Statistics

Problem Statement for "NumericalPerfectionLevel"

Problem Statement

It is a well known fact that of all numbers, the number 4 is the most relevant. Patterns related to the number 4 tend to appear everywhere. For example, the numerical perfection level is closely related to the number 4.

We define the perfection level of a positive integer N as k if N can be expressed as a product of 4 positive integers, each with a perfection level of at least (k-1), and cannot be expressed as a product of 4 positive integers, each with a perfection level greater than (k-1). There is one exception - if it is not possible to express N as a product of 4 positive integers all greater than 1, then the perfection level of N is 0.

Given a long N, return its perfection level.

Definition

Class:
NumericalPerfectionLevel
Method:
getLevel
Parameters:
long
Returns:
int
Method signature:
int getLevel(long N)
(be sure your method is public)

Constraints

  • N will be between 1 and 10000000000000 (10^13), inclusive.

Examples

  1. 4

    Returns: 0

    4 cannot be expressed as a product of 4 numbers all greater than 1.

  2. 144

    Returns: 1

    144 = 4 x 2 x 3 x 6 The level of 4, 2, 3 and 6 is 0.

  3. 1152

    Returns: 1

    One of many possible ways to express 1152 is: 1152 = 144 x 2 x 2 x 2 Although 144's level is 1, the remaining factors are of level 0. There is no way to express 1152 as a product of four level 1 numbers.

  4. 1679616

    Returns: 2

    1679616 = 36 x 36 x 36 x 36 36 = 2 x 2 x 3 x 3

  5. 10000000000000

    Returns: 2

  6. 8796093022208

    Returns: 2

  7. 1000000000007

    Returns: 0

  8. 1

    Returns: 0

  9. 1007775439343

    Returns: 1

  10. 1009736591189

    Returns: 0

  11. 2019473182378

    Returns: 1

  12. 17

    Returns: 0

  13. 57

    Returns: 0

  14. 5957

    Returns: 0

  15. 40774

    Returns: 1

  16. 444106

    Returns: 1

  17. 4877778487

    Returns: 1

  18. 2491516469

    Returns: 1

  19. 554478834

    Returns: 1

  20. 23523850714

    Returns: 1

  21. 89103499485

    Returns: 1

  22. 178684774840

    Returns: 1

  23. 9464190333780

    Returns: 1

  24. 5949464087160

    Returns: 1

  25. 4975943064400

    Returns: 1

  26. 718180362900

    Returns: 1

  27. 3774082099392

    Returns: 2

  28. 8659677826800

    Returns: 2

  29. 7917813342000

    Returns: 2

  30. 23

    Returns: 0

  31. 93

    Returns: 0

  32. 8323

    Returns: 0

  33. 4730

    Returns: 1

  34. 4532759

    Returns: 1

  35. 201471845

    Returns: 1

  36. 181554042

    Returns: 1

  37. 49489219945

    Returns: 1

  38. 2001764380

    Returns: 1

  39. 949426512018

    Returns: 1

  40. 571070068660

    Returns: 1

  41. 8210495475105

    Returns: 1

  42. 4591061150676

    Returns: 1

  43. 8139395904120

    Returns: 1

  44. 7231220651424

    Returns: 1

  45. 9122522159520

    Returns: 2

  46. 7365609066816

    Returns: 2

  47. 9936164937600

    Returns: 2

  48. 47

    Returns: 0

  49. 215

    Returns: 0

  50. 962

    Returns: 0

  51. 379045

    Returns: 1

  52. 5082729

    Returns: 1

  53. 14436142

    Returns: 1

  54. 1311380

    Returns: 1

  55. 11426610013

    Returns: 1

  56. 8505135980

    Returns: 1

  57. 447853848442

    Returns: 1

  58. 274827402850

    Returns: 1

  59. 1870004815140

    Returns: 1

  60. 6448953074850

    Returns: 1

  61. 7121731973400

    Returns: 1

  62. 6038536904400

    Returns: 1

  63. 7196218110900

    Returns: 2

  64. 8791495823880

    Returns: 2

  65. 1926900360000

    Returns: 2

  66. 5990626026000

    Returns: 2

  67. 9189227250000

    Returns: 2

  68. 722909214720

    Returns: 2

  69. 8050579891200

    Returns: 2

  70. 9220780800000

    Returns: 2

  71. 2823864120000

    Returns: 2

  72. 3630682440000

    Returns: 2

  73. 848730960000

    Returns: 2

  74. 8334900000000

    Returns: 2

  75. 8298702720000

    Returns: 2

  76. 502020288000

    Returns: 2

  77. 4482709257600

    Returns: 2

  78. 7530304320000

    Returns: 2

  79. 9780613920000

    Returns: 2

  80. 7068445655040

    Returns: 2

  81. 8591001471360

    Returns: 2

  82. 7889695228800

    Returns: 2

  83. 9372001605120

    Returns: 2

  84. 3327025363200

    Returns: 2

  85. 7650613555200

    Returns: 2

  86. 8973612648000

    Returns: 2

  87. 8136826790400

    Returns: 2

  88. 8715753446400

    Returns: 2

  89. 7819156800000

    Returns: 2

  90. 3751491744000

    Returns: 2

  91. 9097288200000

    Returns: 2

  92. 775797834240

    Returns: 2

  93. 9117282240000

    Returns: 2

  94. 8301338136000

    Returns: 2

  95. 6304359600000

    Returns: 2

  96. 999999999112

    Returns: 1

    Times out if i is int and not long.

  97. 9999995824729

    Returns: 0

  98. 9971252437441

    Returns: 1

    Large 4th power of a prime.

  99. 9999999999001

    Returns: 0

    large prime #1

  100. 9999999999007

    Returns: 0

    large prime #2

  101. 9999999999023

    Returns: 0

    large prime #3

  102. 9999999999049

    Returns: 0

    large prime #4

  103. 9999999999053

    Returns: 0

    large prime #5

  104. 9998250324001

    Returns: 0

    square of large prime #1

  105. 9998313564121

    Returns: 0

    square of large prime #2

  106. 9998503285681

    Returns: 0

    square of large prime #3

  107. 9998617119481

    Returns: 0

    square of large prime #4

  108. 9998667712489

    Returns: 0

    square of large prime #5

  109. 4444444444452

    Returns: 1

  110. 6666666666606

    Returns: 1

  111. 4444444443948

    Returns: 1

  112. 9999999998721

    Returns: 1

  113. 6666666665634

    Returns: 1

  114. 2

    Returns: 0

  115. 3

    Returns: 0

  116. 4

    Returns: 0

  117. 5

    Returns: 0

  118. 6

    Returns: 0

  119. 7

    Returns: 0

  120. 8

    Returns: 0

  121. 9

    Returns: 0

  122. 10

    Returns: 0

  123. 11

    Returns: 0

  124. 12

    Returns: 0

  125. 13

    Returns: 0

  126. 14

    Returns: 0

  127. 15

    Returns: 0

  128. 65536

    Returns: 2

  129. 9999999999999

    Returns: 1

  130. 9876543211237

    Returns: 0

  131. 982451653

    Returns: 0

  132. 999999789103

    Returns: 1

  133. 310042951680

    Returns: 2

  134. 90000767

    Returns: 0

  135. 3446363

    Returns: 0

  136. 671908516352

    Returns: 1

  137. 999999937

    Returns: 0

  138. 1000000000021

    Returns: 1

  139. 9999999999998

    Returns: 0

  140. 8398085878656

    Returns: 2

  141. 610351562500

    Returns: 2

  142. 3448

    Returns: 1

  143. 999999999998

    Returns: 0

  144. 99999999999

    Returns: 1

  145. 1360488960000

    Returns: 2

  146. 10000000000

    Returns: 2

  147. 9999989912199

    Returns: 1

  148. 9213813787357

    Returns: 0

  149. 999999999989

    Returns: 0

  150. 1000000009651

    Returns: 0

  151. 200560490131

    Returns: 0

  152. 9999999991296

    Returns: 2

  153. 761838257287

    Returns: 0

  154. 9932683502149

    Returns: 0

  155. 999999999999

    Returns: 1

  156. 457245678426

    Returns: 1

  157. 1000000007

    Returns: 0

  158. 81

    Returns: 1

  159. 1002500000021

    Returns: 0

  160. 9999999999971

    Returns: 0

  161. 88888888888

    Returns: 1

  162. 35761

    Returns: 0

  163. 136

    Returns: 1

  164. 6400000007

    Returns: 0

  165. 9000009900000

    Returns: 2

  166. 61917364224

    Returns: 2

  167. 274986211500

    Returns: 2

  168. 1073676287

    Returns: 0

  169. 1000000000074

    Returns: 1

  170. 4757441361998

    Returns: 1

  171. 9999900956644

    Returns: 1

  172. 1000009923050

    Returns: 1

  173. 37947324

    Returns: 1

  174. 17179869176

    Returns: 1

  175. 1615568114160

    Returns: 2

  176. 2821109907456

    Returns: 2

  177. 1777777777

    Returns: 0

  178. 68718952447

    Returns: 0

  179. 327680622592

    Returns: 2

  180. 492876847

    Returns: 0

  181. 1777777777777

    Returns: 0

  182. 24

    Returns: 1

  183. 1009846546000

    Returns: 1

  184. 8000000056

    Returns: 1

  185. 2818572288098

    Returns: 0

  186. 8989898989898

    Returns: 0

  187. 10000000

    Returns: 1

  188. 2345671234567

    Returns: 0

  189. 1000034500000

    Returns: 1

  190. 1239846546000

    Returns: 1

  191. 1726272

    Returns: 1

  192. 1099511627776

    Returns: 2

  193. 162

    Returns: 1

  194. 279841

    Returns: 1

  195. 10000000019

    Returns: 0

  196. 10000000103

    Returns: 0

  197. 4294967295

    Returns: 1

  198. 1079916250001

    Returns: 0

  199. 100000000003

    Returns: 0

  200. 1000025469874

    Returns: 0

  201. 32768

    Returns: 1

  202. 2936606468492

    Returns: 1

  203. 9090900000000

    Returns: 2

  204. 4294967296000

    Returns: 2

  205. 9989898989898

    Returns: 1

  206. 9999978364928

    Returns: 2

  207. 64072

    Returns: 1

  208. 212838126

    Returns: 1

  209. 85662167761

    Returns: 1

  210. 210

    Returns: 1

  211. 9000006000001

    Returns: 1

  212. 2147483647

    Returns: 0

  213. 1723681762

    Returns: 0

  214. 1000000000039

    Returns: 0

  215. 152

    Returns: 1

  216. 36

    Returns: 1

  217. 56

    Returns: 1

  218. 424

    Returns: 1

  219. 558

    Returns: 1

  220. 10000000007

    Returns: 0

  221. 8589410296

    Returns: 1

  222. 25600024

    Returns: 1

  223. 80018

    Returns: 0

  224. 10016959

    Returns: 0

  225. 549751619576

    Returns: 1

  226. 6352552888882

    Returns: 1

  227. 16796169999

    Returns: 1

  228. 1435397384

    Returns: 1

  229. 4294967296

    Returns: 2

  230. 39999992

    Returns: 1

  231. 43046721

    Returns: 2

  232. 19940

    Returns: 1

  233. 9999

    Returns: 1

  234. 1000000020001

    Returns: 0

  235. 808

    Returns: 1

  236. 9999990900000

    Returns: 1

  237. 190742528

    Returns: 2

  238. 100236488000

    Returns: 1

  239. 29737131

    Returns: 1

  240. 999999999997

    Returns: 0

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