Problem Statement
Little John has one standard die with numbers one to six on its sides. Each time he throws the die, he gets as many candies from his mom as the number on the top of the die. Johnâs goal is to collect at least candies candies. Then he will eat them all and became a little fat boy.
Return the expected number of throws needed for John to achieve his goal.
Definition
- Class:
- TheDiceGame
- Method:
- expectedThrows
- Parameters:
- int
- Returns:
- double
- Method signature:
- double expectedThrows(int candies)
- (be sure your method is public)
Notes
- The returned value must be accurate to within a relative or absolute value of 1E-9.
Constraints
- candies will be between 1 and 1000000, inclusive.
Examples
1
Returns: 1.0
John needs only one throw to get at least one candy.
2
Returns: 1.1666666666666667
After the first throw, there is a probability of 1/6 that John will need an additional throw.
7
Returns: 2.5216263717421126
47
Returns: 13.90476189046144
9
Returns: 3.0433247837600974
6
Returns: 2.1613940329218106
8
Returns: 2.7752307670324643
3
Returns: 1.3611111111111112
4
Returns: 1.587962962962963
5
Returns: 1.8526234567901234
17
Returns: 5.33319373864191
20
Returns: 6.190195198987439
36
Returns: 10.761904997432147
34
Returns: 10.190480976827903
18
Returns: 5.619895663375334
35
Returns: 10.476194803681265
37
Returns: 11.0476167312735
21
Returns: 6.475816279139172
30
Returns: 9.047634594384022
22
Returns: 6.761784262898289
97
Returns: 28.190476190476154
50
Returns: 14.761904780325601
56
Returns: 16.476190482101313
74
Returns: 21.619047619049557
68
Returns: 19.904761904864905
75
Returns: 21.904761904746998
87
Returns: 25.333333333333048
51
Returns: 15.047619080389286
90
Returns: 26.190476190476236
72
Returns: 21.047619047648613
1147
Returns: 328.1904761904732
1000
Returns: 286.19047619047393
1356
Returns: 387.9047619047577
1124
Returns: 321.61904761904475
1368
Returns: 391.3333333333291
1225
Returns: 350.47619047618707
1387
Returns: 396.7619047619004
1851
Returns: 529.3333333333255
1290
Returns: 369.0476190476153
1572
Returns: 449.619047619042
157147
Returns: 44899.619047563094
151000
Returns: 43143.33333328167
113356
Returns: 32387.90476187565
171124
Returns: 48893.04761898127
198368
Returns: 56677.04761895846
167225
Returns: 47779.04761898426
149387
Returns: 42682.47619042562
190851
Returns: 54529.333333250805
166290
Returns: 47511.90476184211
139572
Returns: 39878.19047614634
757148
Returns: 216328.47618917728
851001
Returns: 243143.61904597818
413357
Returns: 118102.47619008906
971125
Returns: 277464.7619026251
598369
Returns: 170963.04761823636
567226
Returns: 162065.0476183186
749388
Returns: 214111.33333206092
890852
Returns: 254529.6190458209
766291
Returns: 218940.76190343144
239573
Returns: 68449.90476177471
957147
Returns: 273471.0476169719
951000
Returns: 271714.76190271275
913356
Returns: 260959.3333314432
971124
Returns: 277464.4761883394
998368
Returns: 285248.4761882178
967225
Returns: 276350.4761883565
949387
Returns: 271253.9047598626
990851
Returns: 283100.76190253743
966290
Returns: 276083.33333121776
939572
Returns: 268449.61904561886
999996
Returns: 285713.6190453533
999999
Returns: 285714.4761882104
999992
Returns: 285712.4761882105
999996
Returns: 285713.6190453533
999990
Returns: 285711.90475963906
999999
Returns: 285714.4761882104
1000000
Returns: 285714.76190249616
999998
Returns: 285714.19047392474
2005
Returns: 573.3333333333243
101
Returns: 29.33333333333331