function that checks if an element is a member of the list. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">isElement :: Eq a => a -> [a] -> Bool</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> isElement 2 [1,2,3] | ||
+ | True | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | isElement :: Eq a => a -> [a] -> Bool | ||
+ | isElement _ [] = False | ||
+ | isElement a (x:xs) | a == x = True | ||
+ | | otherwise = isElement a xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:7--> | ||
* Create a function that returns the list without the first element. | * Create a function that returns the list without the first element. | ||
+ | </translate> | ||
+ | |||
<syntaxhighlight lang="Haskell">getTail :: [a] -> [a]</syntaxhighlight> | <syntaxhighlight lang="Haskell">getTail :: [a] -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> getTail [1,2,3] | ||
+ | [2,3] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | getTail :: [a] -> [a] | ||
+ | getTail (_:xs) = xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:8--> | ||
* Create a function that returns the list without the last element. | * Create a function that returns the list without the last element. | ||
+ | </translate> | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/ZLmvYTZ6fkw]]</div> | ||
<syntaxhighlight lang="Haskell">getInit :: [a] -> [a]</syntaxhighlight> | <syntaxhighlight lang="Haskell">getInit :: [a] -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> getInit [1,2,3] | ||
+ | [1,2] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | getInit :: [a] -> [a] | ||
+ | getInit [_] = [] | ||
+ | getInit (x:xs) = x : getInit xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:9--> | ||
* Create a function that merge two lists into one list. | * Create a function that merge two lists into one list. | ||
+ | </translate> | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/FFoHC-g3f_g]]</div> | ||
<syntaxhighlight lang="Haskell">combine :: [a] -> [a] -> [a]</syntaxhighlight> | <syntaxhighlight lang="Haskell">combine :: [a] -> [a] -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> combine [1,2,3] [4,5] | ||
+ | [1,2,3,4,5] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | combine :: [a] -> [a] -> [a] | ||
+ | combine [] y = y | ||
+ | combine (x:xs) y = x : combine xs y | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:10--> | ||
+ | * Create a function that finds the maximum in the list of integers. | ||
+ | </translate> | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/ybgM-YeQTco]]</div> | ||
+ | <syntaxhighlight lang="Haskell">max' :: [Int] -> Int</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> max' [3,1,7,5] | ||
+ | 7 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | max' :: [Int] -> Int | ||
+ | max' [x] = x | ||
+ | max' (x:y:z) | x > y = max' (x:z) | ||
+ | | otherwise = max' (y:z) | ||
+ | |||
+ | max'' :: [Int] -> Int | ||
+ | max'' (y:ys) = tmp y ys where | ||
+ | tmp a [] = a | ||
+ | tmp a (x:xs) | x > a = tmp x xs | ||
+ | |otherwise = tmp a xs | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:11--> | ||
* Create a function that reverse a list. | * Create a function that reverse a list. | ||
− | <syntaxhighlight lang="Haskell">reverse :: [a] -> [a]</syntaxhighlight> | + | </translate> |
− | * | + | |
− | <syntaxhighlight lang="Haskell"> | + | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/jlUuZ5fCFgQ]]</div> |
− | * Create a function that product scalar multiplication | + | <syntaxhighlight lang="Haskell">reverse' :: [a] -> [a]</syntaxhighlight> |
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> reverse' [3,1,7,5] | ||
+ | [5,7,1,3] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | reverse' :: [a] -> [a] | ||
+ | reverse' [] = [] | ||
+ | reverse' (x:xs) = (reverse' xs) ++ [x] | ||
+ | |||
+ | reverse'' :: [a] -> [a] | ||
+ | reverse'' n = tmp n [] | ||
+ | where tmp [] ys = ys | ||
+ | tmp (x:xs) ys = tmp xs (x:ys) | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:12--> | ||
+ | * Create a function that product scalar multiplication of two vectors. | ||
+ | </translate> | ||
+ | |||
<syntaxhighlight lang="Haskell">scalar :: [Int] -> [Int] -> Int</syntaxhighlight> | <syntaxhighlight lang="Haskell">scalar :: [Int] -> [Int] -> Int</syntaxhighlight> | ||
− | * Create a function that | + | <syntaxhighlight lang="Haskell" class="myDark"> |
− | <syntaxhighlight lang="Haskell"> | + | *Main> scalar [1,2,3] [4,5,6] |
− | * | + | 32 |
− | <syntaxhighlight lang="Haskell"> | + | </syntaxhighlight> |
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | scalar :: [Int] -> [Int] -> Int | ||
+ | scalar [] [] = 0 | ||
+ | scalar (x:xs) (y:ys) = x*y + scalar xs ys | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | <translate> | ||
+ | = Additional exercises = <!--T:13--> | ||
+ | * Create a function that eliminates all occurrences of zeros in a list. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">nonZeros :: [Int] -> [Int]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> nonZeros [0,1,0,2,3,0,0] | ||
+ | [1,2,3] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:14--> | ||
+ | * Create a function that realizes the left rotation of a list by one element. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">rotateLeft1 :: [a] -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> rotateLeft1 [1,2,3,4,5] | ||
+ | [2,3,4,5,1] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:15--> | ||
+ | * Create a function that realizes the right rotation of a list by one element. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">rotateRight1 :: [a] -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> rotateRight1 [1,2,3,4,5] | ||
+ | [5,1,2,3,4] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:16--> | ||
+ | * Create a function that eliminates all even numbers from a list. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">oddMembers :: [Int] -> [Int]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> oddMembers [0,1,0,2,3,0,0] | ||
+ | [1,3] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:17--> | ||
+ | * Create a function that counts all odd numbers in a given list (define non-recursively using previously defined functions). | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">countOddMembers :: [Int] -> Int</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> countOddMembers [1,0,3,1,4,5] | ||
+ | 4 | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | <!--T:18--> | ||
+ | * Create a function that compares lists of numbers if they are equal. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">compareLists :: Eq a => [a] -> [a] -> Bool </syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> compareLists [5,8,11] [5,8,11] | ||
+ | True | ||
+ | *Main> compareLists [5,8,11] [3,5,8] | ||
+ | False | ||
+ | *Main> compareLists [] [] | ||
+ | True | ||
+ | *Main> compareLists [5,8,11] [5,8,11,13] | ||
+ | False | ||
+ | </syntaxhighlight> |
Latest revision as of 10:39, 9 October 2023
Usage of lists
Find out the results of the following operations:
[3,2,1] > [2,1,0]
[3,2,1] > [2,10,100]
[3,4,2] > [3,4]
[3,4,2] > [2,4]
[3,4,2] == [3,4,2]
Simple functions working with list
Implement following functions:
- Create a function that computes length of a list.
length' :: [a] -> Int
*Main> length' "ABCD"
4
- Create a function that sums the list of integers.
sumIt :: [Int] -> Int
*Main> sumIt [1,2,3]
6
- Create a function that returns the first element in the list.
getHead :: [a] -> a
*Main> getHead [1,2,3]
1
- Create a function that returns the last element in the list.
getLast :: [a] -> a
*Main> getLast [1,2,3]
3
getLast :: [a] -> a
getLast [x] = x
getLast (x:xs) = getLast xs
getLast' :: [a] -> a
getLast' (x:xs) | length xs == 0 = x
| otherwise = getLast' xs
- Create a function that checks if an element is a member of the list.
isElement :: Eq a => a -> [a] -> Bool
*Main> isElement 2 [1,2,3]
True
isElement :: Eq a => a -> [a] -> Bool
isElement _ [] = False
isElement a (x:xs) | a == x = True
| otherwise = isElement a xs
- Create a function that returns the list without the first element.
getTail :: [a] -> [a]
*Main> getTail [1,2,3]
[2,3]
- Create a function that returns the list without the last element.
getInit :: [a] -> [a]
*Main> getInit [1,2,3]
[1,2]
- Create a function that merge two lists into one list.
combine :: [a] -> [a] -> [a]
*Main> combine [1,2,3] [4,5]
[1,2,3,4,5]
- Create a function that finds the maximum in the list of integers.
max' :: [Int] -> Int
*Main> max' [3,1,7,5]
7
max' :: [Int] -> Int
max' [x] = x
max' (x:y:z) | x > y = max' (x:z)
| otherwise = max' (y:z)
max'' :: [Int] -> Int
max'' (y:ys) = tmp y ys where
tmp a [] = a
tmp a (x:xs) | x > a = tmp x xs
|otherwise = tmp a xs
- Create a function that reverse a list.
reverse' :: [a] -> [a]
*Main> reverse' [3,1,7,5]
[5,7,1,3]
reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = (reverse' xs) ++ [x]
reverse'' :: [a] -> [a]
reverse'' n = tmp n []
where tmp [] ys = ys
tmp (x:xs) ys = tmp xs (x:ys)
- Create a function that product scalar multiplication of two vectors.
scalar :: [Int] -> [Int] -> Int
*Main> scalar [1,2,3] [4,5,6]
32
Additional exercises
- Create a function that eliminates all occurrences of zeros in a list.
nonZeros :: [Int] -> [Int]
*Main> nonZeros [0,1,0,2,3,0,0]
[1,2,3]
- Create a function that realizes the left rotation of a list by one element.
rotateLeft1 :: [a] -> [a]
*Main> rotateLeft1 [1,2,3,4,5]
[2,3,4,5,1]
- Create a function that realizes the right rotation of a list by one element.
rotateRight1 :: [a] -> [a]
*Main> rotateRight1 [1,2,3,4,5]
[5,1,2,3,4]
- Create a function that eliminates all even numbers from a list.
oddMembers :: [Int] -> [Int]
*Main> oddMembers [0,1,0,2,3,0,0]
[1,3]
- Create a function that counts all odd numbers in a given list (define non-recursively using previously defined functions).
countOddMembers :: [Int] -> Int
*Main> countOddMembers [1,0,3,1,4,5]
4
- Create a function that compares lists of numbers if they are equal.
compareLists :: Eq a => [a] -> [a] -> Bool
*Main> compareLists [5,8,11] [5,8,11]
True
*Main> compareLists [5,8,11] [3,5,8]
False
*Main> compareLists [] []
True
*Main> compareLists [5,8,11] [5,8,11,13]
False