00-Introduction.ipynb 51 KB
 Ben Glocker committed Jan 16, 2018 1 2 3 4 5 6 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [  Ben Glocker committed Jan 17, 2018 7  "# Introduction to Python (for Algorithms 2)"  Ben Glocker committed Jan 16, 2018 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54  ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "by *James Booth* and *Ghislain Antony Vaillant*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Disclaimer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is by no means a comprehensive introduction to the Python programming language. It covers the essential language features required to implement, test and validate the Algorithms 202 courseworks. It is strongly advised to complement this tutorial with additional reading such as the [official Python documentation](https://docs.python.org/3/), [Python 101](https://leanpub.com/python_101) or the excellent [Hitchhiker's guide to Python](http://docs.python-guide.org/en/latest/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Language basics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Syntax and features" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Hello world" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 55 56 57  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72  "outputs": [], "source": [ "print(\"Hello, world!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Built-in [functions](https://docs.python.org/3/library/functions.html)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 73 74 75  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 76 77 78 79 80 81 82 83 84 85  "outputs": [], "source": [ "print(\"Hello, world!\")\n", "print(\"Hello,\", \"world!\")\n", "print(\"{}, {}!\".format(\"Hello\", \"world\"))" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 86 87 88  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 89 90 91 92 93 94 95 96  "outputs": [], "source": [ "help(print)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 97 98 99  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 100 101 102 103 104 105 106 107  "outputs": [], "source": [ "type(1.0)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 108 109 110  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126  "outputs": [], "source": [ "assert(2 % 2 == 0)\n", "#assert(2 / 2 == 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Built-in [types](https://docs.python.org/3/library/stdtypes.html)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 127 128 129  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171  "outputs": [], "source": [ "# Booleans\n", "B = True\n", "print(type(B))\n", "\n", "# Numeric types\n", "N = 1\n", "print(type(N))\n", "\n", "N = 1.0\n", "print(type(N))\n", "\n", "N = 1j\n", "print(type(N))\n", "\n", "# Strings\n", "N = \"Hello, word\"\n", "print(type(N))\n", "\n", "# Lists\n", "L = [False, 1.0, \"Hello\"]\n", "print(type(L))\n", "\n", "# Ranges\n", "R = range(10)\n", "print(type(R))\n", "\n", "# None\n", "print(type(None))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Dynamic typing" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 172 173 174  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195  "outputs": [], "source": [ "x = 3 # Defines a binding a variable named \"x\",\n", " # to an object of type integer with value 3.\n", "print('x is of type {} with value {}'.format(type(x), x))\n", "\n", "x = 2.0 # Redefine the binding between \"x\" and an\n", " # object of type float with value 2.0.\n", "print('x is of type {} with value {}'.format(type(x), x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Strong typing" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 196 197 198  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 199 200 201 202 203 204 205 206 207  "outputs": [], "source": [ "print(1 + '2') # What is the intent here? \n", " # \"Explicit is better than implicit.\"" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 208 209 210  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226  "outputs": [], "source": [ "print(str(1) + '2') # String concatenation.\n", "print(1 + int('2')) # Integer summation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Variables and scopes" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 227 228 229  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263  "outputs": [], "source": [ "a = 0\n", "\n", "if False:\n", " b = 1\n", "\n", "def my_function(c):\n", " d = 3\n", " print(a) # a is global\n", " print(b) # b is global\n", " print(c) # c is local\n", " print(d) # d is local\n", "\n", "my_function(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Control flow" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### if statements" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 264 265 266  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297  "outputs": [], "source": [ "# simple branching\n", "if condition:\n", " do_something()\n", "\n", "# 2-way branching\n", "if condition:\n", " do_something()\n", "else:\n", " do_other_thing()\n", "\n", "# switch-case style\n", "if condition:\n", " do_something()\n", "elif other_condition:\n", " do_other_thing()\n", "else:\n", " do_default_thing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### while statements" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 298 299 300  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331  "outputs": [], "source": [ "# loop until\n", "while condition:\n", " do_something()\n", "\n", "# loop until with break clause\n", "while condition:\n", " do_something()\n", " if specific_condition:\n", " break # exit while loop regardless\n", " do_other_thing()\n", "\n", "# loop until with break clause\n", "while condition:\n", " do_something()\n", " if specific_condition:\n", " continue # loop-back regardless\n", " do_other_thing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### for statements" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 332 333 334  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 335 336 337 338 339 340 341 342 343  "outputs": [], "source": [ "for n in range(10):\n", " print(n)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 344 345 346  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 347 348 349 350 351 352 353 354 355 356  "outputs": [], "source": [ "numbers = [1, 2, 3]\n", "for number in numbers:\n", " print(number)" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 357 358 359  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383  "outputs": [], "source": [ "ingredients = ['carrots', 'leeks', 'potatoes']\n", "for index, ingredient in enumerate(ingredients):\n", " print(index, ingredient)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data structures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Common concepts" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 384 385 386  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 387 388 389 390 391 392 393 394 395 396 397  "outputs": [], "source": [ "# literals\n", "vowels = ['a', 'e', 'i', 'o', 'u', 'y']\n", "print('vowels: {}'.format(vowels))\n", "\n" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 398 399 400  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 401 402 403 404 405 406 407 408 409 410 411  "outputs": [], "source": [ "# indexing\n", "print('the first vowel is: ' + vowels[0])\n", "print('the last vowel is: ' + vowels[-1])\n", "print('the second-to-last vowel is: ' + vowels[-2])" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 412 413 414  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 415 416 417 418 419 420 421 422 423 424 425 426  "outputs": [], "source": [ "# slicing\n", "print('first three: {}'.format(vowels[:3]))\n", "print('last two: {}'.format(vowels[-2:]))\n", "print('middle ones: {}'.format(vowels[1:-1]))\n", "print('one each two: {}'.format(vowels[::2]))" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 427 428 429  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 430 431 432 433 434 435 436 437 438 439  "outputs": [], "source": [ "# iteration\n", "for vowel in vowels:\n", " print(vowel.upper())" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 440 441 442  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459  "outputs": [], "source": [ "# enumeration\n", "for index, vowel in enumerate(vowels):\n", " print(\"vowel {} is {}\".format(1+index, vowel))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Immutable sequences" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 460 461 462  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 463 464 465 466 467 468 469 470 471  "outputs": [], "source": [ "vowels = ('a', 'e', 'i', 'o', 'u', 'y')\n", "print(type(vowels))" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 472 473 474  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489  "outputs": [], "source": [ "vowels[1] = 'b'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Mutable sequences" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 490 491 492  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 493 494 495 496 497 498 499 500 501  "outputs": [], "source": [ "vowels = ['a', 'e', 'i', 'o', 'u', 'y']\n", "print(type(vowels))" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 502 503 504  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520  "outputs": [], "source": [ "vowels[1] = 'b'\n", "print(vowels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Dictionaries" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 521 522 523  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 524 525 526 527 528 529 530 531 532 533 534 535 536  "outputs": [], "source": [ "# build using literal construct: {k1: v1, k2:v2}\n", "D = {\"one\": 1, \n", " \"two\": 2, \n", " \"three\": 3}\n", "\n", "print('D: {}'.format(D))" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 537 538 539  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 540 541 542 543 544 545 546 547 548 549 550  "outputs": [], "source": [ "# indexing\n", "print(D[\"one\"])\n", "print(D[\"two\"])\n", "print(D[\"three\"])" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 551 552 553  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591  "outputs": [], "source": [ "# iterating\n", "for item in D.items():\n", " print(item)\n", "\n", "for key in D.keys():\n", " print(key)\n", "\n", "for value in D.values():\n", " print(value)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Functions" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Standard definiton\n", "def my_function(arg1, arg2):\n", " # Do something with arg1, arg2\n", " # ...\n", " return result" ] }, { "cell_type": "code", "execution_count": null,  Ben Glocker committed Jan 30, 2018 592 593 594  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617  "outputs": [], "source": [ "# Lambda definition\n", "x_power_x = lambda x: x**x\n", "print(x_power_x(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application: Complexity analysis of bubble sort" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "cell_type": "code",  Ben Glocker committed Feb 20, 2018 618  "execution_count": 2,  Ben Glocker committed Jan 17, 2018 619 620 621  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653  "outputs": [], "source": [ "def bubble_sort(L):\n", " \"\"\"\n", " Sorts the input list inplace using a deterministic version of the bubble sort algorithm [1].\n", " \n", " [1] https://en.wikipedia.org/wiki/Bubble_sort\n", " \"\"\"\n", " max_pass = len(L) - 1\n", " for pass_num in range(max_pass):\n", " for i in range(max_pass-pass_num):\n", " if L[i+1] < L[i]:\n", " L[i], L[i+1] = L[i+1], L[i]\n", " return L\n", "\n", "\n", "def my_sorted(iterable):\n", " \"\"\"\n", " Returns the sorted elements of the iterable as a list.\n", " \"\"\"\n", " return bubble_sort(list(iterable))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unit testing" ] }, { "cell_type": "code",  Ben Glocker committed Feb 20, 2018 654  "execution_count": 3,  Ben Glocker committed Jan 17, 2018 655 656 657  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687  "outputs": [], "source": [ "test_cases = [\n", " [3, 2, 1, 6, 5, 4],\n", " [6, 5, 4, 3, 2, 1], # Worst case\n", " [1, 3, 2, 4, 6, 5], # One pass required\n", "]\n", "\n", "for case in test_cases:\n", " # Validate against built-in sorted\n", " #print(my_sorted(case), sorted(case))\n", " assert(my_sorted(case) == sorted(case))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Complexity analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Data generation" ] }, { "cell_type": "code",  Ben Glocker committed Feb 20, 2018 688  "execution_count": 4,  Ben Glocker committed Jan 16, 2018 689  "metadata": {},  Ben Glocker committed Jan 30, 2018 690 691 692 693 694 695 696 697 698 699 700 701 702  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on method randint in module random:\n", "\n", "randint(a, b) method of random.Random instance\n", " Return random integer in range [a, b], including both end points.\n", "\n" ] } ],  Ben Glocker committed Jan 16, 2018 703 704 705 706 707 708 709  "source": [ "from random import randint\n", "help(randint)" ] }, { "cell_type": "code",  Ben Glocker committed Feb 20, 2018 710  "execution_count": 40,  Ben Glocker committed Jan 16, 2018 711  "metadata": {},  Ben Glocker committed Jan 30, 2018 712 713 714 715 716  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [  Ben Glocker committed Feb 20, 2018 717  "[658042, 242361, 863569, 787057, 225873, 237945, 236740, 938816, 355375, 141558, 892528, 211345, 581149, 33164, 158996, 838642, 498178, 151876, 1675, 23323]\n"  Ben Glocker committed Jan 30, 2018 718 719 720  ] } ],  Ben Glocker committed Jan 16, 2018 721 722  "source": [ "randlist = lambda n: [randint(1e1, 1e6) for i in range(n)]\n",  Ben Glocker committed Jan 30, 2018 723  "print(randlist(20))"  Ben Glocker committed Jan 16, 2018 724 725 726 727 728 729 730 731 732 733 734  ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Timing method" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 735  "execution_count": 34,  Ben Glocker committed Jan 16, 2018 736  "metadata": {},  Ben Glocker committed Jan 30, 2018 737 738 739 740 741 742 743 744 745  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "min = 3.8399983616006945e-06, max = 0.0001740799257258993, mean = 9.804795816620452e-06\n" ] } ],  Ben Glocker committed Jan 16, 2018 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770  "source": [ "def timed(f, *args, **kwargs):\n", " from time import clock\n", " before = clock()\n", " result = f(*args, **kwargs)\n", " after = clock()\n", " return after-before\n", "\n", "# Collect enough time samples\n", "timings = [timed(my_sorted, case) for case in [randlist(6) for n in range(1000)]]\n", "\n", "from statistics import mean\n", "print(\"min = {}, max = {}, mean = {}\".format(\n", " min(timings), max(timings), mean(timings)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Experiment" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 771  "execution_count": 35,  Ben Glocker committed Jan 17, 2018 772 773 774  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 775 776  "outputs": [], "source": [  Ben Glocker committed Jan 17, 2018 777  "sizes = list(range(1, 1000, 100)) + list(range(1000, 10000, 1000))\n",  Ben Glocker committed Jan 16, 2018 778 779 780 781 782 783 784 785 786 787 788 789  "timings = [timed(my_sorted, case) for case in [randlist(size) for size in sizes]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 790  "execution_count": 36,  Ben Glocker committed Jan 17, 2018 791 792 793  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 794 795 796 797 798 799 800 801 802 803  "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "# Uncomment for details about the plot function\n", "#help(plt.plot)" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827  "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 16.67753193491971)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ],  Ben Glocker committed Jan 16, 2018 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844  "source": [ "plt.plot(sizes, timings, linewidth=4)\n", "plt.xlabel('size')\n", "plt.ylabel('time (s)')\n", "plt.xlim(0)\n", "plt.ylim(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fitting" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 845  "execution_count": 38,  Ben Glocker committed Jan 17, 2018 846 847 848  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 849 850 851 852 853 854 855 856 857 858 859  "outputs": [], "source": [ "from numpy import polyfit\n", "# Uncomment for details about polyfit\n", "#help(polyfit)\n", "\n", "poly = polyfit(sizes, timings, deg=2)" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 860  "execution_count": 39,  Ben Glocker committed Jan 17, 2018 861 862 863  "metadata": { "collapsed": true },  Ben Glocker committed Jan 16, 2018 864 865 866 867 868 869 870 871 872 873 874  "outputs": [], "source": [ "from numpy import polyval\n", "# Uncomment for details about polyval\n", "#help(polyval)\n", "\n", "fitted = polyval(poly, sizes)" ] }, { "cell_type": "code",  Ben Glocker committed Jan 30, 2018 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898  "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 17.591113768918017)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EaqOGO3jsKhpjfhWRRkXKvi/0dhkwzFPnV0p5ljGGcbOSHJqEIkICmeCOXkL5ufDNP2Ht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\nVUKD+HuvJoy+uDERIfqfXCn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ],  Ben Glocker committed Jan 16, 2018 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948  "source": [ "plt.plot(sizes, timings, '-', linewidth=4)\n", "plt.plot(sizes, fitted, '--', linewidth=4)\n", "plt.xlabel('size')\n", "plt.ylabel('time (s)')\n", "plt.xlim(0)\n", "plt.ylim(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Going further" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Provide an alternative implementation of bubble sort with the optimization tricks explained in the Wikipedia article.\n", "- Modify the my_sorted function to allow users to choose between the deterministic and the optimized implementations. By default, my_sorted should still be using the determinisitic version.\n", "- Run the experiment above with the optimized bubble sort implementation.\n", "- Compare the deterministic and optimized implementations with a plot.\n", "- Draw some conclusions from this analysis." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }