From 5f7f42ce0b67cd233ade33b845dc44a86b473675 Mon Sep 17 00:00:00 2001 From: Niklas Heim Date: Mon, 1 Apr 2024 19:20:40 +0200 Subject: [PATCH] Lecture 07 (#9) --- .vitepress/config.mts | 1 + code/jarnik.hs | 51 ++++ code/test.hs | 26 ++ img/jarnik-graph.png | Bin 0 -> 132494 bytes img/jarnik.gif | Bin 0 -> 254321 bytes lectures/index.md | 5 + lectures/lecture07.hs | 69 +++++ lectures/lecture07.md | 592 +++++++++++++++++++++++++++++++++++++++++ lectures/lecture07.pdf | Bin 0 -> 61588 bytes 9 files changed, 744 insertions(+) create mode 100644 code/jarnik.hs create mode 100644 code/test.hs create mode 100644 img/jarnik-graph.png create mode 100644 img/jarnik.gif create mode 100644 lectures/lecture07.hs create mode 100644 lectures/lecture07.md create mode 100644 lectures/lecture07.pdf diff --git a/.vitepress/config.mts b/.vitepress/config.mts index c290c2c..e699946 100644 --- a/.vitepress/config.mts +++ b/.vitepress/config.mts @@ -33,6 +33,7 @@ export default defineConfig({ { text: '04: Pattern Matching & Lazy Evaluation', link: '/lectures/lecture04'}, { text: '05: Macros & Interpreters', link: '/lectures/lecture05'}, { text: '06: Lambda Calculus', link: '/lectures/lecture06'}, + { text: '07: Haskell', link: '/lectures/lecture07'}, { text: 'Bonus: Immutable datastructures', link: '/lectures/bonus'}, ] }, diff --git a/code/jarnik.hs b/code/jarnik.hs new file mode 100644 index 0000000..d6ee656 --- /dev/null +++ b/code/jarnik.hs @@ -0,0 +1,51 @@ +import Data.List + +type Vertex = Char +type Edge = (Vertex,Vertex) +type Weight = Int +type Graph = [(Edge,Weight)] + +graph :: Graph +graph = [(('A','B'), 7) + ,(('A','D'), 5) + ,(('D','B'), 9) + ,(('C','B'), 8) + ,(('E','B'), 7) + ,(('C','E'), 5) + ,(('D','E'), 15) + ,(('D','F'), 6) + ,(('F','E'), 8) + ,(('F','G'), 11) + ,(('E','G'), 9) + ] + +deduplicate :: [Vertex] -> [Vertex] +deduplicate [] = [] +deduplicate (v:vs) = v:(deduplicate filtered) + where filtered = [ u | u <- vs, u /= v ] + +vertices :: Graph -> [Vertex] +vertices g = deduplicate $ concat [ [a,b] | ((a,b), _) <- g ] + +sortGraph :: Graph -> Graph +sortGraph g = sortOn snd g + +checkEdge :: Edge -> [Vertex] -> Bool +checkEdge (a,b) visit = p /= q + where p = a `elem` visit + q = b `elem` visit + +findEdge :: [Vertex] -> Graph -> (Edge, Weight) +findEdge visit graph = head [ (e,w) | (e,w) <- graph, checkEdge e visit ] + +jarnik :: Graph -> Graph +jarnik graph = iter vs [] where + graph' = sortGraph graph + (_:vs) = vertices graph + + iter :: [Vertex] -> Graph -> Graph + iter [] tree = tree + iter visit tree = iter visit' tree' where + edge@((a,b),_) = findEdge visit graph' + visit' = [ v | v <- visit, v /= a && v /= b ] + tree' = edge:tree diff --git a/code/test.hs b/code/test.hs new file mode 100644 index 0000000..5dd6faa --- /dev/null +++ b/code/test.hs @@ -0,0 +1,26 @@ +-- average matrix w h = + +transpose ([]:_) = [] +transpose x = (map head x) : transpose (map tail x) + +mat :: [[Int]] +mat = [[1..4] + ,[1..4]] + +avg n = map mean . 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