From 5e531ce0c6e87adb0763dc78cff439ac47932ad2 Mon Sep 17 00:00:00 2001 From: Nils Pukropp Date: Fri, 19 Jan 2024 04:41:07 +0100 Subject: [PATCH] tut 12 --- Tutorium/tut12/README.md | 272 ++++++++++++++++++++++++++++++- Tutorium/tut12/slides.pdf | Bin 102810 -> 204172 bytes Tutorium/tut12/src/functional.py | 44 ++--- 3 files changed, 290 insertions(+), 26 deletions(-) diff --git a/Tutorium/tut12/README.md b/Tutorium/tut12/README.md index 7713766..efed339 100644 --- a/Tutorium/tut12/README.md +++ b/Tutorium/tut12/README.md @@ -14,6 +14,213 @@ Musterlösung 11 - Wiederholung Types - Functions! --- +# Musterlösung - Exercise 11 + +--- + +# Aufgabe 11.1 - Generatoren; `generators.py` [`10p`] + +--- + +## Aufgabe 11.1 a - collatz; [`2.5p`] +Es seien $i \in \mathbb{N}_0$ und $n \in \mathbb{N}$, so ist die Collatz-Folge definiert als + +$$ +\begin{align*} + c_0 &= n \\ + c_{i+1} &= + \begin{cases} + \frac{c_i}{2}, &c_i\mod 2 = 0 \\ + 3 \cdot c_i + 1, &c_i\mod 2 = 1 + \end{cases} +\end{align*} +$$ + +Dabei gilt $c_i = 1$ als Abbruchbedingung des Generators + +--- + +## Aufgabe 11.1 a - collatz; [`2.5p`] + +```python +def collatz(n: int) -> Generator[int, None, None]: + if n < 1: + return + while n > 1: + yield n + if n % 2 == 0: + n = n // 2 + else: + n = 3 * n + 1 + yield n +``` + +--- + +## Aufgabe 11.1 b - random; [`2.5p`] + +--- + +## Aufgabe 11.1 b - random; [`2.5p`] + +```python +def random(seed: int, a: int, b: int, m: int) -> Iterator[int]: + yi = seed + while True: + yield yi + yi = (a * yi + b) % m +``` + +--- + +## Aufgabe 11.1 c - chunks; [`2.5p`] + +--- + +## Aufgabe 11.1 c - chunks; [`2.5p`] + +```python +def chunks[T](iter: Iterator[T], n: int) -> Iterator[list[T]]: + while True: + xs = [] + try: + for _ in range(n): + xs.append(next(iter)) + yield xs + except StopIteration: + if xs: + yield xs + break +``` + +--- + +## Aufgabe 11.1 d - flatten; [`2.5p`] + +--- + +## Aufgabe 11.1 d - flatten; [`2.5p`] + +```python +def flatten[T](iters: Iterator[list[T]]) -> Iterator[T]: + for iter in iters: + yield from iter +``` + +--- + +# Aufgabe 11.2 - Graphen; `graphs.py` [`10p`] + +Typaliase als Hilfestellung +```python +type GDict[T] = dict[T, set[T]] +type Graph[T] = GDict[T] +``` + +--- + +## Aufgabe 11.2 a - is_graph; [`2.5p`] + +--- + +## Aufgabe 11.2 a - is_graph; [`2.5p`] + +```python +def is_graph(d: GDict[Any]) -> bool: + for vals in d.values(): + for val in vals: + if val not in d.keys(): + return False + return True + +``` + +--- + +## Aufgabe 11.2 b - to_graph; [`2.5p`] + +--- + +## Aufgabe 11.2 b - to_graph; [`2.5p`] + +```python +def to_graph[T](d: GDict[T]) -> Graph[T]: + res = dict() + for k, vals in d.items(): + for val in vals: + if val not in d: + res[val] = set() + res[k] = vals + return res +``` + +--- + +## Aufgabe 11.2 c - nodes, edges; [`2.5p`] + +--- + +## Aufgabe 11.2 c - nodes, edges; [`2.5p`] + +```python +def edges[T](graph: Graph[T]) -> Iterator[tuple[T, T]]: + for key, value in graph.items(): + for v in value: + yield (key, v) + + +def nodes[T](graph: Graph[T]) -> Iterator[T]: + yield from graph.keys() +``` + +--- + +## Aufgabe 11.2 d - invert_graph; [`2.5p`] + +--- + +## Aufgabe 11.2 d - invert_graph; [`2.5p`] + +```python +def invert_graph[T](graph: Graph[T]) -> Graph[T]: + res = dict() + for n in nodes(graph): + res[n] = set() + for a, b in edges(graph): + res[b].add(a) + return res +``` + +--- + +## Aufgabe 11.2 e - has_cycle; [`0p`] + +--- + +## Aufgabe 11.2 e - has_cycle; [`0p`] + +```python +def find_cycle[T](graph: Graph[T], start: T, visited: set[T]) -> bool: + assert start in graph + if start in visited: + return True + for value in graph[start]: + if find_cycle(graph, value, visited | {start}): + return True + return False + + +def has_cycle(graph: Graph[Any]) -> bool: + return any(find_cycle(graph, node, set()) for node in graph) +``` + +--- + +## Aufgabe 11.3 - Erfahrungen `NOTES.md`; [`0p`] + +### Tragt eure Stunden ein! + +--- # Type annotations (Wiederholung) @@ -279,7 +486,7 @@ print(add_but_variable(3, 2)) # 5 - Verketten von Funktionen ```python def compose[T](*funcs: Callable[[T], T]) -> Callable[[T], T]: - return reduce(lambda f, g: lambda n: f(g(n)), funcs) + return fold(lambda f, g: lambda n: f(g(n)), funcs) f: Callable[[int], int] = lambda n: n + 42 g: Callable[[int], int] = lambda n: n ** 2 @@ -295,7 +502,7 @@ print(add_but_variable(3, 2)) # 5 - nehmen eine oder mehrere `Callable` als Argument - geben ein `Callable` zurück -### Higher-Order-Functions - `map` +### Higher-Order-Function - `map` - Wendet ein `Callable` auf jedes Element in einem `Iterable` an @@ -309,11 +516,68 @@ print(add_but_variable(3, 2)) # 5 --- -### Higher-Order-Functions - `filter` +### Higher-Order-Function - `filter` - `filter` verarbeitet Datenstrukturen anhand eines Prädikats (`Callable`) - behält nur Elemente die das Prädikat erfüllen ```python def filter[T](predicate: Callable[[T], bool], xs: Iterable[T]) -> Iterable[T]: return [x for x in xs if predicate(x)] - ``` \ No newline at end of file + + predicate: Callable[[int | None] bool] = lambda e: bool(e) + none_free_list: list[int] = list(filter(predicate, [1, 2, 3, None, 5, 6])) + print(none_free_list) # [1, 2, 3, 5, 6] - kein None + ``` + +--- + +### Higher-Order-Function - `fold` + +- Kombiniert Elemente einer Datenstruktur + ```python + def fold[T](func: Callable[[T, T], T], xs: Iterable[T]) -> T: + it: Iterator[T] = iter(xs) + value: T | None = None + for x in it: + match value: + case None: + value = x + case _: + value = func(value, x) + if not value: + raise TypeError("can't fold empty list") + return value + + sum: Callable[[Iterable[int]], int] = lambda xs: fold(lambda x, y: x + y, xs) + print(sum([1, 2, 3, 4])) # 10 + ``` + +--- + +### keine Higher-Order-Function - `flatten` + +- Nimmt mehrdimensionale Listen und macht eine Liste draus + ```python + def flatten(xs: Iterable[Any]) -> Iterable[Any]: + new_list = [] + for s in xs: + if isinstance(s, Iterable): + new_list += flatten(s) + else: + new_list.append(s) + return new_list + + flattened = list(flatten([[1, 2, 3], 4, [[5, 6], 7, [8, 9]]])) + print(flattened) # [1, 2, 3, 4, 5, 6, 7, 8, 9] + ``` +- nimmt weder `Callable` als Argumente +- gibt kein `Callable` zurück +- ist keine Higher-Order-Function + +--- + +# Fragen zur funktionalen Programmierung? + +--- + +# Weitere allgemeine Fragen? \ No newline at end of file diff --git a/Tutorium/tut12/slides.pdf b/Tutorium/tut12/slides.pdf index 447744754a64bacbbf60fb91ee3fd42b11634ad4..b219e00db86e95f91ed6487d7c99caa2830c0745 100644 GIT binary patch delta 195628 zcmY(qV{qV4&@CL>wv&x*+qSW>?alsTb7O35+qP{R8{5hIf8Kka54WnP>r~g7nlD|| z)6-`%3ZSAp5aM}3xf1wT!5-Zb9F<^xPFEB#88pi!j95WcNO&nH861vBl?n)D_s>lEl*JyTN)`r=k=9+=ih2= z;NrP0F1xQhj6_A(4AEBEu`{S2E|WuXf}MXlfFhZB^q9jynmv+krhn{8w`D1UfM$#$ z_%z02(PJwg5`3E3S$^vem;yqQ@HvM9O)oOg*A^NlbwP?fSFhho!uzpx3fANP>RFNx z@8`JKTm(OgqDj0ps}dr}rP6QM^=F(3UviU-;^9)yE2Bv)G8dgShXZui4hSnxJlNTEhzQ)brLI{-Y8jLAz9)>IlQ zowZU{IyrR=UR0Gl{;q92Qg_tY<{`aZX0Kl_zrS5d;pZLe5!;MsRyL&!h``qq1kQW< z?LY@>=LJ-9=vrUL)~8M|&iy31J4Jn@zXJy8do7GURu6BLAVb#pN{v4``@DpKFD*e%}*KX;nyC-;^i%$>IoMoyV~hU z8-K@p-OMP{TFjEw0LiHI02l}c6O(AbUk9_hPt78>y(07+$M#M-629K-+3UVs!$tZE?w~gkiUl65B`^E4ajJA6NB9zm+0O zaen4$nF$@W%X{!(Tjg!qaIYWqHig$UHH9z6+Jv{uF~F#aVTuc@9*k}OsWQ;tWOjom zr^oh-&ldo-Ow>&NpWFds;YdLJ0kCkhvHm~#Q>C*}P1u6yms2zA8bDnrtwM%^VWrPE zLxb=Du4s!LVnA~B4Gu{&74O>YX&o?>vD<`vJd! zkC#|@xh8|$REsSH{!=pqZM;$3(l&qF{QCcbimi-&ulFEU^aUHUm!(4q0g{meWNrt()wS_ za^(@TJls_OcWI?s-HBkF7l-@m5l_H8ReXb zBLqMq0ryY+0Q#M=ufdLh^eAZ7G5Zhvg*wD4mAc6+d-TJ2jlRUxC&VtEf z?B3%vg9>~Lt-lK_uKu`*@8Y8(_lwktDc7qk_tf|nhF7-PZQC_dL`a6E&}H&ZwHz#! zlULuJ1f3~#ITvMr{#2vBvr}CsR#Ub>Q;H9i&GMdHGp)+wrib#dl6t_0f8yxaEN<#acr=#pUE0RPcb; 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Callable[[T, T], T], xs: Iterable[T]) -> T: case _: value = func(value, x) if not value: - raise TypeError("can't reduce empty list") + raise TypeError("can't fold empty list") return value def flatten(xs: Iterable[Any]) -> Iterable[Any]: new_list = [] for s in xs: if isinstance(s, Iterable): - new_list.append(flatten(s)) + new_list += flatten(s) else: - new_list.append([s]) + new_list.append(s) return new_list def compose[T](*funcs: Callable[[T], T]) -> Callable[[T], T]: - return reduce(lambda f, g: lambda n: f(g(n)), funcs) + return fold(lambda f, g: lambda n: f(g(n)), funcs) def poly(x: float) -> Callable[[float, float], Callable[[float], float]]: @@ -45,39 +45,39 @@ def main(): fhg: Callable[[int], int] = compose(f, g, h) - # f(g(h(0))) <=> ((0 - 3) ** 2) + 42 = 52 - print(fhg(0)) - print(compose(f, g, h)(0)) + # f(g(h(0))) <=> ((0 - 3) ** 2) + 42 = 51 + assert (tmp := fhg(0)) == 51 + assert compose(f, g, h)(0) == 51 + assert list(filter(lambda e: bool(e), [1, 2, 3, None, 5, 6])) == [1, 2, 3, 5, 6] + assert list(filter(lambda e: not bool(e), [1, 2, 3, None, 5, 6])) == [None] - print(list(filter(lambda e: bool(e), [1, 2, 3, None, 5, 6]))) - print(list(filter(lambda e: not bool(e), [1, 2, 3, None, 5, 6]))) - - print(list(map(lambda e: str(e), [1, 2, 3, 4, 5, 6, "hello_functional"]))) - - print(list( + assert list(map(lambda e: str(e), [1, 2, 3, 4, 5, 6, "hello_functional"])) == ["1", "2", "3", "4", "5", "6", "hello_functional"] + + assert list( filter(lambda e: len(e) > 1, map(lambda e: str(e), - [1, 2, 3, 4, "hello_world"])))) + [1, 2, 3, 4, "hello_world"]))) == ["hello_world"] - print(list(filter(lambda e: isinstance(e, int), [1, 2, 3, "hello"]))) - print(list(flatten([[1, 2, 3], 4, [[5, 6], 7, [8, 9]]]))) + assert list(filter(lambda e: isinstance(e, int), [1, 2, 3, "hello"])) == [1, 2, 3] + assert (tmp := list(flatten([[1, 2, 3], 4, [[5, 6], 7, [8, 9]]]))) == [1, 2, 3, 4, 5, 6, 7, 8, 9], f"{tmp}" def add(a: int, b: int) -> int: return a + b add_but_variable: Callable[[int, int], int] = add - print(add_but_variable(3, 2)) # 5 + assert add_but_variable(3, 2) == 5 add2: Callable[[int, int], int] = lambda x, y: x + y - print(add2(2, 3)) + assert add2(2, 3) == 5 - print((lambda x, y: x + y)(3, 4)) + assert (lambda x, y: x + y)(3, 4) == 7 - print(reduce(lambda x, y: x + y, [1, 2, 3, 4])) # 10 + sum: Callable[[Iterable[int]], int] = lambda xs: fold(lambda x, y: x + y, xs) + assert sum([1, 2, 3, 4]) == 10 - print(poly(3)(2, 3)(5)) + assert poly(3)(2, 3)(5) == 2 * 3 ** 2 + 3 * 3 + 5 if __name__ == '__main__': main() \ No newline at end of file