Simulations Team Teach • 347 min read

Simulations:

3.16, 3.17: Simulations and Algorithmic Efficiency

What is a Simulation?

• A simulation, in context of computer science, is a digital representation of a situation in the real world.
• Examples:
  • Experiments: When an experiment is to dangerous to perform in the real world or too expensive, a simulation can be made of it and be performed digitally.
  • Training and Education: Simulations such as flight simulators and medical simulation can be very practical in aiding dangerous proffesions to receive training.
  • Video Games: Some video games try to aim to be as releastic as possible with physics and graphics to try to simulate the real world.

Simple Dice Roll ```python import random def roll_die(): # Gives random integer between 1 and 6 return random.randint(1, 6) # Defines the variable "result" as the result of function roll_die() result = roll_die() print("Roll:", result) ``` Roll: 2

Dice Roll ```python import random def roll_die(): # Gives random integer between 1 and 6 return random.randint(1, 6) def main(): # Allows user to control how many rolls are executed num_rolls = int(input("How many times would you like to roll the die? ")) # Makes sure that the entered value is a valid integer if num_rolls <= 0: print("Please enter a valid number of rolls.") return print("Rolling the die", num_rolls, "times:") for i in range(num_rolls): roll_result = roll_die() print("Roll", i + 1, ":", roll_result) if __name__ == "__main__": main() ``` Rolling the die 3 times: Roll 1 : 3 Roll 2 : 5 Roll 3 : 5 ## Popcorn Hack #1 -Create a similation that generates a random number using the random library and randint like shown above. Be creative. ```python #Enter code here import random def test_score(): return random.randint(1, 100) result = test_score() print("Your test score is:", result) ``` Your test score is: 76 ## 3.17 Algorithmic Efficiency - A problem is a general description of a task that can (or cannot) be solved algorithmically - A decision problem is a problem with a yes/no answer - An optimization problem is a problem with the goal of finding the "best" solution among many - Efficiency is an estimate of the amount of computational resources used by an algorithm - An algorithm's efficiency is determined through formal or mathematically reasoning One way do demonstrate how algorithmic efficiency can be used to improve a program is through a simple sorting program. ## Bubble Sort Bubble Sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which means the list is sorted. ```python def bubble_sort(list): n = len(list) for i in range(n): for j in range(0, n - i - 1): if list[j] > list[j + 1]: list[j], list[j + 1] = list[j + 1], list[j] import random list = [random.randint(1, 10000) for _ in range(10000)] bubble_sort(list) print("Bubble Sorted listay is:", list) ``` Bubble Sorted listay is: [1, 1, 2, 2, 3, 4, 7, 8, 8, 9, 10, 10, 13, 14, 14, 16, 16, 17, 19, 21, 22, 23, 23, 24, 26, 30, 32, 32, 35, 37, 38, 43, 46, 50, 53, 53, 53, 55, 55, 55, 55, 59, 61, 64, 67, 67, 67, 68, 68, 68, 69, 71, 71, 72, 73, 74, 74, 76, 77, 81, 81, 82, 83, 83, 84, 85, 85, 85, 86, 88, 89, 89, 91, 92, 94, 94, 94, 95, 96, 97, 98, 99, 100, 100, 100, 103, 103, 104, 104, 105, 107, 108, 109, 109, 110, 110, 113, 113, 114, 114, 114, 115, 115, 118, 118, 118, 119, 119, 120, 121, 122, 125, 126, 126, 126, 132, 134, 135, 135, 136, 138, 139, 141, 141, 142, 142, 142, 142, 143, 144, 144, 145, 148, 148, 149, 150, 151, 152, 154, 155, 155, 158, 159, 160, 164, 164, 164, 165, 166, 167, 168, 168, 169, 169, 170, 171, 172, 173, 175, 175, 175, 177, 177, 178, 179, 180, 180, 182, 183, 184, 185, 187, 187, 189, 192, 192, 193, 194, 194, 194, 195, 195, 196, 197, 197, 198, 198, 198, 200, 201, 203, 204, 204, 205, 207, 207, 208, 209, 210, 211, 212, 213, 214, 214, 214, 217, 217, 217, 219, 219, 219, 220, 220, 221, 221, 224, 225, 227, 227, 227, 228, 228, 229, 232, 233, 234, 235, 235, 238, 238, 240, 241, 242, 243, 243, 245, 245, 246, 247, 247, 247, 248, 254, 255, 257, 257, 258, 259, 259, 261, 262, 263, 264, 266, 266, 266, 268, 268, 268, 270, 270, 272, 272, 272, 273, 274, 276, 277, 277, 278, 278, 279, 280, 280, 281, 283, 284, 284, 286, 286, 291, 293, 294, 296, 296, 298, 300, 302, 302, 303, 304, 304, 306, 307, 308, 309, 311, 311, 313, 314, 316, 318, 318, 319, 319, 320, 320, 321, 322, 323, 323, 324, 324, 325, 325, 327, 329, 329, 330, 330, 335, 335, 336, 338, 339, 342, 342, 343, 343, 345, 346, 349, 351, 353, 354, 355, 356, 356, 356, 357, 357, 359, 359, 360, 361, 363, 364, 364, 365, 368, 369, 369, 370, 371, 372, 373, 375, 375, 376, 376, 377, 378, 379, 380, 380, 380, 383, 386, 390, 391, 393, 393, 394, 395, 395, 397, 398, 398, 399, 400, 400, 402, 403, 404, 405, 405, 406, 406, 407, 408, 408, 408, 409, 412, 413, 414, 414, 414, 415, 416, 417, 417, 418, 420, 420, 420, 421, 421, 423, 425, 425, 426, 426, 427, 428, 432, 432, 433, 434, 434, 434, 437, 439, 439, 440, 440, 440, 442, 443, 444, 444, 445, 445, 446, 448, 450, 450, 451, 453, 453, 454, 455, 456, 456, 457, 458, 458, 459, 460, 461, 462, 463, 465, 465, 466, 467, 467, 468, 468, 468, 469, 471, 471, 471, 474, 478, 480, 480, 481, 481, 481, 482, 483, 484, 485, 486, 486, 487, 488, 489, 489, 493, 493, 495, 495, 495, 496, 496, 499, 499, 500, 500, 506, 506, 507, 508, 511, 511, 513, 514, 515, 515, 517, 517, 520, 520, 521, 523, 524, 524, 525, 525, 526, 528, 529, 530, 531, 532, 533, 533, 537, 539, 539, 541, 542, 543, 545, 546, 549, 549, 550, 552, 553, 553, 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941, 941, 943, 945, 946, 947, 947, 948, 949, 951, 952, 952, 952, 954, 957, 958, 958, 959, 959, 959, 961, 961, 961, 962, 962, 964, 966, 967, 968, 969, 972, 972, 973, 973, 974, 976, 976, 976, 977, 977, 980, 980, 982, 983, 987, 988, 989, 989, 990, 990, 991, 992, 993, 993, 993, 994, 996, 997, 997, 999, 999, 1000, 1000, 1001, 1004, 1005, 1005, 1008, 1009, 1013, 1014, 1015, 1016, 1017, 1017, 1018, 1018, 1018, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1025, 1027, 1027, 1030, 1032, 1032, 1034, 1036, 1037, 1038, 1039, 1039, 1040, 1040, 1041, 1041, 1041, 1042, 1042, 1044, 1046, 1047, 1047, 1048, 1048, 1048, 1048, 1048, 1051, 1051, 1052, 1053, 1054, 1054, 1054, 1054, 1054, 1055, 1055, 1056, 1059, 1060, 1061, 1061, 1063, 1063, 1064, 1065, 1065, 1066, 1068, 1070, 1070, 1070, 1071, 1072, 1072, 1073, 1074, 1075, 1075, 1076, 1077, 1078, 1081, 1084, 1085, 1087, 1088, 1090, 1091, 1093, 1094, 1095, 1095, 1096, 1097, 1098, 1101, 1101, 1101, 1102, 1103, 1105, 1107, 1110, 1111, 1111, 1112, 1112, 1114, 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1288, 1288, 1289, 1289, 1290, 1290, 1290, 1291, 1292, 1292, 1294, 1294, 1296, 1296, 1296, 1297, 1300, 1300, 1301, 1301, 1303, 1303, 1303, 1305, 1306, 1308, 1314, 1314, 1315, 1316, 1316, 1316, 1317, 1318, 1318, 1318, 1318, 1321, 1322, 1323, 1324, 1325, 1326, 1328, 1333, 1333, 1333, 1333, 1333, 1336, 1336, 1337, 1337, 1338, 1339, 1339, 1339, 1342, 1342, 1343, 1345, 1346, 1347, 1347, 1349, 1350, 1350, 1351, 1352, 1352, 1353, 1353, 1355, 1357, 1358, 1359, 1360, 1360, 1362, 1362, 1362, 1363, 1364, 1366, 1367, 1367, 1369, 1371, 1372, 1372, 1373, 1373, 1374, 1377, 1377, 1378, 1378, 1382, 1384, 1385, 1385, 1386, 1386, 1387, 1387, 1389, 1390, 1393, 1393, 1394, 1396, 1396, 1396, 1397, 1397, 1398, 1398, 1399, 1402, 1403, 1404, 1405, 1405, 1406, 1409, 1409, 1410, 1411, 1412, 1412, 1415, 1415, 1416, 1419, 1419, 1419, 1420, 1420, 1422, 1422, 1424, 1427, 1427, 1430, 1435, 1436, 1437, 1438, 1439, 1439, 1440, 1440, 1441, 1441, 1442, 1443, 1444, 1445, 1451, 1452, 1454, 1454, 1458, 1458, 1459, 1460, 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9567, 9568, 9569, 9571, 9573, 9576, 9576, 9578, 9579, 9580, 9584, 9586, 9587, 9592, 9592, 9594, 9595, 9596, 9598, 9604, 9605, 9605, 9606, 9606, 9608, 9612, 9614, 9614, 9614, 9615, 9618, 9620, 9621, 9622, 9622, 9623, 9623, 9625, 9625, 9626, 9628, 9629, 9630, 9631, 9632, 9632, 9632, 9633, 9634, 9634, 9635, 9635, 9636, 9636, 9640, 9640, 9641, 9641, 9641, 9642, 9642, 9643, 9643, 9643, 9645, 9645, 9646, 9646, 9646, 9647, 9650, 9651, 9651, 9653, 9654, 9654, 9655, 9655, 9656, 9656, 9659, 9660, 9660, 9661, 9661, 9662, 9664, 9666, 9666, 9666, 9667, 9668, 9669, 9670, 9672, 9673, 9674, 9677, 9679, 9679, 9680, 9680, 9681, 9681, 9683, 9685, 9686, 9687, 9691, 9691, 9691, 9693, 9696, 9697, 9697, 9698, 9699, 9701, 9701, 9703, 9704, 9705, 9706, 9708, 9708, 9708, 9709, 9710, 9710, 9711, 9715, 9715, 9716, 9716, 9716, 9717, 9718, 9719, 9720, 9720, 9721, 9722, 9722, 9724, 9724, 9728, 9728, 9729, 9731, 9733, 9733, 9735, 9736, 9737, 9739, 9740, 9742, 9743, 9744, 9745, 9745, 9746, 9747, 9750, 9750, 9750, 9752, 9753, 9754, 9754, 9756, 9757, 9757, 9758, 9758, 9760, 9760, 9766, 9768, 9770, 9770, 9774, 9775, 9776, 9776, 9776, 9778, 9779, 9781, 9783, 9783, 9783, 9783, 9785, 9786, 9787, 9788, 9788, 9790, 9790, 9793, 9794, 9795, 9795, 9795, 9796, 9798, 9800, 9801, 9801, 9801, 9802, 9803, 9804, 9807, 9807, 9808, 9810, 9811, 9811, 9811, 9814, 9814, 9814, 9815, 9816, 9817, 9817, 9817, 9817, 9818, 9818, 9819, 9820, 9821, 9821, 9822, 9824, 9824, 9825, 9825, 9825, 9826, 9827, 9828, 9829, 9831, 9832, 9834, 9835, 9835, 9836, 9837, 9838, 9839, 9840, 9840, 9840, 9841, 9841, 9843, 9845, 9845, 9845, 9847, 9848, 9848, 9848, 9848, 9848, 9850, 9850, 9851, 9852, 9853, 9853, 9854, 9855, 9856, 9858, 9858, 9858, 9860, 9860, 9862, 9862, 9863, 9864, 9867, 9870, 9872, 9873, 9873, 9874, 9875, 9875, 9877, 9877, 9879, 9881, 9881, 9882, 9882, 9882, 9883, 9883, 9884, 9884, 9884, 9886, 9887, 9887, 9889, 9890, 9891, 9891, 9892, 9892, 9893, 9894, 9895, 9895, 9897, 9897, 9899, 9901, 9901, 9902, 9903, 9904, 9904, 9904, 9905, 9906, 9906, 9907, 9907, 9907, 9907, 9908, 9908, 9910, 9910, 9910, 9911, 9911, 9911, 9913, 9913, 9913, 9916, 9917, 9917, 9919, 9920, 9921, 9924, 9927, 9929, 9930, 9931, 9932, 9933, 9933, 9933, 9934, 9935, 9938, 9939, 9942, 9943, 9945, 9945, 9949, 9949, 9949, 9950, 9952, 9953, 9955, 9955, 9956, 9957, 9959, 9959, 9960, 9961, 9961, 9962, 9962, 9963, 9964, 9964, 9967, 9968, 9972, 9974, 9975, 9975, 9978, 9978, 9978, 9979, 9981, 9981, 9983, 9984, 9985, 9986, 9987, 9987, 9988, 9988, 9988, 9993, 9993, 9994, 9994, 9995, 9998, 10000, 10000, 10000] ## Popcorn Hack 2 - Using bubble sort, make multiple strings that sort alphabetically. ```python #Enter code here def bubble_sort(strings): n = len(strings) for i in range(n): for j in range(0, n-i-1): if strings[j] > strings[j+1]: strings[j], strings[j+1] = strings[j+1], strings[j] # List of strings to be sorted strings = ["tesla", "audi", "jeep", "mustang", "bmw"] # Call the bubble_sort function to sort the strings bubble_sort(strings) # Display the sorted strings for string in strings: print(string) ``` audi bmw jeep mustang tesla ## Quick Sort Quick Sort is a popular divide-and-conquer sorting algorithm. It divides the array into smaller sub-arrays and recursively sorts them. It's generally more efficient than Bubble Sort for larger lists. ```python def quick_sort(list): if len(list) <= 1: return list else: pivot = list[0] less_than_pivot = [x for x in list[1:] if x <= pivot] greater_than_pivot = [x for x in list[1:] if x > pivot] return quick_sort(less_than_pivot) + [pivot] + quick_sort(greater_than_pivot) import random list = [random.randint(1, 10000) for _ in range(10000)] list = quick_sort(list) print("Quick Sorted listay is:", list) ``` Quick Sorted listay is: [1, 2, 4, 4, 5, 5, 5, 6, 6, 8, 9, 10, 10, 14, 14, 15, 16, 18, 21, 22, 22, 22, 22, 24, 24, 25, 26, 27, 27, 27, 27, 27, 29, 30, 31, 31, 32, 33, 33, 35, 35, 36, 37, 37, 38, 40, 41, 41, 42, 43, 44, 44, 45, 45, 46, 49, 51, 53, 53, 54, 54, 55, 56, 57, 57, 59, 62, 62, 63, 63, 64, 64, 65, 67, 67, 68, 68, 68, 69, 69, 70, 70, 72, 72, 73, 75, 77, 77, 79, 79, 80, 80, 80, 82, 83, 84, 84, 84, 85, 85, 88, 89, 90, 90, 94, 97, 98, 101, 101, 102, 105, 105, 105, 106, 106, 108, 109, 110, 111, 111, 112, 113, 115, 115, 116, 116, 119, 120, 121, 122, 128, 128, 129, 135, 136, 136, 137, 137, 138, 141, 142, 143, 145, 145, 147, 150, 151, 151, 152, 153, 154, 154, 156, 157, 157, 157, 158, 162, 163, 163, 165, 165, 166, 166, 166, 168, 169, 172, 174, 175, 175, 181, 183, 184, 184, 184, 187, 188, 188, 189, 189, 191, 192, 192, 193, 193, 193, 193, 193, 194, 194, 194, 196, 197, 198, 199, 199, 201, 201, 204, 204, 208, 208, 209, 210, 210, 210, 212, 215, 216, 216, 216, 216, 217, 217, 217, 218, 219, 220, 222, 223, 225, 225, 225, 226, 227, 227, 229, 231, 232, 233, 234, 236, 239, 240, 241, 241, 241, 242, 243, 243, 244, 245, 246, 248, 249, 249, 249, 251, 253, 253, 255, 258, 259, 259, 263, 264, 266, 266, 268, 271, 271, 271, 272, 272, 275, 275, 276, 277, 277, 279, 279, 284, 286, 286, 286, 289, 289, 289, 289, 290, 290, 293, 293, 294, 295, 296, 298, 300, 301, 302, 303, 304, 305, 306, 307, 307, 307, 307, 309, 309, 312, 312, 315, 315, 317, 317, 317, 318, 320, 320, 320, 321, 323, 325, 325, 326, 326, 326, 326, 327, 327, 329, 330, 330, 330, 330, 330, 330, 331, 331, 332, 333, 333, 335, 337, 337, 337, 338, 339, 339, 340, 340, 341, 341, 341, 344, 344, 345, 347, 347, 348, 349, 350, 350, 351, 351, 351, 351, 352, 353, 353, 354, 356, 356, 357, 359, 361, 362, 364, 365, 365, 368, 368, 369, 369, 370, 370, 372, 374, 374, 375, 375, 376, 378, 381, 382, 384, 384, 384, 384, 386, 387, 389, 389, 392, 392, 392, 392, 393, 393, 394, 394, 397, 398, 398, 400, 401, 402, 402, 402, 403, 406, 406, 407, 407, 410, 410, 413, 414, 415, 415, 417, 419, 420, 423, 423, 424, 429, 430, 430, 431, 431, 433, 433, 434, 434, 434, 435, 435, 438, 438, 440, 440, 446, 450, 450, 457, 458, 458, 460, 460, 461, 461, 462, 462, 465, 466, 467, 467, 468, 468, 468, 470, 471, 472, 473, 473, 474, 476, 476, 477, 478, 478, 479, 479, 480, 480, 482, 483, 486, 487, 487, 488, 491, 491, 493, 495, 495, 496, 497, 498, 499, 500, 501, 501, 502, 505, 505, 505, 506, 507, 508, 509, 509, 511, 511, 511, 512, 512, 513, 514, 514, 515, 516, 517, 517, 517, 518, 518, 518, 519, 519, 521, 522, 525, 526, 527, 528, 528, 528, 528, 529, 529, 530, 531, 531, 532, 532, 534, 535, 537, 537, 539, 539, 540, 540, 543, 543, 544, 544, 545, 545, 546, 548, 548, 549, 552, 554, 554, 554, 557, 558, 559, 559, 562, 562, 564, 565, 565, 566, 566, 567, 567, 570, 570, 573, 573, 574, 574, 575, 578, 579, 580, 580, 583, 584, 585, 586, 587, 588, 588, 588, 588, 590, 592, 592, 592, 593, 594, 595, 596, 596, 596, 601, 601, 601, 602, 602, 603, 603, 605, 606, 606, 607, 607, 607, 608, 608, 609, 610, 610, 610, 611, 611, 612, 612, 613, 614, 615, 616, 620, 621, 621, 621, 623, 624, 625, 626, 626, 627, 627, 628, 628, 630, 632, 632, 632, 636, 636, 636, 637, 637, 638, 639, 642, 642, 643, 643, 644, 648, 648, 649, 649, 649, 650, 652, 652, 653, 653, 654, 654, 657, 657, 658, 658, 659, 660, 661, 661, 662, 662, 663, 665, 666, 667, 668, 668, 668, 669, 669, 669, 670, 671, 672, 676, 677, 678, 681, 682, 683, 685, 686, 687, 691, 692, 692, 694, 694, 694, 695, 696, 696, 696, 700, 702, 704, 707, 708, 709, 709, 712, 712, 714, 714, 714, 715, 715, 715, 717, 717, 718, 718, 719, 719, 719, 719, 720, 721, 721, 722, 723, 724, 724, 725, 726, 726, 726, 726, 728, 729, 732, 732, 732, 734, 734, 735, 735, 735, 736, 737, 738, 739, 740, 740, 742, 743, 744, 746, 746, 746, 747, 749, 749, 750, 750, 754, 756, 756, 756, 757, 758, 759, 759, 761, 762, 762, 763, 763, 764, 765, 765, 767, 770, 771, 772, 773, 774, 776, 777, 778, 778, 780, 780, 781, 781, 781, 781, 782, 783, 784, 785, 785, 788, 789, 791, 792, 792, 793, 793, 795, 796, 797, 799, 799, 799, 799, 800, 803, 804, 804, 804, 805, 806, 807, 810, 811, 814, 814, 815, 816, 816, 818, 819, 819, 819, 821, 824, 824, 824, 825, 826, 828, 828, 829, 829, 832, 832, 834, 836, 836, 836, 837, 837, 838, 839, 839, 841, 842, 842, 842, 842, 843, 843, 843, 846, 848, 849, 850, 851, 851, 851, 851, 852, 853, 854, 856, 858, 858, 858, 859, 860, 861, 862, 862, 862, 863, 864, 864, 864, 866, 866, 868, 870, 871, 872, 874, 875, 876, 877, 880, 881, 881, 882, 884, 885, 886, 887, 887, 887, 887, 888, 888, 889, 889, 890, 890, 890, 892, 893, 895, 895, 899, 899, 899, 900, 902, 904, 905, 907, 909, 910, 910, 912, 913, 914, 916, 916, 916, 918, 919, 921, 922, 924, 925, 925, 926, 927, 927, 928, 928, 930, 933, 933, 934, 935, 936, 937, 938, 938, 938, 939, 939, 939, 940, 940, 942, 942, 946, 947, 947, 948, 949, 950, 953, 954, 955, 955, 955, 956, 956, 957, 958, 959, 960, 964, 966, 966, 966, 969, 969, 972, 972, 972, 974, 975, 975, 975, 979, 980, 981, 984, 984, 986, 987, 987, 988, 988, 988, 989, 990, 993, 994, 994, 994, 995, 995, 996, 996, 997, 998, 999, 1002, 1003, 1003, 1004, 1005, 1007, 1007, 1007, 1007, 1008, 1009, 1010, 1011, 1011, 1012, 1012, 1013, 1013, 1015, 1015, 1018, 1018, 1019, 1019, 1020, 1020, 1020, 1020, 1025, 1025, 1026, 1026, 1027, 1027, 1027, 1029, 1029, 1031, 1031, 1033, 1034, 1036, 1036, 1039, 1039, 1040, 1041, 1041, 1042, 1044, 1045, 1047, 1047, 1049, 1049, 1051, 1051, 1053, 1056, 1059, 1059, 1060, 1062, 1063, 1063, 1063, 1063, 1064, 1064, 1066, 1066, 1066, 1067, 1068, 1068, 1069, 1069, 1070, 1070, 1070, 1074, 1075, 1079, 1087, 1088, 1089, 1090, 1090, 1092, 1094, 1094, 1095, 1096, 1097, 1099, 1100, 1100, 1101, 1104, 1106, 1107, 1107, 1108, 1109, 1109, 1111, 1112, 1112, 1113, 1113, 1114, 1115, 1117, 1117, 1117, 1119, 1121, 1121, 1121, 1125, 1129, 1129, 1129, 1130, 1132, 1133, 1133, 1136, 1136, 1136, 1138, 1140, 1140, 1140, 1142, 1142, 1143, 1144, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1154, 1154, 1155, 1155, 1156, 1156, 1157, 1158, 1158, 1160, 1160, 1162, 1164, 1164, 1167, 1167, 1167, 1167, 1169, 1169, 1169, 1169, 1171, 1173, 1174, 1175, 1176, 1176, 1176, 1177, 1177, 1178, 1179, 1181, 1184, 1186, 1186, 1187, 1187, 1187, 1190, 1192, 1193, 1194, 1196, 1198, 1198, 1199, 1199, 1201, 1203, 1205, 1205, 1206, 1206, 1207, 1207, 1207, 1208, 1208, 1210, 1211, 1211, 1211, 1211, 1212, 1214, 1215, 1215, 1216, 1217, 1217, 1218, 1218, 1220, 1220, 1220, 1222, 1222, 1223, 1225, 1231, 1232, 1232, 1233, 1233, 1234, 1235, 1236, 1238, 1239, 1239, 1240, 1242, 1244, 1244, 1245, 1247, 1247, 1248, 1249, 1250, 1252, 1252, 1254, 1254, 1255, 1259, 1259, 1260, 1260, 1261, 1261, 1262, 1264, 1264, 1264, 1265, 1265, 1266, 1266, 1268, 1269, 1269, 1269, 1271, 1272, 1273, 1273, 1274, 1274, 1276, 1276, 1278, 1279, 1279, 1280, 1282, 1284, 1285, 1286, 1287, 1288, 1289, 1289, 1292, 1292, 1293, 1294, 1295, 1295, 1296, 1300, 1302, 1302, 1303, 1303, 1304, 1304, 1304, 1305, 1305, 1306, 1307, 1308, 1309, 1311, 1313, 1313, 1313, 1314, 1314, 1315, 1317, 1319, 1320, 1320, 1322, 1324, 1325, 1325, 1326, 1327, 1328, 1328, 1328, 1328, 1331, 1332, 1335, 1335, 1336, 1336, 1339, 1340, 1340, 1340, 1341, 1345, 1346, 1346, 1350, 1350, 1351, 1351, 1352, 1352, 1352, 1354, 1356, 1356, 1358, 1358, 1360, 1361, 1362, 1362, 1363, 1363, 1364, 1365, 1366, 1366, 1366, 1366, 1367, 1367, 1368, 1370, 1373, 1373, 1375, 1375, 1377, 1378, 1380, 1382, 1382, 1383, 1383, 1383, 1384, 1384, 1384, 1385, 1385, 1386, 1387, 1387, 1387, 1387, 1388, 1389, 1389, 1391, 1391, 1392, 1394, 1396, 1396, 1398, 1399, 1399, 1400, 1400, 1400, 1401, 1401, 1404, 1404, 1405, 1407, 1408, 1409, 1409, 1411, 1412, 1413, 1413, 1414, 1415, 1417, 1417, 1418, 1419, 1420, 1420, 1421, 1422, 1424, 1424, 1424, 1424, 1424, 1425, 1426, 1427, 1429, 1429, 1429, 1429, 1431, 1433, 1435, 1435, 1437, 1438, 1438, 1439, 1440, 1443, 1443, 1445, 1448, 1448, 1450, 1451, 1452, 1453, 1454, 1454, 1455, 1456, 1457, 1457, 1458, 1458, 1461, 1462, 1463, 1463, 1467, 1469, 1469, 1470, 1470, 1470, 1471, 1473, 1473, 1475, 1475, 1476, 1477, 1478, 1478, 1479, 1482, 1485, 1485, 1486, 1490, 1490, 1491, 1493, 1494, 1494, 1494, 1494, 1496, 1497, 1498, 1498, 1498, 1498, 1499, 1499, 1501, 1501, 1501, 1503, 1504, 1504, 1506, 1506, 1507, 1507, 1508, 1508, 1510, 1511, 1513, 1514, 1514, 1514, 1515, 1516, 1517, 1518, 1518, 1520, 1520, 1525, 1528, 1531, 1532, 1534, 1536, 1537, 1537, 1539, 1539, 1540, 1541, 1542, 1542, 1544, 1547, 1547, 1548, 1550, 1550, 1552, 1552, 1554, 1555, 1555, 1558, 1559, 1560, 1561, 1562, 1563, 1566, 1569, 1569, 1571, 1572, 1572, 1573, 1574, 1574, 1577, 1578, 1579, 1580, 1581, 1581, 1581, 1582, 1582, 1583, 1583, 1584, 1585, 1587, 1587, 1587, 1588, 1589, 1589, 1590, 1590, 1590, 1591, 1591, 1592, 1592, 1593, 1593, 1594, 1596, 1596, 1597, 1598, 1599, 1600, 1601, 1602, 1602, 1605, 1606, 1606, 1609, 1610, 1611, 1613, 1613, 1616, 1616, 1616, 1616, 1617, 1618, 1618, 1619, 1621, 1621, 1622, 1623, 1624, 1624, 1624, 1625, 1628, 1628, 1629, 1630, 1630, 1630, 1631, 1631, 1633, 1633, 1633, 1634, 1635, 1637, 1638, 1639, 1640, 1642, 1642, 1642, 1642, 1644, 1646, 1649, 1649, 1649, 1652, 1652, 1653, 1655, 1657, 1658, 1659, 1662, 1663, 1664, 1664, 1664, 1664, 1666, 1666, 1666, 1666, 1667, 1669, 1670, 1671, 1671, 1672, 1672, 1672, 1673, 1674, 1674, 1674, 1674, 1676, 1678, 1678, 1678, 1679, 1680, 1680, 1682, 1684, 1684, 1685, 1686, 1686, 1689, 1689, 1689, 1689, 1690, 1690, 1695, 1698, 1700, 1700, 1700, 1703, 1704, 1705, 1706, 1706, 1707, 1708, 1712, 1714, 1715, 1717, 1718, 1718, 1720, 1721, 1722, 1723, 1723, 1723, 1724, 1725, 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9205, 9206, 9208, 9209, 9210, 9210, 9211, 9212, 9212, 9212, 9212, 9212, 9213, 9214, 9214, 9215, 9216, 9216, 9216, 9217, 9217, 9219, 9219, 9222, 9224, 9224, 9225, 9226, 9228, 9232, 9232, 9233, 9233, 9233, 9234, 9235, 9236, 9237, 9238, 9239, 9239, 9240, 9242, 9243, 9243, 9243, 9245, 9246, 9247, 9247, 9248, 9250, 9250, 9250, 9250, 9251, 9251, 9252, 9252, 9253, 9253, 9253, 9254, 9256, 9259, 9259, 9264, 9266, 9269, 9269, 9269, 9271, 9272, 9272, 9273, 9274, 9274, 9275, 9275, 9276, 9277, 9277, 9278, 9278, 9278, 9284, 9285, 9286, 9286, 9290, 9290, 9292, 9294, 9298, 9299, 9299, 9300, 9300, 9300, 9301, 9301, 9303, 9303, 9304, 9304, 9304, 9305, 9308, 9309, 9316, 9319, 9321, 9323, 9325, 9326, 9326, 9326, 9327, 9328, 9328, 9329, 9329, 9329, 9329, 9330, 9330, 9330, 9333, 9333, 9334, 9334, 9335, 9335, 9340, 9340, 9341, 9342, 9343, 9343, 9343, 9345, 9345, 9350, 9350, 9352, 9356, 9357, 9358, 9358, 9358, 9360, 9363, 9363, 9365, 9365, 9366, 9366, 9368, 9368, 9370, 9371, 9372, 9375, 9377, 9377, 9381, 9382, 9385, 9385, 9388, 9390, 9390, 9390, 9391, 9391, 9392, 9392, 9394, 9394, 9396, 9397, 9404, 9410, 9411, 9414, 9415, 9416, 9416, 9416, 9417, 9418, 9419, 9419, 9421, 9422, 9422, 9425, 9425, 9426, 9426, 9427, 9429, 9429, 9429, 9432, 9434, 9434, 9435, 9435, 9436, 9436, 9437, 9438, 9439, 9441, 9441, 9442, 9443, 9444, 9444, 9446, 9447, 9450, 9451, 9452, 9453, 9456, 9457, 9458, 9460, 9461, 9461, 9462, 9463, 9464, 9468, 9469, 9469, 9471, 9471, 9473, 9473, 9473, 9473, 9474, 9477, 9478, 9478, 9480, 9480, 9481, 9481, 9481, 9483, 9483, 9484, 9486, 9486, 9488, 9492, 9492, 9492, 9497, 9497, 9497, 9497, 9499, 9501, 9502, 9503, 9504, 9504, 9504, 9504, 9505, 9509, 9512, 9513, 9515, 9516, 9516, 9517, 9518, 9518, 9520, 9523, 9528, 9528, 9528, 9529, 9532, 9533, 9533, 9534, 9537, 9539, 9541, 9543, 9543, 9547, 9548, 9548, 9548, 9549, 9550, 9551, 9551, 9553, 9554, 9554, 9554, 9555, 9556, 9558, 9559, 9560, 9560, 9564, 9565, 9565, 9565, 9565, 9567, 9567, 9568, 9569, 9569, 9572, 9573, 9574, 9575, 9575, 9576, 9576, 9578, 9578, 9582, 9586, 9587, 9588, 9588, 9589, 9589, 9590, 9590, 9591, 9592, 9593, 9595, 9595, 9597, 9597, 9600, 9601, 9601, 9602, 9603, 9604, 9607, 9607, 9608, 9609, 9610, 9611, 9611, 9611, 9612, 9612, 9612, 9616, 9619, 9619, 9621, 9621, 9622, 9624, 9626, 9626, 9627, 9628, 9631, 9632, 9633, 9633, 9633, 9634, 9636, 9638, 9639, 9640, 9642, 9644, 9647, 9649, 9650, 9651, 9651, 9651, 9652, 9652, 9653, 9654, 9654, 9655, 9657, 9658, 9658, 9658, 9659, 9660, 9660, 9660, 9661, 9661, 9662, 9663, 9663, 9663, 9664, 9665, 9666, 9669, 9670, 9670, 9671, 9672, 9673, 9673, 9674, 9675, 9675, 9675, 9676, 9677, 9680, 9681, 9682, 9684, 9685, 9685, 9689, 9692, 9692, 9693, 9697, 9698, 9698, 9698, 9699, 9700, 9701, 9706, 9706, 9707, 9707, 9708, 9708, 9709, 9710, 9712, 9712, 9715, 9715, 9715, 9715, 9715, 9718, 9718, 9718, 9719, 9719, 9721, 9721, 9721, 9723, 9728, 9729, 9730, 9733, 9733, 9734, 9734, 9738, 9739, 9739, 9741, 9743, 9743, 9744, 9745, 9748, 9748, 9749, 9750, 9750, 9750, 9753, 9753, 9755, 9756, 9756, 9757, 9757, 9757, 9761, 9762, 9763, 9763, 9765, 9765, 9766, 9766, 9770, 9770, 9770, 9772, 9773, 9774, 9776, 9776, 9777, 9777, 9779, 9779, 9780, 9780, 9781, 9782, 9782, 9782, 9783, 9784, 9785, 9786, 9786, 9789, 9790, 9791, 9791, 9791, 9792, 9794, 9797, 9797, 9800, 9800, 9802, 9802, 9803, 9803, 9804, 9804, 9804, 9804, 9805, 9805, 9805, 9806, 9810, 9810, 9811, 9812, 9813, 9813, 9814, 9815, 9815, 9818, 9818, 9820, 9820, 9820, 9822, 9823, 9823, 9824, 9826, 9827, 9830, 9831, 9833, 9833, 9835, 9835, 9835, 9836, 9839, 9840, 9841, 9842, 9843, 9846, 9847, 9848, 9850, 9851, 9851, 9851, 9851, 9852, 9852, 9853, 9853, 9853, 9854, 9855, 9857, 9857, 9857, 9858, 9859, 9859, 9859, 9860, 9861, 9863, 9863, 9866, 9866, 9866, 9870, 9875, 9875, 9877, 9878, 9878, 9879, 9880, 9881, 9884, 9886, 9886, 9887, 9889, 9889, 9889, 9890, 9892, 9893, 9894, 9894, 9896, 9896, 9897, 9898, 9899, 9901, 9901, 9902, 9903, 9905, 9906, 9907, 9907, 9907, 9907, 9909, 9912, 9913, 9914, 9914, 9915, 9915, 9917, 9917, 9917, 9917, 9919, 9921, 9922, 9924, 9925, 9927, 9927, 9928, 9928, 9929, 9929, 9932, 9932, 9933, 9933, 9934, 9935, 9937, 9937, 9937, 9939, 9939, 9939, 9939, 9940, 9943, 9943, 9944, 9944, 9945, 9945, 9945, 9948, 9949, 9950, 9952, 9952, 9952, 9953, 9954, 9954, 9954, 9955, 9955, 9958, 9959, 9959, 9959, 9961, 9962, 9963, 9964, 9966, 9966, 9966, 9967, 9968, 9970, 9971, 9971, 9972, 9972, 9973, 9973, 9975, 9975, 9975, 9976, 9980, 9981, 9981, 9981, 9981, 9984, 9985, 9985, 9986, 9986, 9988, 9989, 9990, 9990, 9991, 9992, 9995, 9996, 9997, 9998, 9998, 9999, 9999] ## Homework Hacks # Hack 1 - Create a random decision maker that choses between 2 string options. ```python #Enter code here import random def random_decision(option1, option2): # Simulate a coin flip (0 for heads, 1 for tails) coin_flip = random.randint(0, 1) if coin_flip == 0: return option1 else: return option2 option1 = "Option A" option2 = "Option B" decision = random_decision(option1, option2) print("Randomly chosen option: " + decision) ``` Randomly chosen option: Option B # Hack 2 Modify the following function that calculates the sum of a range of numbers from 1-99999999 more efficient. Hints: - The formula for finding the sum of an arithmetic series is n/2 * (first_number + last_number) where n is the number of terms. - To find the number of terms in a list, use len(list) - To index the first term of a list, use list[0] and to index the last term, use list[-1]. ```python def calculate_sum(numbers): n = len(numbers) # Number of terms first_number = numbers[0] # The first term last_number = numbers[-1] # The last term total = n * (first_number + last_number) // 2 # Use the formula for the sum of an arithmetic series return total numbers = list(range(1, 99999999)) print(calculate_sum(numbers)) ``` 4999999850000001