Problem Statement
Let t be the time between your arrival to the station if you stand still on the escalator and the arrival of the last train before your arrival. Assume that t is a random variable uniformly distributed between 0 and T.
Return the probability of catching an earlier train if you choose to walk down the escalator instead of standing still on it.
Definition
- Class:
- SubwayTrip
- Method:
- earlierTrain
- Parameters:
- int, int, int, int
- Returns:
- double
- Method signature:
- double earlierTrain(int Ve, int Vy, int L, int T)
- (be sure your method is public)
Notes
- The returned value must have an absolute or relative error less than 1e-9.
Constraints
- Ve will be between 10 and 60, inclusive.
- Vy will be between 1 and 10, inclusive.
- L will be between 10 and 100, inclusive.
- T will be between 2 and 20, inclusive.
Examples
10
10
20
2
Returns: 0.5
If you stand still, it'll take you 20/10 = 2 minutes to reach the bottom of the escalator. If you choose to walk, it'll make you 20/(10+10) = 1 minute. In the second case you save 1 minute and in 50% of the cases it'll allow you to catch an earlier train.
50
5
55
20
Returns: 0.005000000000000004
34
3
85
7
Returns: 0.028957528957528934
10
10
100
4
Returns: 1.0
Here, if you choose to walk instead of stand still, you will save 5 minutes and you will certainly be guaranteed to catch an earlier train.
60
10
100
20
Returns: 0.011904761904761906
60
1
10
20
Returns: 1.3661202185792296E-4
48
4
73
15
Returns: 0.007799145299145288
54
9
88
6
Returns: 0.03880070546737213
53
10
41
12
Returns: 0.010232604572227215
34
7
75
3
Returns: 0.1255380200860832
17
10
18
3
Returns: 0.13071895424836602
59
9
31
2
Returns: 0.034770687936191425
41
1
17
18
Returns: 5.484578655310384E-4
44
5
75
3
Returns: 0.05797773654916518
30
6
50
5
Returns: 0.055555555555555566
27
3
67
12
Returns: 0.020679012345679003
48
1
25
7
Returns: 0.001518464528668612
47
8
65
10
Returns: 0.02011605415860735
34
1
84
15
Returns: 0.0047058823529411795
10
8
73
12
Returns: 0.2703703703703704
10
1
97
16
Returns: 0.05511363636363638
32
10
68
7
Returns: 0.07227891156462586
10
8
72
14
Returns: 0.22857142857142862
54
8
31
15
Returns: 0.004938271604938271
34
7
60
9
Returns: 0.03347680535628885
13
2
45
12
Returns: 0.038461538461538484
12
10
56
18
Returns: 0.11784511784511784
52
1
62
8
Returns: 0.0028120464441219297
18
4
48
12
Returns: 0.04040404040404039
60
8
14
14
Returns: 0.00196078431372549
42
8
92
6
Returns: 0.05841269841269839
13
10
19
7
Returns: 0.09077878643096036
49
5
23
11
Returns: 0.003951075379646807
56
6
99
10
Returns: 0.01710829493087557
14
8
64
18
Returns: 0.09235209235209234
15
10
20
4
Returns: 0.13333333333333333
48
6
59
20
Returns: 0.006828703703703703
13
9
14
16
Returns: 0.02753496503496504
44
9
50
14
Returns: 0.013783386424895863
16
10
82
12
Returns: 0.1642628205128205
19
6
24
15
Returns: 0.020210526315789467
27
1
61
14
Returns: 0.0057634164777021915
22
5
72
8
Returns: 0.07575757575757579
14
7
21
17
Returns: 0.029411764705882353
50
2
46
9
Returns: 0.003931623931623929
38
6
13
13
Returns: 0.003588516746411481
60
4
44
18
Returns: 0.0025462962962962956
32
8
29
19
Returns: 0.009539473684210525
21
7
18
9
Returns: 0.023809523809523808
13
5
58
15
Returns: 0.08262108262108266
13
9
95
20
Returns: 0.14947552447552448
48
9
71
19
Returns: 0.012292243767313018
47
2
84
2
Returns: 0.03647416413373865
10
8
50
2
Returns: 1.0
25
8
73
20
Returns: 0.035393939393939394
34
5
48
12
Returns: 0.01508295625942685
24
6
59
16
Returns: 0.03072916666666666
31
3
58
18
Returns: 0.009171410499683742
56
9
44
12
Returns: 0.00906593406593406
42
7
100
15
Returns: 0.02267573696145125
54
7
33
20
Returns: 0.0035063752276866997
12
7
22
4
Returns: 0.16885964912280702
45
4
72
3
Returns: 0.043537414965986454
56
1
82
4
Returns: 0.006422305764411027
41
2
46
2
Returns: 0.02609188882586503
56
4
68
12
Returns: 0.006746031746031742
20
10
100
2
Returns: 0.8333333333333335
10
1
100
2
Returns: 0.4545454545454547
34
3
85
16
Returns: 0.01266891891891891
10
10
100
20
Returns: 0.25
10
9
100
7
Returns: 0.6766917293233083