TopCoder Statistics - Problem Statement

Problem Statement

Every day Elly travels from her home to the center of the city. There are n+1 stations along the way, numbered 0 through n in the order in which they lie on the railroad. The station 0 is Elly's home, and n is the final station.

The public transportation system in her town has ticket prices which depend on how close to the last station you buy the ticket. A ticket can be bought at any of the stations. We assume the girl has enough time to buy the ticket while the train has stopped at any of the stations.
You are given a int[] ticketPrice with n elements. For each i between 0 and n-1, inclusive, ticketPrice[i] is the price of a ticket from station i to station n. These prices are non-increasing: a ticket for a shorter trip will never cost more than a ticket for a longer trip.

Elly knows that her train is always checked by a single conductor. Every day the conductor boards the train at some station i and checks everyone's tickets while the train rides between stations i and i+1. The conductor chooses the number i uniformly at random from the set {0, 1, ..., n-1}. In other words, the conductor randomly chooses one of the n segments of the railroad.

You are given an int fine. If the conductor catches Elly without a ticket, she will have to pay fine dollars instead of the price of the ticket. (I.e., after paying the fine she is allowed to continue her trip without buying a ticket.)

Elly wants to minimize the expected cost of her trip. Find out which ticket she should purchase (if any), and return the optimal expected cost of her trip.

Definition

Class:: EllysTickets
Method:: getPrice
Parameters:: int[], int
Returns:: double
Method signature:: double getPrice(int[] ticketPrice, int fine)
(be sure your method is public)

Notes

Your return value must have an absolute or a relative error smaller than 1e-9.
Please note that if the girl buys a ticket at station X and the conductor boards at the same station, she will not be fined, since she will have a ticket when he checks her before the next station.

Constraints

ticketPrice will contain between 1 and 50 elements, inclusive.
Each element of ticketPrice will be between 1 and 1000, inclusive.
The ticket prices in ticketPrice will be non-increasing.
fine will be between 1 and 1000, inclusive.

Examples

{8, 5, 3}

10

Returns: 6.666666666666667

One possible strategy for Elly is to buy the ticket from her home (station 0) to the center of the city (station 3). This ticket costs 8 dollars. As she is guaranteed not to be fined, this is also the expected cost of her trip. However, the optimal strategy is to ride the first segment without a ticket and then to buy the ticket from station 1 to station 3. With this strategy the probability that she will be fined is 1/3: she will get a fine if and only if the conductor boards the train at station 0. Thus, with probability 1/3 she will pay the 10 dollar fine and with probability 2/3 she will pay 5 dollars for the ticket. This means that the expected cost of this strategy is 1/3 * 10 + 2/3 * 5 = 20/3 = approximately 6.667 dollars.
{50, 40, 30, 20, 10}

42

Returns: 33.2

It is obvious that Elly should not buy the ticket at station 0: the fine is cheaper than this ticket. The optimal strategy for this test case is to buy the ticket at station 3. If Elly does so, she will be fined with probability 60%, but she will only pay $20 if she isn't fined.
{999, 888, 777, 666, 555, 444, 333, 222, 111}

42

Returns: 42.0

Here the fine is so low, it is best to not buy a ticket at all.
{13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13}

17

Returns: 13.0

In this case apparently it doesn't matter where you buy the ticket. Thus, it is optimal to buy it at station 0 and avoid the chance of being fined.
{951, 924, 908, 907, 889, 880, 870, 810, 770, 731, 716, 713, 687, 677, 650, 645, 608, 598, 556, 472, 470, 446, 446, 410, 401, 352, 337, 337, 226, 191, 189, 183, 176, 173, 168, 148, 100, 92, 84, 57, 41, 17}

344

Returns: 296.6428571428571
{1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1}

500

Returns: 490.02
{1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980, 979, 978, 977, 976, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

500

Returns: 262.5
{1}

100

Returns: 1.0
{100}

1

Returns: 1.0
{936, 871, 861, 777, 746, 737, 703, 636, 631, 539, 533, 488, 410, 350, 300, 270, 182, 68, 24}

172

Returns: 161.05263157894737
{906, 466, 387}

522

Returns: 477.0
{938, 849, 847, 846, 834, 802, 800, 794, 768, 759, 755, 738, 724, 719, 698, 693, 680, 664, 643, 626, 613, 601, 598, 568, 515, 508, 466, 465, 465, 434, 393, 340, 333, 315, 283, 263, 261, 228, 167, 141, 127, 110, 92, 89, 77, 43, 18, 14}

139

Returns: 133.0
{993, 931, 895, 889, 848, 826, 779, 763, 586, 573, 455, 386, 355, 278, 274, 123, 114, 6}

425

Returns: 374.6666666666667
{847, 837, 810, 772, 772, 729, 710, 448, 385, 380, 64}

62

Returns: 62.0
{1000, 992, 973, 947, 908, 891, 888, 875, 842, 804, 651, 626, 594, 573, 571, 557, 520, 516, 472, 467, 442, 429, 425, 418, 366, 351, 346, 334, 275, 272, 263, 204, 139, 129, 113, 75}

980

Returns: 719.9722222222222
{948, 936, 914, 862, 860, 843, 806, 798, 794, 766, 755, 746, 688, 681, 521, 507, 507, 492, 489, 438, 390, 386, 292, 291, 290, 283, 248, 244, 202, 151, 141, 118, 59, 33}

31

Returns: 31.0
{985, 971, 962, 758, 703, 703, 680, 669, 652, 642, 632, 622, 598, 555, 552, 496, 423, 414, 392, 381, 378, 374, 295, 290, 231, 218, 183, 169, 112, 87, 40, 34}

664

Returns: 543.5
{691, 614, 465, 422, 162}

442

Returns: 386.0
{986, 981, 975, 944, 927, 912, 911, 906, 838, 817, 782, 775, 760, 717, 712, 707, 697, 686, 675, 655, 644, 623, 538, 526, 522, 509, 486, 423, 378, 342, 342, 341, 325, 309, 220, 207, 203, 181, 178, 98}

584

Returns: 517.45
{958, 951, 872, 868, 837, 835, 823, 811, 805, 796, 730, 709, 687, 671, 670, 655, 644, 633, 630, 592, 496, 480, 454, 443, 431, 430, 393, 363, 349, 327, 258, 206, 203, 203, 196, 139, 138, 114, 88, 68, 53, 33, 20, 18, 5}

483

Returns: 396.82222222222225
{867, 850, 833, 765, 710, 675, 654, 589, 543, 488, 459, 438, 412, 402, 395, 253, 226, 222, 190, 151, 114, 103, 66, 25}

296

Returns: 265.6666666666667
{940, 818, 770, 743, 691, 682, 664, 651, 638, 605, 530, 416, 300, 286, 276, 150, 116, 103, 93, 50}

414

Returns: 348.0
{750, 750, 743, 510, 349, 288, 265, 245}

118

Returns: 118.0
{964, 903, 841, 784, 762, 760, 748, 724, 717, 703, 646, 636, 633, 601, 600, 593, 587, 577, 508, 481, 445, 410, 403, 399, 362, 357, 356, 331, 301, 288, 272, 247, 239, 157, 134, 111, 109, 99, 97, 65, 53, 18, 8, 6}

947

Returns: 666.2954545454545
{986, 981, 930, 913, 909, 894, 870, 865, 857, 848, 839, 826, 814, 798, 795, 778, 770, 754, 746, 724, 716, 715, 689, 669, 660, 624, 585, 564, 549, 513, 481, 455, 439, 434, 409, 401, 374, 374, 344, 339, 272, 272, 263, 201, 174, 170, 163, 159, 126}

216

Returns: 211.71428571428572
{971, 932, 921, 906, 904, 899, 899, 875, 870, 834, 810, 752, 716, 691, 675, 655, 653, 601, 571, 541, 540, 538, 509, 429, 383, 375, 341, 329, 268, 263, 224, 153, 153, 131, 110, 96, 84, 80, 78, 67, 60, 36, 4, 3}

351

Returns: 292.5
{995, 978, 964, 904, 845, 831, 793, 769, 766, 629, 534, 523, 519, 489, 486, 471, 417, 389, 207, 184, 181, 151, 61, 12}

264

Returns: 247.08333333333334
{1000, 934, 905, 901, 875, 858, 845, 826, 816, 801, 798, 772, 710, 667, 665, 654, 616, 614, 611, 596, 590, 567, 544, 540, 520, 516, 443, 372, 359, 301, 287, 275, 272, 270, 247, 236, 229, 229, 187, 142, 135, 124, 109, 87, 77, 53, 48, 45, 28, 22}

137

Returns: 128.6
{694, 534, 382, 7}

578

Returns: 435.25
{979, 888, 883, 882, 860, 790, 779, 763, 763, 695, 694, 667, 648, 642, 539, 490, 482, 452, 441, 435, 409, 394, 388, 362, 352, 351, 260, 238, 228, 189, 94, 88, 68, 66, 48, 27, 16, 13}

140

Returns: 128.6315789473684
{976, 969, 892, 810, 760, 751, 745, 740, 732, 729, 720, 652, 591, 553, 537, 537, 412, 409, 405, 386, 301, 291, 282, 231, 216, 214, 183, 163, 161, 136, 97, 32, 12}

739

Returns: 566.4545454545455
{947, 715, 663, 529, 375, 319, 74}

649

Returns: 531.5714285714286
{961, 922, 917, 882, 810, 677, 569, 538, 499, 496, 434, 429, 427, 279, 226, 179, 165, 132, 110, 105, 17}

528

Returns: 427.33333333333337
{990, 977, 962, 942, 920, 889, 850, 846, 820, 815, 801, 790, 724, 657, 656, 655, 654, 638, 633, 604, 543, 487, 460, 451, 390, 266, 249, 218, 136, 105, 35, 23, 20, 8}

140

Returns: 127.64705882352942
{997, 853, 819, 718, 699, 565, 562, 517, 449, 231, 43, 6}

845

Returns: 681.6666666666667
{938, 880, 876, 873, 817, 764, 748, 705, 669, 651, 556, 548, 537, 512, 509, 504, 467, 446, 415, 372, 359, 349, 343, 328, 322, 258, 242, 212, 210, 202, 192, 185, 166, 158, 128, 73, 54, 17, 16, 4, 4}

958

Returns: 643.5609756097562
{841, 622, 96}

322

Returns: 246.66666666666666
{947, 934, 891, 887, 863, 852, 835, 831, 820, 807, 806, 801, 758, 756, 738, 713, 708, 647, 636, 606, 577, 567, 532, 527, 525, 433, 424, 421, 401, 384, 378, 347, 331, 329, 328, 248, 236, 216, 170, 114, 87, 76, 55, 35, 1}

661

Returns: 559.6666666666666
{936, 891, 891, 882, 876, 809, 809, 779, 722, 663, 634, 617, 615, 572, 558, 546, 518, 515, 417, 339, 339, 305, 291, 241, 186, 182, 162, 155, 118, 85, 80, 55, 23}

958

Returns: 695.3939393939395
{878, 850, 841, 759, 711, 637, 598, 569, 551, 328, 292, 248, 184, 123}

901

Returns: 696.3571428571429
{989, 898, 831, 809, 769, 764, 720, 718, 710, 683, 639, 639, 613, 582, 578, 537, 532, 496, 473, 466, 465, 438, 385, 358, 318, 312, 312, 301, 273, 257, 174, 169, 157, 124, 98, 40}

729

Returns: 592.0
{922, 917, 912, 851, 814, 769, 728, 714, 627, 584, 562, 493, 412, 369, 363, 337, 316, 283, 281, 249, 247, 162, 126, 120, 50, 50, 48, 12}

790

Returns: 564.4642857142857
{878, 845, 825, 808, 746, 705, 686, 666, 593, 585, 565, 559, 531, 513, 410, 398, 391, 384, 364, 293, 292, 245, 225, 142, 135, 88, 37}

556

Returns: 478.07407407407413
{905, 859, 859, 837, 826, 825, 812, 809, 785, 627, 537, 518, 504, 472, 178, 178, 169, 113, 16}

871

Returns: 688.6315789473684
{945, 911, 843, 793, 730, 720, 640, 630, 620, 590, 513, 266, 247, 243, 213, 196, 175, 165, 145, 131, 129, 62, 48}

967

Returns: 601.2608695652174
{893, 887, 832, 65}

340

Returns: 271.25
{954, 927, 901, 892, 878, 868, 834, 804, 782, 751, 750, 692, 690, 675, 673, 664, 647, 627, 504, 457, 423, 410, 390, 385, 382, 381, 370, 306, 252, 211, 175, 157, 125, 85}

588

Returns: 518.1176470588235
{952, 718, 679, 487, 377, 300, 271, 246, 211, 205, 69, 47}

203

Returns: 180.66666666666669
{997, 970, 930, 929, 926, 834, 805, 755, 704, 684, 628, 613, 597, 563, 545, 539, 528, 527, 526, 510, 465, 463, 457, 449, 448, 323, 312, 297, 227, 208, 205, 195, 189, 176, 137, 57, 55, 48, 45, 38}

449

Returns: 382.4
{949, 876, 869, 865, 834, 804, 786, 763, 686, 598, 567, 546, 509, 508, 424, 399, 394, 371, 348, 318, 270, 204, 193, 184, 71, 55, 40, 31}

698

Returns: 559.1785714285714
{912, 891, 880, 839, 811, 769, 742, 683, 665, 658, 650, 650, 617, 605, 575, 540, 525, 520, 515, 504, 488, 484, 482, 473, 462, 454, 446, 431, 389, 386, 351, 309, 261, 254, 205, 155, 69, 58, 25}

322

Returns: 302.53846153846155
{940, 937, 924, 917, 888, 885, 841, 802, 796, 778, 774, 749, 744, 697, 683, 675, 674, 655, 655, 613, 524, 498, 360, 352, 350, 345, 308, 279, 257, 208, 159, 150, 143, 134, 134, 63, 46, 26, 22}

1

Returns: 1.0
{995, 992, 987, 976, 886, 858, 732, 705, 619, 581, 545, 492, 486, 459, 418, 398, 391, 364, 344, 305, 274, 271, 247, 245, 213, 206, 194, 191, 132, 119, 53, 28}

897

Returns: 627.5625
{859, 827, 649, 629, 606, 570, 536, 535, 518, 457, 415, 404, 401, 314, 169, 149, 144, 53, 38, 23, 8}

131

Returns: 116.14285714285714
{404, 61}

113

Returns: 87.0
{922, 884, 803, 755, 732, 690, 660, 644, 609, 508, 498, 433, 422, 340, 337, 311, 255, 116, 28, 11}

469

Returns: 416.04999999999995
{992, 946, 925, 881, 860, 843, 809, 786, 781, 749, 740, 732, 724, 701, 694, 659, 649, 612, 583, 556, 542, 498, 491, 461, 358, 358, 337, 322, 320, 319, 312, 192, 174, 158, 134, 93, 91, 86, 34, 25}

822

Returns: 636.4
{940, 813, 752, 602, 582, 535, 446, 376, 220, 58}

566

Returns: 496.8
{998, 967, 954, 949, 904, 895, 772, 737, 735, 726, 715, 664, 528, 499, 497, 468, 435, 423, 392, 383, 381, 369, 363, 305, 297, 269, 268, 244, 193, 180, 155, 93, 40, 28, 25}

812

Returns: 607.3428571428572
{991, 977, 947, 946, 944, 901, 867, 845, 818, 806, 775, 770, 693, 662, 661, 625, 578, 553, 524, 522, 504, 490, 488, 475, 406, 402, 381, 342, 322, 317, 296, 277, 270, 247, 230, 217, 208, 203, 186, 162, 138, 98, 89, 84, 71, 39}

781

Returns: 599.6739130434783
{974, 918, 902, 749, 705, 687, 556, 543, 440, 410, 385, 376, 306, 278, 268, 237, 234, 200, 176, 97}

732

Returns: 554.9000000000001
{992, 987, 976, 968, 922, 893, 891, 843, 843, 798, 796, 788, 786, 731, 726, 720, 719, 697, 656, 624, 603, 589, 578, 554, 522, 477, 444, 439, 434, 407, 406, 391, 378, 358, 353, 338, 315, 303, 191, 142, 100, 72, 69, 52, 40, 38, 11, 11}

678

Returns: 570.7291666666667
{974, 846, 832, 631, 597, 557, 529, 506, 459, 393, 381, 371, 330, 299, 272, 266, 233, 119, 110, 108, 89}

619

Returns: 489.85714285714283
{973, 923, 919, 860, 852, 846, 824, 792, 777, 710, 700, 694, 674, 671, 642, 636, 608, 606, 576, 559, 501, 499, 487, 442, 409, 392, 385, 372, 364, 362, 349, 335, 307, 296, 183, 173, 170, 147, 139, 92, 90, 79, 62, 48, 19, 9}

467

Returns: 392.9130434782609
{804, 759, 742}

617

Returns: 617.0
{936, 936, 877, 866, 729, 712, 704, 699, 697, 685, 671, 593, 563, 540, 510, 504, 486, 482, 430, 412, 390, 336, 329, 327, 287, 245, 225, 205, 144, 74, 29, 13, 10}

621

Returns: 517.3636363636364
{840, 822, 809, 781, 725, 719, 684, 643, 628, 556, 552, 522, 502, 501, 465, 451, 354, 329, 317, 304, 246, 234, 220, 211, 210, 208, 141, 124, 124, 123, 90, 88, 5}

796

Returns: 568.3030303030303
{1000, 994, 969, 930, 904, 869, 857, 730, 704, 691, 645, 596, 532, 529, 498, 403, 384, 369, 358, 356, 329, 292, 289, 287, 284, 281, 244, 203, 193, 191, 150, 132, 131, 79, 72, 9}

583

Returns: 461.75
{999, 960, 928, 893, 890, 877, 855, 855, 793, 780, 761, 761, 751, 750, 747, 743, 638, 623, 616, 599, 560, 545, 501, 495, 403, 399, 351, 350, 350, 333, 287, 217, 216, 205, 187, 142, 141, 133, 99, 75, 44, 25}

13

Returns: 13.0
{585, 460, 458, 176}

927

Returns: 576.75
{957, 942, 905, 746, 703, 670, 532, 439, 393, 182, 166, 113, 82, 56}

298

Returns: 256.57142857142856
{988, 938, 920, 918, 908, 865, 860, 783, 779, 737, 736, 713, 708, 681, 678, 663, 642, 608, 597, 571, 565, 545, 456, 422, 417, 399, 341, 331, 289, 267, 241, 234, 229, 228, 202, 192, 181, 145, 105, 94, 86, 77, 53, 32, 10, 5}

296

Returns: 262.7826086956522
{925, 907, 886, 854, 829, 796, 773, 706, 659, 578, 574, 543, 480, 412, 400, 372, 354, 344, 288, 177, 133, 129}

448

Returns: 411.04545454545456
{983, 949, 876, 857, 847, 768, 761, 733, 730, 725, 720, 719, 700, 686, 629, 613, 608, 606, 604, 602, 601, 489, 479, 472, 406, 369, 351, 342, 328, 296, 266, 216, 212, 190, 166, 144, 131, 89, 86, 52, 50}

428

Returns: 376.2926829268293
{950, 943, 938, 918, 845, 833, 764, 595, 539, 522, 476, 458, 347, 336, 291, 277, 269, 250, 231, 207, 198, 192, 170, 149, 129, 108, 94, 66}

222

Returns: 208.71428571428572
{988, 959, 892, 760, 744, 720, 618, 594, 571, 489, 434, 429, 424, 398, 346, 287, 230, 227, 222, 114, 25, 23}

133

Returns: 123.18181818181819
{869, 813, 512, 490, 372, 317, 148, 27}

954

Returns: 622.5
{996, 975, 971, 916, 884, 857, 780, 719, 533, 516, 475, 466, 464, 357, 273, 270, 237, 235, 234, 216, 164, 110, 5}

695

Returns: 529.8695652173914
{956, 913, 888, 886, 867, 857, 813, 810, 805, 784, 764, 750, 748, 743, 720, 709, 666, 660, 637, 595, 567, 501, 411, 393, 384, 374, 330, 323, 320, 300, 227, 216, 214, 212, 117, 98, 88, 66, 49, 44, 41, 31, 31, 22}

90

Returns: 84.40909090909092
{992, 986, 977, 973, 873, 804, 803, 746, 717, 713, 712, 694, 684, 684, 657, 600, 591, 573, 541, 527, 527, 432, 424, 346, 280, 254, 216, 208, 201, 165, 164, 58, 4}

562

Returns: 485.0909090909091
{859, 790, 655, 604, 536, 520, 432, 408}

281

Returns: 281.0
{998, 993, 985, 953, 922, 900, 889, 879, 856, 836, 797, 793, 762, 755, 748, 729, 700, 694, 684, 660, 651, 650, 636, 633, 624, 571, 535, 519, 486, 441, 415, 412, 398, 294, 233, 224, 215, 172, 171, 154, 97, 57, 46, 21, 19, 19, 12, 2}

49

Returns: 46.083333333333336
{974, 974, 903, 875, 863, 840, 832, 804, 770, 753, 726, 689, 680, 673, 643, 636, 577, 546, 493, 468, 405, 372, 366, 360, 358, 294, 281, 237, 112, 95, 24, 10, 10, 8}

11

Returns: 10.911764705882351
{966, 916, 911, 872, 839, 825, 777, 752, 735, 712, 692, 681, 671, 645, 636, 633, 611, 574, 557, 523, 508, 502, 501, 456, 449, 425, 409, 401, 400, 391, 346, 305, 250, 224, 212, 199, 193, 165, 144, 125, 120, 102, 91, 19}

852

Returns: 663.0
{971, 948, 948, 931, 930, 858, 776, 776, 773, 771, 750, 735, 718, 642, 616, 614, 608, 607, 601, 599, 596, 582, 582, 538, 494, 440, 426, 424, 415, 415, 314, 306, 304, 297, 290, 276, 245, 223, 205, 189, 185, 155, 132, 130, 111, 75, 62, 54, 37, 25}

61

Returns: 60.04
{497, 444, 63}

475

Returns: 337.66666666666663
{716, 599, 562, 546, 501, 458, 390, 372, 350, 284}

811

Returns: 611.8000000000001
{839, 717, 625, 517, 477, 449, 383, 302}

163

Returns: 163.0
{982, 940, 918, 807, 795, 771, 743, 713, 703, 703, 698, 562, 528, 483, 442, 434, 416, 412, 377, 328, 241, 150, 74, 70, 65, 21}

219

Returns: 196.69230769230768
{962, 925, 859, 850, 843, 839, 807, 706, 664, 663, 662, 634, 478, 395, 310, 232, 225, 192, 177, 153, 152, 123, 47}

801

Returns: 603.0869565217391
{713, 480}

310

Returns: 310.0
{920, 908, 789, 788, 568, 540, 496, 460, 455, 418, 388, 325, 320, 307, 303, 142, 54, 25, 8}

36

Returns: 34.52631578947368
{976, 971, 946, 932, 932, 907, 867, 855, 847, 842, 802, 679, 678, 674, 599, 591, 585, 567, 555, 544, 499, 482, 464, 435, 431, 423, 380, 348, 330, 293, 273, 68, 29, 22}

115

Returns: 109.94117647058823
{715, 598}

46

Returns: 46.0
{988, 944, 812, 712, 704, 638, 633, 601, 497, 491, 448, 397, 343, 326, 246, 187, 154, 95, 12}

866

Returns: 652.3684210526316
{968, 864, 820, 794, 786, 780, 653, 574, 492, 483, 369, 323, 296, 285, 239, 183, 149, 75}

279

Returns: 263.0
{983, 858, 838, 799, 631, 598, 522, 493, 465, 429, 413, 383, 334, 306, 271, 255, 221, 169, 145}

970

Returns: 663.4736842105264
{932, 892, 889, 887, 875, 871, 839, 811, 795, 742, 646, 570, 567, 498, 469, 465, 413, 370, 307, 304, 295, 289, 272, 250, 225, 192, 182, 163, 51, 17, 6}

204

Returns: 189.19354838709677
{988, 894, 887, 733, 723, 722, 673, 639, 565, 482, 480, 350, 325, 282, 240, 204, 170, 128, 125, 103, 89}

588

Returns: 471.42857142857144
{876, 286, 190, 146, 134}

274

Returns: 222.8
{1}

1

Returns: 1.0
{1000}

1

Returns: 1.0
{1}

1000

Returns: 1.0
{1000}

1000

Returns: 1000.0
{10, 10 }

1

Returns: 1.0
{3 }

2

Returns: 2.0
{2 }

1

Returns: 1.0
{5, 5, 5 }

2

Returns: 2.0
{100, 100, 100 }

10

Returns: 10.0
{10 }

1

Returns: 1.0
{1000 }

2

Returns: 2.0
{8, 5, 3 }

1

Returns: 1.0
{950, 920, 870, 800 }

799

Returns: 799.0
{100, 50 }

1

Returns: 1.0
{100, 100, 100 }

1

Returns: 1.0
{100 }

1

Returns: 1.0
{88, 77 }

7

Returns: 7.0
{100 }

50

Returns: 50.0
{20 }

1

Returns: 1.0
{40, 30, 20, 10 }

1

Returns: 1.0
{50 }

1

Returns: 1.0
{9, 8, 7 }

1

Returns: 1.0
{100, 100 }

1

Returns: 1.0
{42 }

1

Returns: 1.0
{100 }

10

Returns: 10.0
{5, 4, 3 }

1

Returns: 1.0
{50, 50 }

1

Returns: 1.0
{1000 }

1

Returns: 1.0
{5 }

1

Returns: 1.0
{10 }

5

Returns: 5.0
{6, 5, 4 }

1

Returns: 1.0
{5, 5 }

1

Returns: 1.0
{2, 2 }

1

Returns: 1.0
{5, 5 }

2

Returns: 2.0
{1000, 999, 998 }

1

Returns: 1.0
{8, 5, 3 }

10

Returns: 6.666666666666667

Statistics

Problem Statement for "EllysTickets"

Problem Statement

Definition

Notes

Constraints

Examples