Statistics

Problem Statement for "SpiralNumbers"

Problem Statement

Consider all positive integers written in the following manner (you can imagine an infinite spiral). 
                 21  22  23  24  25  26
                 20   7   8   9  10 ...
                 19   6   1   2  11 ...
                 18   5   4   3  12 ...
                 17  16  15  14  13 ...
You task is to determine the position (row,column) of a given number N, assuming that the center (number 1) has position (0,0). Rows are numbered from top to bottom, columns are numbered from left to right (for example, number 3 is at (1,1)). Your method should return a string containing the position of N in form (R,C) where R is the row and C is the column. R and C must not contain any leading zeroes.

Definition

Class:
SpiralNumbers
Method:
getPosition
Parameters:
int
Returns:
String
Method signature:
String getPosition(int N)
(be sure your method is public)

Constraints

  • N will be between 1 and 2,147,483,647, inclusive.

Examples

  1. 2

    Returns: "(0,1)"

  2. 3

    Returns: "(1,1)"

  3. 7

    Returns: "(-1,-1)"

  4. 17

    Returns: "(2,-2)"

  5. 24

    Returns: "(-2,1)"

  6. 830

    Returns: "(-14,3)"

  7. 765409

    Returns: "(-437,221)"

  8. 3577

    Returns: "(30,-6)"

  9. 1241

    Returns: "(-2,18)"

  10. 5393

    Returns: "(27,37)"

  11. 9575

    Returns: "(49,-19)"

  12. 6319

    Returns: "(38,40)"

  13. 8738

    Returns: "(42,47)"

  14. 9724

    Returns: "(-49,-28)"

  15. 7803

    Returns: "(-14,-44)"

  16. 1354389

    Returns: "(582,-74)"

  17. 1197879

    Returns: "(-495,-547)"

  18. 1051382

    Returns: "(244,513)"

  19. 1694284

    Returns: "(651,270)"

  20. 1765429

    Returns: "(-664,-148)"

  21. 1746739269

    Returns: "(20065,-20897)"

  22. 1581653398

    Returns: "(19388,-19885)"

  23. 1504049281

    Returns: "(13635,-19391)"

  24. 1335708714

    Returns: "(7231,18274)"

  25. 1988569709

    Returns: "(11763,22297)"

  26. 1089242603

    Returns: "(16502,4912)"

  27. 1643347426

    Returns: "(2288,-20269)"

  28. 1981814007

    Returns: "(22259,16059)"

  29. 1880603329

    Returns: "(21683,-15055)"

  30. 1882376233

    Returns: "(-9543,-21693)"

  31. 2147483638

    Returns: "(-23170,18527)"

  32. 2147483639

    Returns: "(-23170,18528)"

  33. 2147483640

    Returns: "(-23170,18529)"

  34. 2147483641

    Returns: "(-23170,18530)"

  35. 2147483642

    Returns: "(-23170,18531)"

  36. 2147483643

    Returns: "(-23170,18532)"

  37. 2147483644

    Returns: "(-23170,18533)"

  38. 2147483645

    Returns: "(-23170,18534)"

  39. 2147483646

    Returns: "(-23170,18535)"

  40. 2147483647

    Returns: "(-23170,18536)"

  41. 1156340025

    Returns: "(-17002,17002)"

  42. 1247573041

    Returns: "(-17660,17660)"

  43. 647549809

    Returns: "(-12723,12723)"

  44. 667033929

    Returns: "(-12913,12913)"

  45. 968018769

    Returns: "(-15556,15556)"

  46. 3886

    Returns: "(-10,-31)"

  47. 5630

    Returns: "(-33,38)"

  48. 7221

    Returns: "(-42,38)"

  49. 15489

    Returns: "(-50,-62)"

  50. 9983

    Returns: "(50,-32)"

  51. 14712

    Returns: "(10,61)"

  52. 18894

    Returns: "(56,69)"

  53. 11455

    Returns: "(-48,54)"

  54. 18431

    Returns: "(68,-2)"

  55. 18830

    Returns: "(-8,69)"

  56. 3421

    Returns: "(-27,-29)"

  57. 12534

    Returns: "(56,-45)"

  58. 19978

    Returns: "(26,71)"

  59. 1406

    Returns: "(18,19)"

  60. 12831

    Returns: "(5,57)"

  61. 1403228077

    Returns: "(18730,4794)"

  62. 1176144492

    Returns: "(-17147,14614)"

  63. 742077057

    Returns: "(-8645,13621)"

  64. 1487275698

    Returns: "(-2810,19283)"

  65. 1982325633

    Returns: "(5842,22262)"

  66. 1091291954

    Returns: "(-16517,-2754)"

  67. 822976965

    Returns: "(14344,10036)"

  68. 2000000001

    Returns: "(9799,22361)"

  69. 1595633577

    Returns: "(10579,19973)"

  70. 1924141339

    Returns: "(-18819,21933)"

  71. 1723303803

    Returns: "(-20756,-4610)"

  72. 1935569301

    Returns: "(-12722,21998)"

  73. 1752361901

    Returns: "(-2351,20931)"

  74. 1817007465

    Returns: "(-10275,-21313)"

  75. 1927261228

    Returns: "(-21950,-14623)"

  76. 2000000001

    Returns: "(9799,22361)"

  77. 1713054241

    Returns: "(-15775,20695)"

  78. 1424967331

    Returns: "(-18874,-796)"

  79. 1137762248

    Returns: "(-16865,-1248)"

  80. 937619661

    Returns: "(-15310,-10670)"

  81. 1

    Returns: "(0,0)"

  82. 3157729

    Returns: "(-888,888)"

  83. 2147483646

    Returns: "(-23170,18535)"

  84. 999999

    Returns: "(500,-498)"

  85. 2147483647

    Returns: "(-23170,18536)"

  86. 1

    Returns: "(0,0)"

  87. 2147483000

    Returns: "(-23170,17889)"

  88. 2000000000

    Returns: "(9798,22361)"

  89. 3158128

    Returns: "(-490,889)"

  90. 2

    Returns: "(0,1)"

  91. 765409

    Returns: "(-437,221)"

  92. 1000000000

    Returns: "(-15811,1682)"

  93. 10000000

    Returns: "(-174,-1581)"

  94. 2100000000

    Returns: "(22913,-636)"

  95. 9

    Returns: "(-1,1)"

  96. 2147483631

    Returns: "(-23170,18520)"

  97. 2147483640

    Returns: "(-23170,18529)"

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