Statistics

Problem Statement for "Prank"

Problem Statement

Jane tries her best to stay fit. Knowing this, her sister decided to play a prank on Jane: after Jane's old scale broke down, her sister got her a new scale that shows the square of a person's weight, instead of the real weight.

Not noticing the change, Jane has been using the scale for a while. One morning she screamed "Oh no! I gained apparentGain pounds!". Given an int apparentGain (the difference between the square of Jane's current weight and the square of her previous weight), return a int[] containing Jane's possible real weights after the latest measurement, sorted in ascending order.

All weights (displayed and real, previous and current) are positive integers.

Definition

Class:
Prank
Method:
realWeight
Parameters:
int
Returns:
int[]
Method signature:
int[] realWeight(int apparentGain)
(be sure your method is public)

Constraints

  • apparentGain will be between 1 and 100000, inclusive.

Examples

  1. 233

    Returns: {117 }

    If Jane had previously weighed 116 pounds, the scale would have shown 116^2 = 13456. If she gained 1 pound, the scale would show 117^2 = 13689, for an apparent gain of 13689 - 13456 = 233.

  2. 15

    Returns: {4, 8 }

    Assuming in this example Jane is actually a small animal, she could have gone from 1 to 4 or from 7 to 8.

  3. 1440

    Returns: {38, 39, 42, 46, 49, 53, 66, 77, 94, 123, 182, 361 }

  4. 100000

    Returns: {325, 350, 550, 665, 1025, 1270, 2510, 3133, 5005, 6254, 12502, 25001 }

    This is the largest input.

  5. 93301

    Returns: {3595, 46651 }

    Watch out for overflow!

  6. 3

    Returns: {2 }

  7. 15

    Returns: {4, 8 }

  8. 45

    Returns: {7, 9, 23 }

  9. 96

    Returns: {10, 11, 14, 25 }

  10. 192

    Returns: {14, 16, 19, 26, 49 }

  11. 240

    Returns: {16, 17, 19, 23, 32, 61 }

  12. 480

    Returns: {22, 23, 26, 29, 34, 43, 62, 121 }

  13. 720

    Returns: {27, 28, 29, 36, 41, 49, 63, 92, 181 }

  14. 960

    Returns: {31, 32, 34, 38, 46, 53, 64, 83, 122, 241 }

  15. 1440

    Returns: {38, 39, 42, 46, 49, 53, 66, 77, 94, 123, 182, 361 }

  16. 2880

    Returns: {54, 56, 58, 61, 63, 72, 82, 89, 98, 126, 149, 184, 243, 362, 721 }

  17. 3360

    Returns: {58, 59, 61, 62, 71, 74, 82, 94, 113, 127, 146, 173, 214, 283, 422, 841 }

  18. 5040

    Returns: {71, 72, 73, 81, 83, 88, 99, 104, 117, 136, 149, 187, 216, 257, 319, 423, 632, 1261 }

  19. 6720

    Returns: {82, 83, 86, 88, 94, 101, 104, 121, 127, 134, 152, 178, 218, 247, 286, 341, 424, 563, 842, 1681 }

  20. 10080

    Returns: {101, 102, 103, 106, 107, 114, 118, 129, 141, 146, 158, 183, 194, 222, 262, 289, 323, 367, 426, 509, 634, 843, 1262, 2521 }

  21. 20160

    Returns: {142, 143, 144, 146, 153, 157, 162, 166, 176, 179, 198, 208, 234, 261, 272, 298, 331, 351, 374, 432, 514, 569, 638, 727, 846, 1013, 1264, 1683, 2522, 5041 }

  22. 30240

    Returns: {174, 177, 178, 183, 186, 191, 194, 213, 222, 229, 246, 251, 282, 298, 307, 339, 381, 398, 438, 519, 554, 642, 766, 849, 953, 1087, 1266, 1517, 1894, 2523, 3782, 7561 }

  23. 40320

    Returns: {201, 202, 204, 206, 212, 214, 223, 228, 236, 258, 269, 282, 292, 316, 323, 347, 366, 388, 444, 501, 524, 578, 646, 687, 734, 852, 1018, 1129, 1268, 1447, 1686, 2021, 2524, 3363, 5042, 10081 }

  24. 60480

    Returns: {246, 247, 248, 249, 258, 264, 269, 282, 286, 303, 312, 326, 334, 363, 381, 402, 418, 456, 467, 534, 568, 587, 654, 741, 776, 858, 961, 1023, 1094, 1272, 1522, 1689, 1898, 2167, 2526, 3029, 3784, 5043, 7562, 15121 }

  25. 80640

    Returns: {284, 286, 288, 292, 297, 306, 314, 324, 332, 352, 358, 379, 383, 396, 416, 468, 493, 522, 544, 596, 611, 662, 702, 748, 864, 981, 1028, 1138, 1276, 1359, 1454, 1692, 2026, 2249, 2528, 2887, 3366, 4037, 5044, 6723, 10082, 20161 }

  26. 92681

    Returns: {46341 }

  27. 93725

    Returns: {369, 465, 1887, 2049, 9375, 46863 }

  28. 94455

    Returns: {1072, 3156, 5252, 9448, 15744, 47228 }

  29. 95665

    Returns: {313, 551, 929, 2527, 9569, 47833 }

  30. 96907

    Returns: {48454 }

  31. 97253

    Returns: {3747, 48627 }

  32. 98221

    Returns: {49111 }

  33. 99099

    Returns: {318, 330, 418, 470, 482, 550, 590, 682, 818, 1290, 1518, 2370, 3818, 4510, 5510, 7082, 16518, 49550 }

  34. 99997

    Returns: {319, 2641, 49999 }

  35. 99999

    Returns: {320, 468, 1240, 5560, 16668, 50000 }

  36. 85171

    Returns: {830, 42586 }

  37. 96740

    Returns: {726, 3462, 4842, 24186 }

  38. 10498

    Returns: { }

  39. 648

    Returns: {27, 33, 57, 83, 163 }

  40. 30765

    Returns: {199, 457, 743, 1033, 2201, 3079, 5129, 15383 }

  41. 13469

    Returns: {6735 }

  42. 24342

    Returns: { }

  43. 1594

    Returns: { }

  44. 6271

    Returns: {3136 }

  45. 22640

    Returns: {303, 576, 1137, 1419, 2832, 5661 }

  46. 7356

    Returns: {616, 1840 }

  47. 64420

    Returns: {3226, 16106 }

  48. 83735

    Returns: {8376, 41868 }

  49. 19855

    Returns: {152, 208, 532, 908, 1988, 9928 }

  50. 31292

    Returns: {7824 }

  51. 948

    Returns: {82, 238 }

  52. 20934

    Returns: { }

  53. 9298

    Returns: { }

  54. 79400

    Returns: {447, 819, 1995, 3975, 9927, 19851 }

  55. 87157

    Returns: {6229, 43579 }

  56. 9006

    Returns: { }

  57. 18143

    Returns: {9072 }

  58. 23916

    Returns: {1996, 5980 }

  59. 94926

    Returns: { }

  60. 98318

    Returns: { }

  61. 16

    Returns: {5 }

  62. 10000

    Returns: {125, 145, 260, 505, 629, 1252, 2501 }

  63. 99994

    Returns: { }

  64. 50000

    Returns: {225, 300, 525, 645, 1260, 2505, 3129, 6252, 12501 }

  65. 93303

    Returns: {772, 2232, 5188, 6668, 15552, 46652 }

  66. 96001

    Returns: {48001 }

  67. 1

    Returns: { }

  68. 2168

    Returns: {273, 543 }

  69. 94005

    Returns: {1067, 3141, 5227, 9403, 15669, 47003 }

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