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Problem Statement for "GuessingNextElement"

Problem Statement

An integer arithmetic progression is a sequence defined by two positive integers, p and q, where p is the first element in the sequence, and all other elements are obtained by adding q to the previous element. For example, if p = 1 and q = 2, the sequence would be: 1, 3, 5, 7, ...

An integer geometric progression is a sequence defined by two positive integers, p and q, where p is the first element in the sequence, and all other elements are obtained by multiplying the previous element by q. For example, if p = 3 and q = 2, the sequence would be: 3, 6, 12, ...

You are given a int[] A, which contains either an integer arithmetic or geometric progression. Determine which one it is and return the next element in the sequence. It is guaranteed that A will uniquely represent either an arithmetic or geometric progression and that result will fit in a 32-bit signed integer.

Definition

Class:
GuessingNextElement
Method:
guess
Parameters:
int[]
Returns:
int
Method signature:
int guess(int[] A)
(be sure your method is public)

Constraints

  • A will contain between 3 and 50 elements, inclusive.
  • Each element of A will be between 1 and 10^6, inclusive.
  • A will be sorted in ascending order.
  • A will uniquely represent either an arithmetic or geometric progression.

Examples

  1. {364,843,1322,1801}

    Returns: 2280

    This sequence represents an arithmetic progression where p = 364 and q = 479. The next element is 1801 + 479 = 2280.

  2. {315,785,1255,1725,2195,2665}

    Returns: 3135

  3. {394,1172,1950,2728,3506,4284,5062,5840}

    Returns: 6618

  4. {944,1073,1202,1331,1460,1589,1718,1847,1976,2105}

    Returns: 2234

  5. {162,549,936,1323,1710,2097,2484,2871,3258,3645,4032,4419}

    Returns: 4806

  6. {165,983,1801,2619,3437,4255,5073,5891,6709,7527,8345,9163,9981,10799}

    Returns: 11617

  7. {467,1309,2151,2993,3835,4677,5519,6361,7203,8045,8887,9729,10571,11413,12255,13097}

    Returns: 13939

  8. {403,415,427,439,451,463,475,487,499,511,523,535,547,559,571,583,595,607}

    Returns: 619

  9. {866,1459,2052,2645,3238,3831,4424,5017,5610,6203,6796,7389,7982,8575,9168,9761,10354,10947,11540,12133}

    Returns: 12726

  10. {480,976,1472,1968,2464,2960,3456,3952,4448,4944,5440,5936,6432,6928,7424,7920,8416,8912,9408,9904,10400,10896}

    Returns: 11392

  11. {716,769,822,875,928,981,1034,1087,1140,1193,1246,1299,1352,1405,1458,1511,1564,1617,1670,1723,1776,1829,1882,1935}

    Returns: 1988

  12. {103,1016,1929,2842,3755,4668,5581,6494,7407,8320,9233,10146,11059,11972,12885,13798,14711,15624,16537,17450,18363,19276,20189,21102,22015,22928}

    Returns: 23841

  13. {470,1260,2050,2840,3630,4420,5210,6000,6790,7580,8370,9160,9950,10740,11530,12320,13110,13900,14690,15480,16270,17060,17850,18640,19430,20220,21010,21800}

    Returns: 22590

  14. {239,377,515,653,791,929,1067,1205,1343,1481,1619,1757,1895,2033,2171,2309,2447,2585,2723,2861,2999,3137,3275,3413,3551,3689,3827,3965,4103,4241}

    Returns: 4379

  15. {346,1055,1764,2473,3182,3891,4600,5309,6018,6727,7436,8145,8854,9563,10272,10981,11690,12399,13108,13817,14526,15235,15944,16653,17362,18071,18780,19489,20198,20907,21616,22325}

    Returns: 23034

  16. {881,1479,2077,2675,3273,3871,4469,5067,5665,6263,6861,7459,8057,8655,9253,9851,10449,11047,11645,12243,12841,13439,14037,14635,15233,15831,16429,17027,17625,18223,18821,19419,20017,20615}

    Returns: 21213

  17. {140,994,1848,2702,3556,4410,5264,6118,6972,7826,8680,9534,10388,11242,12096,12950,13804,14658,15512,16366,17220,18074,18928,19782,20636,21490,22344,23198,24052,24906,25760,26614,27468,28322,29176,30030}

    Returns: 30884

  18. {820,956,1092,1228,1364,1500,1636,1772,1908,2044,2180,2316,2452,2588,2724,2860,2996,3132,3268,3404,3540,3676,3812,3948,4084,4220,4356,4492,4628,4764,4900,5036,5172,5308,5444,5580,5716,5852}

    Returns: 5988

  19. {838,900,962,1024,1086,1148,1210,1272,1334,1396,1458,1520,1582,1644,1706,1768,1830,1892,1954,2016,2078,2140,2202,2264,2326,2388,2450,2512,2574,2636,2698,2760,2822,2884,2946,3008,3070,3132,3194,3256}

    Returns: 3318

  20. {179,608,1037,1466,1895,2324,2753,3182,3611,4040,4469,4898,5327,5756,6185,6614,7043,7472,7901,8330,8759,9188,9617,10046,10475,10904,11333,11762,12191,12620,13049,13478,13907,14336,14765,15194,15623,16052,16481,16910,17339,17768}

    Returns: 18197

  21. {890,1352,1814,2276,2738,3200,3662,4124,4586,5048,5510,5972,6434,6896,7358,7820,8282,8744,9206,9668,10130,10592,11054,11516,11978,12440,12902,13364,13826,14288,14750,15212,15674,16136,16598,17060,17522,17984,18446,18908,19370,19832,20294,20756}

    Returns: 21218

  22. {530,721,912,1103,1294,1485,1676,1867,2058,2249,2440,2631,2822,3013,3204,3395,3586,3777,3968,4159,4350,4541,4732,4923,5114,5305,5496,5687,5878,6069,6260,6451,6642,6833,7024,7215,7406,7597,7788,7979,8170,8361,8552,8743,8934,9125}

    Returns: 9316

  23. {166,391,616,841,1066,1291,1516,1741,1966,2191,2416,2641,2866,3091,3316,3541,3766,3991,4216,4441,4666,4891,5116,5341,5566,5791,6016,6241,6466,6691,6916,7141,7366,7591,7816,8041,8266,8491,8716,8941,9166,9391,9616,9841,10066,10291,10516,10741}

    Returns: 10966

  24. {973,1161,1349,1537,1725,1913,2101,2289,2477,2665,2853,3041,3229,3417,3605,3793,3981,4169,4357,4545,4733,4921,5109,5297,5485,5673,5861,6049,6237,6425,6613,6801,6989,7177,7365,7553,7741,7929,8117,8305,8493,8681,8869,9057,9245,9433,9621,9809,9997,10185}

    Returns: 10373

  25. {30,60,120,240,480,960,1920,3840,7680,15360,30720,61440,122880,245760,491520}

    Returns: 983040

  26. {33,231,1617,11319,79233}

    Returns: 554631

    This

  27. {9,18,36,72,144,288,576,1152,2304,4608,9216,18432,36864,73728,147456,294912}

    Returns: 589824

  28. {13,117,1053,9477,85293}

    Returns: 767637

    This sequence represents a geometric progression where p = 13 and q = 9. The next element is 85293 * 9 = 76737.

  29. {17,34,68,136,272,544,1088,2176,4352,8704,17408,34816,69632,139264,278528}

    Returns: 557056

  30. {11,22,44,88,176,352,704,1408,2816,5632,11264,22528,45056,90112,180224,360448}

    Returns: 720896

  31. {4,16,64,256,1024,4096,16384,65536}

    Returns: 262144

  32. {33,132,528,2112,8448,33792,135168}

    Returns: 540672

  33. {27,54,108,216,432,864,1728,3456,6912,13824,27648,55296,110592,221184,442368}

    Returns: 884736

  34. {3,15,75,375,1875,9375,46875}

    Returns: 234375

  35. {15,30,60,120,240,480,960,1920,3840,7680,15360,30720,61440,122880,245760,491520}

    Returns: 983040

  36. {27,54,108,216,432,864,1728,3456,6912,13824,27648,55296,110592,221184,442368}

    Returns: 884736

  37. {21,42,84,168,336,672,1344,2688,5376,10752,21504,43008,86016,172032,344064}

    Returns: 688128

  38. {22,220,2200,22000}

    Returns: 220000

  39. {27,54,108,216,432,864,1728,3456,6912,13824,27648,55296,110592,221184,442368}

    Returns: 884736

  40. {10,20,40,80,160,320,640,1280,2560,5120,10240,20480,40960,81920,163840,327680}

    Returns: 655360

  41. {12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49152,98304,196608,393216}

    Returns: 786432

  42. {35,245,1715,12005,84035}

    Returns: 588245

  43. {5,10,20,40,80,160,320,640,1280,2560,5120,10240,20480,40960,81920,163840,327680}

    Returns: 655360

  44. {28,56,112,224,448,896,1792,3584,7168,14336,28672,57344,114688,229376,458752}

    Returns: 917504

  45. {1,1000,1000000}

    Returns: 1000000000

  46. {250000, 500000, 1000000}

    Returns: 2000000

  47. {250000, 500000, 1000000 }

    Returns: 2000000

  48. {2, 3, 4 }

    Returns: 5

  49. {3, 4, 5 }

    Returns: 6

  50. {4, 6, 8 }

    Returns: 10

  51. {2, 4, 6 }

    Returns: 8

  52. {1, 2, 4 }

    Returns: 8

  53. {10000, 100000, 1000000 }

    Returns: 10000000

  54. {1, 5, 9, 13 }

    Returns: 17

  55. {100000, 200000, 400000 }

    Returns: 800000

  56. {2, 3, 4, 5 }

    Returns: 6

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