539 lines
35 KiB
Plaintext
539 lines
35 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Algorytm sortowania bąbelkowego"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Algorytym sortowania bąbelkowego (ang. bubble sort algorithm)**\n",
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"polega na porównywaniu par elementów leżących obok siebie i, jeśli jest to potrzebne, zmienianiu ich kolejności. Nazwa metody wzięła się stąd, że kolejne porównania powodują “wypychanie” kolejnego największego elementu na koniec."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Przebieg sortowania\n",
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"\n",
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"* Porównujemy pierwszy i drugi element tabeli i - jeśli trzeba - to zamieniamy je miejscami. Następnie podobnie porównujemy drugi i trzeci element i - jeśli to konieczne - zamieniamy je miejscami, itd.\n",
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"* Powyższe operacje wykonujemy, aż dojdziemy do końca tabeli.\n",
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"* Następnie ponownie rozpoczynamy porównywanie elementów od początku tabeli.\n",
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"* Sortowanie kończymy, gdy podczas kolejnego przejścia przez całą tabelę nie wykonana zostanie żadna zamiana.\n",
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"\n",
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""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Sortowanie bąbelkowe - pseudokod\n",
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"\n",
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"```c\n",
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"BUBBLE-SORT(n, T)\n",
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" for i := 1 to n\n",
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" do for j := n downto i + 1\n",
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" do if T[j] < T[j - 1]\n",
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" then swap T[j] and T[j-1]\n",
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"```\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Złożoność czasowa\n",
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"\n",
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"Algorytm wykonuje $n-1$ przejść, a w każdym przejściu wykonuje $n-k$ porównań (gdzie $k=1,2...n-1$ to numer przejścia), przez co jego teoretyczna złożoność czasowa wynosi $O(n^{2})$."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Optymalizacja\n",
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"\n",
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"Algorytm można rozbudować tak, by czas optymistyczny był lepszy, poprzez dodanie dodanie flagi informującej, czy w danej iteracji doszło do zmiany. Flaga jest zerowana na wejściu w przebiegu pętli, w przypadku natrafienia na zmianę jest podnoszona, a po wykonaniu przejścia sprawdzana. "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Sortowanie bąbelkowe - python\n",
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"\n",
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"Poniższy program przeprowadza sortowanie listy z losowo ustawionymi wartościami o podanym przez użytkownika rozmiarze."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"#zaimportowanie bibliotek\n",
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"import matplotlib.pyplot as plt #tworzenie wykresów\n",
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"from matplotlib.animation import FuncAnimation #animacja\n",
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"from IPython.display import HTML #animacja jako HTML\n",
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"import random #generowanie liczb pseudolosowych"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"#funkcja pomocnicza do zamiany elementów i, j listy A\n",
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"def swap(A, i, j):\n",
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" \n",
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" if i != j:\n",
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" A[i], A[j] = A[j], A[i]\n",
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" \n",
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"#algorytm sortowania\n",
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"def bubblesort(A):\n",
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"\n",
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" if len(A) == 1:\n",
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" return\n",
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"\n",
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" swapped = True\n",
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" for i in range(len(A) - 1):\n",
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" if not swapped:\n",
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" break\n",
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" swapped = False\n",
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" for j in range(len(A) - 1 - i):\n",
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" if A[j] > A[j + 1]:\n",
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" swap(A, j, j + 1)\n",
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" swapped = True\n",
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" yield A"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Podaj liczbę elementów w tablicy:\n",
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"10\n"
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]
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}
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],
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"source": [
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"#podaj liczbę elementów w tablicy\n",
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"#stwórz listę pseudolosowych elementów \n",
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"N = int(input(\"Podaj liczbę elementów w tablicy:\\n\")) \n",
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"A = [i for i in range(1, N+1)] \n",
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"random.shuffle(A)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"#obiekt generujący\n",
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"generator = bubblesort(A)\n",
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"\n",
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"#zainicjalizuj wykres i oś\n",
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"fig, ax = plt.subplots() \n",
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"\n",
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"rects = ax.bar(range(len(A)), A, align=\"edge\")\n",
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"\n",
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"#ustaw limit widoku dla osi x i y\n",
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"ax.set_xlim(0, len(A)) \n",
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"ax.set_ylim(0, int(1.1*len(A))) \n",
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"\n",
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"#ustaw tekst z liczbą operacji w odniesieniu do współrzędnych osi (do animacji)\n",
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"text = ax.text(0.02, 0.95, \"\", transform=ax.transAxes)\n",
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"iteration = [0]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"#funkcja animacji\n",
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"def animate(A, rects, iteration): \n",
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"\n",
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" #ustala wielkość słupka adekwatną do wielkości elementu tablicy\n",
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" for rect, val in zip(rects, A): \n",
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" rect.set_height(val)\n",
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" \n",
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" #iteracja po każdym dokonanym porównaniu\n",
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" #(liczba operacji)\n",
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" iteration[0] += 1\n",
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" text.set_text(\"Liczba operacji : {}\".format(iteration[0]))\n",
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"\n",
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"\n",
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"anim = FuncAnimation(fig, func=animate, \n",
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" fargs=(rects, iteration), frames=generator, interval=500, \n",
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" repeat=False)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Animacja sortowania bąbelkowego"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"\">\n",
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" Your browser does not support the video tag.\n",
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"</video>"
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],
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"text/plain": [
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"<IPython.core.display.HTML object>"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"HTML(anim.to_html5_video())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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|
"metadata": {},
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|
"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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},
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"name": "python",
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"version": "3.9.0"
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}
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},
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}
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