183 lines
4.0 KiB
Plaintext
183 lines
4.0 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "0609fa9a-6337-43c0-a8d2-f947558066ac",
|
|
"metadata": {
|
|
"editable": false,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"import { assertEquals } from \"jsr:@std/assert\"\n",
|
|
"import \"https://git.amgdhg.de/kg/tslib/raw/branch/main/logger.ts\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e2253715-005d-4a31-b577-4ba32a314da6",
|
|
"metadata": {
|
|
"editable": false,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": [
|
|
"# Aufgabe 01.07.1 - Fakultät\n",
|
|
"\n",
|
|
"Eine wichtige mathematische Funktion ist die Fakultät:\n",
|
|
"$$n! = 1\\cdot2\\cdot3\\cdots(n-2)\\cdot(n-1)\\cdot n$$\n",
|
|
"zum Beispiel:\n",
|
|
"$$5!=1\\cdot2\\cdot3\\cdot4\\cdot5=120$$\n",
|
|
"\n",
|
|
"Ziel soll sein, die Funktion `fakultaet` rekursiv zu programmieren. Dafür gibt es zunächst einige Vorüberlegungen:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "81e736ba-89cd-4d1a-9b98-8475de6820bd",
|
|
"metadata": {
|
|
"editable": false,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": [
|
|
"## Teil 1\n",
|
|
"Notiere zunächst die rekursiven Funktionsaufrufe für das konkrete Zahlenbeispiel $n=5$:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"id": "58f5ec36-ae74-4ff0-9e47-4f0f83adbd7b",
|
|
"metadata": {
|
|
"editable": true,
|
|
"raw_mimetype": "",
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ba4b1f2a-51cc-47ff-8b1f-f8444cddd7b9",
|
|
"metadata": {
|
|
"editable": false,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": [
|
|
"## Teil 2\n",
|
|
"Wann bricht die Rekursion ab, d.h. wann wird nicht mehr erneut die Funktion `fakultaet` aufgerufen?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"id": "261e0c80-0169-424f-840a-47c774029ced",
|
|
"metadata": {
|
|
"editable": true,
|
|
"raw_mimetype": "",
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "37316573-632d-440f-9674-1dddbd5039f3",
|
|
"metadata": {
|
|
"editable": false,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"source": [
|
|
"## Teil 3\n",
|
|
"Programmiere die Funktion `fakultaet`:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "b8c40034-1b97-458a-9e30-648c41cb3d7c",
|
|
"metadata": {
|
|
"editable": true,
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "e114cca7-8b8a-4f7e-8861-1a507a679d3d",
|
|
"metadata": {
|
|
"editable": false,
|
|
"jupyter": {
|
|
"source_hidden": true
|
|
},
|
|
"slideshow": {
|
|
"slide_type": ""
|
|
},
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"let _nr = \"01.07.1\"\n",
|
|
"Deno.test(`${_nr}: function`, () => {\n",
|
|
" assertEquals(typeof fakultaet, 'function')\n",
|
|
"})\n",
|
|
"Deno.test(`${_nr}: Parameter`, () => {\n",
|
|
" assertEquals(fakultaet.length, 1)\n",
|
|
"})\n",
|
|
"Deno.test(`${_nr}: fakultaet(1)=1`, () => {\n",
|
|
" assertEquals(fakultaet(1), 1)\n",
|
|
"})\n",
|
|
"Deno.test(`${_nr}: fakultaet(3)=6`, () => {\n",
|
|
" assertEquals(fakultaet(3), 6)\n",
|
|
"})\n",
|
|
"Deno.test(`${_nr}: fakultaet(5)=120`, () => {\n",
|
|
" assertEquals(fakultaet(5), 120)\n",
|
|
"})\n",
|
|
"Deno.test(`${_nr}: fakultaet(11)=39916800`, () => {\n",
|
|
" assertEquals(fakultaet(11), 39916800)\n",
|
|
"})"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Deno",
|
|
"language": "typescript",
|
|
"name": "deno"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": "typescript",
|
|
"file_extension": ".ts",
|
|
"mimetype": "text/x.typescript",
|
|
"name": "typescript",
|
|
"nbconvert_exporter": "script",
|
|
"pygments_lexer": "typescript",
|
|
"version": "5.8.3"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|