PFP Laboratory 2 - Revision history

Beh01: /* Functions working with lists and tuples */

2022-09-29T10:51:10Z

Functions working with lists and tuples

Beh01 at 10:48, 29 September 2022

2022-09-29T10:48:51Z

Beh01 at 10:09, 29 September 2022

2022-09-29T10:09:51Z

Beh01 at 10:04, 29 September 2022

2022-09-29T10:04:30Z

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Beh01: Created page with "== Simple functions working with list == Implement following functions: * Create a function that computes length of a list. length' :: [a] -> I..."

2022-09-29T10:00:40Z

Created page with "== Simple functions working with list == Implement following functions: * Create a function that computes length of a list. <syntaxhighlight lang="Haskell">length' :: [a] -> I..."

New page

== Simple functions working with list ==
Implement following functions:
* Create a function that computes length of a list.
<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>

* Create a function that sums the list of integers.

<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" 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>

* Create a function that returns the first element in the list.

<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>

* Create a function that returns the last element in the list.

<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" 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>

* Create a function that checks if an element is a member of the list.

<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>

* Create a function that returns the list without the first element.

<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>

* Create a function that returns the list without the last element.

<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" 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>

* Create a function that merge two lists into one list.

<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" 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>

* Create a function that finds the maximum in the list of integers.

<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>

* Create a function that reverse a list.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/jlUuZ5fCFgQ]]</div>
<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>

* Create a function that product scalar multiplication if two vectors.

<syntaxhighlight lang="Haskell">scalar :: [Int] -> [Int] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> scalar [1,2,3] [4,5,6]
32
</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>

@@ Line 354: / Line 354: @@
 divisors'' :: Int -> [Int]
 divisors'' n =  [x | x<-[1..n], n `mod` x == 0]
 </syntaxhighlight>
 [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BVU17842]]
 </div>
 <div style="clear:both"></div>

← Older revision		Revision as of 10:48, 29 September 2022
Line 1:		Line 1:
		+	== More Functions ==
		+	Implement following functions:
		+	* Term combination is a selection of items from a collection, such that (unlike permutations) the order of elements in this selection does not matter. Compute the number of possible combinations if we are taking k things from the collection of n things.
		+	<syntaxhighlight lang="Haskell">combinations :: Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> combinations 8 5
		+	56
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	factorial :: Int -> Int
		+	factorial 0 = 1
		+	factorial n = n * factorial (n-1)
		+
		+	combinations :: Int -> Int -> Int
		+	combinations n k = factorial n `div` (factorial k * factorial (n-k))
		+
		+	combinations' :: Int -> Int -> Int
		+	combinations' n k = fromIntegral(factorial n) `div` fromIntegral(factorial k * factorial (n-k))
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/WRUF28416]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	* Implement a function that computes the number of solutions for a quadratic equation. This quadratic equation will be given using standard coefficients: a, b, c.
		+	<syntaxhighlight lang="Haskell">numberOfRoots :: Int -> Int -> Int -> Int
		+	-- To simplify the solution, let construct can be used
		+	f x y = let a = x + y
		+	in a * a
		+	</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> numberOfRoots 1 4 2
		+	2
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	numberOfRoots :: Int -> Int -> Int -> Int
		+	numberOfRoots a b c = let d = bb - 4 a *c
		+	in if d<0 then 0 else if d == 0 then 1 else 2
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/WRUF28416]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	* Implement a function that computes greatest common divider for two given numbers. <div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/uNs9Zqetu7k]]</div>
		+	<syntaxhighlight lang="Haskell">gcd' :: Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> gcd' 30 18
		+	6
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	gcd' :: Int -> Int -> Int
		+	gcd' a b \| a > b = gcd' (a-b) b
		+	\| a < b = gcd' a (b-a)
		+	\| a==b = a
		+
		+	gcd2 :: Int -> Int -> Int
		+	gcd2 a 0 = a
		+	gcd2 a b = gcd2 b (a `mod` b)
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/WRUF28416]]
		+	</div>
		+	<div style="clear:both"></div>
		+	* Implement a function that compute, if a given number is a prime number. <div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/XSc8qjd4StQ]]</div>
		+	<syntaxhighlight lang="Haskell">isPrime :: Int -> Bool</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> isPrime 7
		+	True
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	isPrime :: Int -> Bool
		+	isPrime 1 = False
		+	isPrime y = isPrimeTest y (y-1) where
		+	isPrimeTest _ 1 = True
		+	isPrimeTest n x \| n `mod` x ==0 = False
		+	\| otherwise = isPrimeTest n (x-1)
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/WRUF28416]]
		+	</div>
		+	<div style="clear:both"></div>
		+
	== Simple functions working with list ==		== Simple functions working with list ==
	Implement following functions:		Implement following functions:

@@ Line 91: / Line 91: @@
 isElement a (x:xs) | a == x = True
                     | otherwise = isElement a xs
 </syntaxhighlight>
 [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
@@ Line 196: / Line 179: @@
    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]]
@@ Line 371: / Line 336: @@
    tmp 0 = (0,1)
    tmp x = fibStep (tmp (x-1))
 </syntaxhighlight>
 [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BVU17842]]
 </div>
 <div style="clear:both"></div>