TopCoder Statistics - Problem Statement

Problem Statement

Prince Gogo is the charming prince of the Kingdom of Ducks, where slimes and ducks live in peace and harmony.

Today, Prince Gogo purchased N toastbooks, numbered 0 through N-1. Each toastbook contains some knowledge and grants it to the person who eats it. It is known that no two toastbooks contain the same knowledge.

Initially, Gogo doesn't know any of the knowledge inside the toastbooks. He intends to eat them all and gain as many pieces of knowledge as possible. Furthermore, some of the books require a specific piece of knowledge in order to understand its knowledge. This will be given as a int[] prerequisite. If there is no required knowledge to understand the toastbook number i, prerequisite[i] will be -1. Otherwise, prerequisite[i] will be the number of the toastbook that contains the knowledge necessary to understand book i. If Gogo eats some book x without having the required knowledge, he will not gain the knowledge inside the book, even if he later gains the knowledge from the book prerequisite[x].

Unfortunately, Gogo forgot to number the toastbooks when he purchased them. Hence, he is forced to eat all N toastbooks in a random order. Return the expected number of toastbooks that Gogo will understand.

Definition

Class:: PrinceXToastbook
Method:: eat
Parameters:: int[]
Returns:: double
Method signature:: double eat(int[] prerequisite)
(be sure your method is public)

Notes

The expected value of a random variable can be imagined as the average value of very many independent experiments.
The returned value must have an absolute or relative error less than 10^-9.

Constraints

prerequisite will contain between 2 and 50 elements, inclusive.
Each element of prerequisite will be between -1 and N-1, inclusive, where N is the number of elements in prerequisite.
For all i, prerequisite[i] will not be i.

Examples

{-1, 0}

Returns: 1.5

There are only two possible orders. If Gogo eats book 0 first, he gains the knowledge in both books. If Gogo eats book 1 first, he lacks the required knowledge to understand the book 1 when he read it. Hence, he will only gain the knowledge in book 0. Therefore, the expected number of books that Gogo will understand is the average of the two, which is 1.5.
{-1, 0, 1}

Returns: 1.6666666666666667

There are 6 possible orders. The number of books understood is as follows: 0, 1, 2: 3 0, 2, 1: 2 1, 0, 2: 1 1, 2, 0: 1 2, 0, 1: 2 2, 1, 0: 1 Hence, the expected number of books that Gogo will understand is their average, which is (3+2+1+1+2+1)/6 = 10/6.
{1, -1, 1}

Returns: 2.0
{1, 0}

Returns: 0.0

Each book has the other book as a prerequisite. Gogo will not be able to understand either one, regardless of the order in which he eats them.
{-1, -1}

Returns: 2.0
{1,-1}

Returns: 1.5
{1,2,0}

Returns: 0.0
{7,5,5,7,2,3,4,1}

Returns: 0.0
{-1,19,5,11,3,7,16,0,11,-1,15,3,4,6,12,23,11,13,20,8,12,5,14,14}

Returns: 2.75
{30,40,20,15,25,46,45,10,6,21,29,45,-1,18,39,45,22,22,17,36,33,23,9,44,4,28,32,22,47,3,33,41,47,3,19,1,31,27,44,44,1,35,12,28,40,39,27,8}

Returns: 1.5
{16,8,7,7,11,21,0,34,33,5,9,19,32,5,32,11,13,15,6,28,5,29,13,12,13,9,44,2,41,3,39,41,37,14,41,21,11,29,13,22,10,3,28,28,41,23,37,19,40}

Returns: 0.0
{6,41,5,27,36,7,0,35,41,49,38,26,9,44,-1,10,45,33,29,1,30,32,21,4,37,10,34,12,33,35,20,17,25,0,45,39,20,13,0,11,47,46,1,41,4,20,39,9,11,39}

Returns: 1.0
{16,2,33,1,18,42,32,27,47,13,31,42,27,15,29,5,22,46,27,5,36,37,4,6,27,34,-1,32,11,37,37,46,8,7,44,5,14,10,0,9,47,43,26,26,5,38,33,21,29,46}

Returns: 2.7279761904761908
{40,24,1,28,30,47,22,49,5,41,12,-1,43,34,8,10,33,29,49,32,4,36,33,44,13,36,12,7,27,35,26,20,16,15,33,9,-1,26,9,41,35,27,1,15,30,19,49,16,33,33}

Returns: 3.0
{5,5,5,5,5,-1,5}

Returns: 4.0
{6,0,1,2,3,4,5}

Returns: 0.0
{6,0,-1,2,3,4,5}

Returns: 1.7182539682539684
{4,2,-1,-1,3,6,1}

Returns: 3.3749999999999996
{-1,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 7.0
{1,2,3,4,5,6,7,8,9,10,11,12,0}

Returns: 0.0
{1,2,3,4,-1,6,7,8,9,10,11,12,0}

Returns: 1.7182818284467591
{3,2,-1,-1,-1,-1,10,4,-1,5,-1,-1,8}

Returns: 10.0
{24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,-1}

Returns: 13.0
{24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23}

Returns: 0.0
{24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,-1,15,16,17,18,19,20,21,22,23}

Returns: 1.7182818284590455
{-1,-1,10,-1,-1,-1,-1,-1,11,-1,-1,-1,-1,-1,-1,-1,20,20,-1,0,-1,-1,-1,-1,19}

Returns: 21.666666666666668
{29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,-1,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29}

Returns: 25.0
{48,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}

Returns: 0.0
{48,0,1,2,3,4,-1,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}

Returns: 1.7182818284590455
{-1,-1,44,0,7,37,1,-1,34,-1,9,-1,-1,10,32,7,-1,-1,30,-1,-1,-1,16,-1,34,8,28,29,46,30,-1,12,11,32,-1,1,39,-1,-1,-1,-1,19,33,34,20,37,-1,30,40}

Returns: 31.20833333333334
{40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,-1,40,40,40,40,40,40,40,40,40}

Returns: 25.5
{49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{49,0,1,-1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 1.7182818284590455
{-1,43,6,19,0,47,-1,11,-1,35,30,32,31,21,44,19,46,2,-1,-1,39,-1,30,35,5,4,11,29,35,4,34,13,18,15,2,-1,13,21,35,16,32,40,19,2,8,2,19,35,21,31}

Returns: 17.774999999999995
{7,7,7,7,7,7,7,-1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}

Returns: 25.5
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1,49,0}

Returns: 1.718281828459045
{18,-1,14,19,34,13,1,-1,-1,48,-1,45,-1,-1,-1,6,8,44,-1,-1,-1,25,7,7,-1,-1,40,20,29,-1,44,16,-1,34,-1,-1,-1,6,18,24,-1,-1,43,-1,-1,12,24,41,-1,29}

Returns: 34.66666666666667
{48,5,4,35,43,11,17,16,17,7,6,20,10,43,20,5,49,16,27,23,43,25,11,37,25,4,14,28,20,42,15,16,16,28,49,49,18,13,37,22,46,5,14,-1,27,3,13,21,5,43}

Returns: 5.455753968253968
{20,-1,1,49,19,4,22,29,6,42,49,16,16,49,46,5,1,12,49,9,1,22,41,17,13,41,19,25,1,3,38,37,18,43,1,9,1,3,37,6,13,13,1,34,16,24,22,35,38,-1}

Returns: 10.005753968253972
{20,-1,20,12,32,-1,32,25,39,39,5,1,-1,29,47,44,20,10,12,3,48,15,4,-1,3,28,23,1,1,5,39,32,1,14,9,9,23,3,25,23,45,12,13,39,3,32,47,10,12,6}

Returns: 13.933333333333326
{23,34,12,4,-1,-1,22,42,27,3,5,35,-1,45,19,-1,41,39,26,42,34,43,34,34,8,17,8,-1,13,8,27,41,30,19,-1,15,19,23,29,2,15,-1,5,4,0,-1,43,41,40,1}

Returns: 19.63333333333333
{20,30,6,39,-1,47,-1,31,20,38,22,-1,3,18,35,-1,-1,49,-1,37,-1,3,16,-1,23,11,18,30,-1,30,-1,-1,39,42,31,-1,-1,-1,39,-1,25,31,37,10,49,48,6,11,11,-1}

Returns: 29.875000000000007
{-1,34,40,4,-1,-1,-1,22,-1,-1,-1,-1,-1,-1,-1,25,-1,-1,-1,26,44,6,-1,30,-1,-1,-1,-1,-1,47,-1,8,-1,-1,46,14,-1,-1,-1,16,-1,-1,-1,2,-1,42,-1,-1,32,17}

Returns: 40.333333333333336
{-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,33,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,-1,-1,-1,-1,-1}

Returns: 49.0
{-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

Returns: 49.5
{-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

Returns: 50.0
{-1,0,-1,2,-1,4,-1,6,-1,8,-1,10,-1,12,-1,14,-1,16,-1,18,-1,20,-1,22,-1,24,-1,26,-1,28,-1,30,-1,32,-1,34,-1,36,-1,38,-1,40,-1,42,-1,44,-1,46,-1,48}

Returns: 37.5
{-1,0,1,-1,3,4,-1,6,7,-1,9,10,-1,12,13,-1,15,16,-1,18,19,-1,21,22,-1,24,25,-1,27,28,-1,30,31,-1,33,34,-1,36,37,-1,39,40,-1,42,43,-1,45,46,-1,48}

Returns: 28.166666666666675
{-1,0,1,2,-1,4,5,6,-1,8,9,10,-1,12,13,14,-1,16,17,18,-1,20,21,22,-1,24,25,26,-1,28,29,30,-1,32,33,34,-1,36,37,38,-1,40,41,42,-1,44,45,46,-1,48}

Returns: 22.0
{-1,0,1,2,3,-1,5,6,7,8,-1,10,11,12,13,-1,15,16,17,18,-1,20,21,22,23,-1,25,26,27,28,-1,30,31,32,33,-1,35,36,37,38,-1,40,41,42,43,-1,45,46,47,48}

Returns: 17.166666666666664
{-1,0,1,2,3,4,-1,6,7,8,9,10,-1,12,13,14,15,16,-1,18,19,20,21,22,-1,24,25,26,27,28,-1,30,31,32,33,34,-1,36,37,38,39,40,-1,42,43,44,45,46,-1,48}

Returns: 15.244444444444438
{-1,0,1,2,3,4,5,-1,7,8,9,10,11,12,-1,14,15,16,17,18,19,-1,21,22,23,24,25,26,-1,28,29,30,31,32,33,-1,35,36,37,38,39,40,-1,42,43,44,45,46,47,-1}

Returns: 13.027777777777775
{-1,0,1,2,3,4,5,6,-1,8,9,10,11,12,13,14,-1,16,17,18,19,20,21,22,-1,24,25,26,27,28,29,30,-1,32,33,34,35,36,37,38,-1,40,41,42,43,44,45,46,-1,48}

Returns: 11.809672619047618
{-1,0,1,2,3,4,5,6,7,-1,9,10,11,12,13,14,15,16,-1,18,19,20,21,22,23,24,25,-1,27,28,29,30,31,32,33,34,-1,36,37,38,39,40,41,42,43,-1,45,46,47,48}

Returns: 10.308074294532625
{-1,0,1,2,3,4,5,6,7,8,-1,10,11,12,13,14,15,16,17,18,-1,20,21,22,23,24,25,26,27,28,-1,30,31,32,33,34,35,36,37,38,-1,40,41,42,43,44,45,46,47,48}

Returns: 8.591409005731922
{-1,0,1,2,3,4,5,6,7,8,9,-1,11,12,13,14,15,16,17,18,19,20,-1,22,23,24,25,26,27,28,29,30,31,-1,33,34,35,36,37,38,39,40,41,42,-1,44,45,46,47,48}

Returns: 8.591182860349525
{-1,0,1,2,3,4,5,6,7,8,9,10,-1,12,13,14,15,16,17,18,19,20,21,22,-1,24,25,26,27,28,29,30,31,32,33,34,-1,36,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 8.373127313144675
{-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,-1,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 3.436563656918091
{-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 1.7182818284590455
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0}

Returns: 0.0
{49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,0,-1}

Returns: 1.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,0,-1,48}

Returns: 1.5
{1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,21,20,23,22,25,24,27,26,29,28,31,30,33,32,35,34,37,36,39,38,41,40,43,42,45,44,47,46,49,48}

Returns: 0.0
{1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,21,20,23,22,25,-1,27,26,29,28,31,30,33,32,35,34,37,36,39,38,41,40,43,42,45,44,47,46,49,48}

Returns: 1.5
{1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,-1,17,16,19,-1,21,20,23,22,25,-1,27,26,29,28,31,30,33,32,35,34,-1,36,39,38,41,40,-1,-1,-1,44,47,46,49,48}

Returns: 9.5
{1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{2,0,1,5,3,4,8,6,7,11,9,10,14,12,13,17,15,16,20,18,19,23,21,22,26,24,25,29,27,28,32,30,31,35,33,34,38,36,37,41,39,40,44,42,43,47,45,46,-1,48}

Returns: 1.5
{2,0,1,5,3,4,8,6,7,11,9,10,14,12,13,17,15,16,20,18,19,23,21,22,26,24,25,29,27,28,32,30,31,35,33,34,38,36,37,-1,39,40,44,42,43,47,45,46,-1,48}

Returns: 3.166666666666667
{2,0,1,5,3,4,8,6,7,11,-1,-1,-1,12,-1,17,15,16,20,18,19,23,21,22,26,24,25,29,27,-1,32,30,31,35,33,-1,38,36,37,-1,39,40,44,42,43,47,45,46,-1,48}

Returns: 11.5
{1,2,0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{3,0,1,2,7,4,5,6,11,8,9,10,15,12,13,14,19,16,17,18,23,20,21,22,27,24,25,26,31,28,29,30,35,32,33,34,39,36,37,38,43,40,41,42,47,44,45,46,-1,48}

Returns: 1.5
{3,0,1,2,7,4,5,6,11,8,-1,10,15,12,13,14,19,16,17,18,23,20,21,22,27,24,25,26,31,28,29,30,35,32,33,34,39,36,37,38,43,40,41,42,47,44,45,46,-1,48}

Returns: 3.208333333333333
{3,0,1,2,-1,4,5,6,11,8,-1,10,15,12,-1,14,19,16,-1,18,23,20,21,22,27,24,25,26,31,28,29,30,35,32,33,34,-1,36,37,38,43,40,41,42,47,44,45,46,-1,48}

Returns: 10.041666666666666
{1,2,3,0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{4,0,1,2,3,9,5,6,7,8,14,10,11,12,13,19,15,16,17,18,24,20,21,22,23,29,25,26,27,28,34,30,31,32,33,39,35,36,37,38,44,40,41,42,43,49,45,46,47,48}

Returns: 0.0
{4,0,1,2,3,9,5,6,7,8,14,10,11,12,13,19,15,16,17,18,24,20,21,22,23,29,25,26,27,28,34,30,31,32,33,39,35,36,37,38,44,-1,41,42,43,49,45,46,47,48}

Returns: 1.7166666666666668
{4,0,1,2,3,9,5,6,7,8,14,10,11,12,13,19,15,-1,17,18,24,-1,21,22,-1,29,25,26,-1,28,34,30,31,32,33,39,35,36,-1,38,44,-1,-1,42,43,49,45,46,47,48}

Returns: 11.025
{1,2,3,4,0,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,0,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{6,0,1,2,3,4,5,13,7,8,9,10,11,12,20,14,15,16,17,18,19,27,21,22,23,24,25,26,34,28,29,30,31,32,33,41,35,36,37,38,39,40,48,42,43,44,45,46,47,-1}

Returns: 1.0
{6,0,1,2,3,4,5,13,7,8,9,10,11,12,20,14,15,16,17,18,19,27,-1,22,23,24,25,26,34,28,29,30,31,32,33,41,35,36,37,38,39,40,48,42,43,44,45,46,47,-1}

Returns: 2.7182539682539684
{6,0,1,2,3,4,5,13,7,8,-1,10,11,12,20,14,15,-1,17,18,19,27,-1,22,23,24,25,26,34,28,29,30,31,32,33,-1,35,-1,37,38,39,40,48,42,-1,44,-1,46,47,-1}

Returns: 12.588095238095235
{1,2,3,4,5,6,0,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,0,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,5,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,5,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22,35,24,25,26,27,28,29,30,31,32,33,34,47,36,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 1.5
{11,0,1,2,3,4,5,6,7,8,9,-1,23,12,13,14,15,16,17,18,19,20,21,22,35,24,25,26,27,28,29,30,31,32,33,34,47,36,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 3.2182818282861687
{11,0,1,2,-1,4,5,6,-1,8,9,-1,23,12,13,14,15,16,17,-1,19,20,21,22,35,24,25,26,27,28,29,30,31,32,33,34,47,36,37,38,39,40,41,42,43,44,-1,46,-1,48}

Returns: 10.028230323239004
{1,2,3,4,5,6,7,8,9,10,11,0,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,0,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,5,6,7,8,9,10,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,-1,38,39,40,41,42,43,44,45,46,47,48}

Returns: 1.7182818282861687
{18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,-1,31,32,33,34,35,36,-1,38,39,40,41,42,43,44,45,46,47,48}

Returns: 3.4365636567452142
{18,0,-1,2,3,4,5,6,-1,-1,9,10,11,12,13,14,15,16,17,-1,19,20,21,22,23,24,25,26,27,28,29,-1,-1,32,33,34,35,36,-1,38,39,40,41,42,43,44,45,-1,47,48}

Returns: 12.257622959923303
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 1.5
{23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,-1,35,36,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 3.2182818284590455
{23,0,1,2,3,4,5,6,7,8,9,-1,11,12,13,14,15,16,17,-1,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,-1,35,36,37,38,39,40,41,-1,43,44,45,-1,-1,48}

Returns: 10.081454529761086
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{24,0,1,2,3,4,5,6,7,-1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 1.7182818284590453
{24,-1,1,2,3,4,-1,6,7,-1,9,-1,11,12,13,-1,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,-1,37,38,39,40,41,42,43,44,45,46,-1,48}

Returns: 11.746512147521873
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,-1}

Returns: 1.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 0.0
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}

Returns: 1.0
{-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Returns: 25.5
{-1,0,1,0,3,0,5,0,7,0,9,0,11,0,13,0,15,0,17,0,19,0,21,0,23,0,25,0,27,0,29,0,31,0,33,0,35,0,37,0,39,0,41,0,43,0,45,0,47,0}

Returns: 17.499999999999996
{-1,0,1,2,0,4,5,0,7,8,0,10,11,0,13,14,0,16,17,0,19,20,0,22,23,0,25,26,0,28,29,0,31,32,0,34,35,0,37,38,0,40,41,0,43,44,0,46,47,0}

Returns: 12.833333333333327
{-1,0,1,2,3,4,0,6,7,8,9,0,11,12,13,14,0,16,17,18,19,0,21,22,23,24,0,26,27,28,29,0,31,32,33,34,0,36,37,38,39,0,41,42,43,44,0,46,47,48}

Returns: 8.17916666666667
{-1,0,1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,0,31,32,33,34,35,36,37,38,39,0,41,42,43,44,45,46,47,48}

Returns: 4.591409105940357
{-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,0,41,42,43,44,45,46,47,48}

Returns: 3.1548454580644756
{-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,0}

Returns: 2.936563656918091
{-1,0,0,2,0,4,5,0,7,8,9,0,11,12,13,14,0,16,17,18,19,20,0,22,23,24,25,26,27,0,29,30,31,32,33,34,35,0,37,38,39,40,41,42,43,44,0,46,47,48}

Returns: 7.899484953703708
{1, -1, -1, -1, 5, 7, 9, 9, 10, -1, -1, 8, -1, 15, 45, 32, 45, 19, 23, 18, -1, 3, 30, 13, 13, 13, -1, 2, 3, 4, 5, 6, 7, 7, 7, 13, 1, 2, 14, 15, 15, 34, 22, 22, 22, -1, -1, 2, 21, 1 }

Returns: 18.051614858906515
{-1, -1, -1, -1, -1, -1, -1, -1, 1, 0, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 13, -1, 4 }

Returns: 47.0
{-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48 }

Returns: 1.7182818284590455
{-1, -1, 0, 4, 2, 3, 4, 5, 2, 12, 25, 24, 43, 47, 45, 32, 46, 32, 9, 10, 15, 29, 12, 42, 29, 28, 31, 1, 2, 3, -1, -1, -1, 21, 42, 14, 13, 19, 18, 21, 30, 49, 1, -1, -1, 32, 37, 33, 21, 20 }

Returns: 13.298269675925928
{-1, 0, 0, 2, 6, 3, 3, 20, 7, 11, 15, 7, 0, -1, 3, 7, 3, 6, 11, 10, 14, 7, 14, 3, 2, 15, 17, 1, 6, 10, -1 }

Returns: 5.253676146384481
{-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

Returns: 14.5
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }

Returns: 29.0
{-1, 0, 1 }

Returns: 1.6666666666666667
{1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4 }

Returns: 0.0
{49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 }

Returns: 0.0
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }

Returns: 50.0
{20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, -1, 20, 30, 20, 30, -1, 13, 30, 10, 30, 20, 30, 20, 30, -1, 20, 25, 20, 14 }

Returns: 3.0
{-1, -1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, -1, -1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

Returns: 4.718281828459045
{2, 0, 1, 2, 3, 4 }

Returns: 0.0
{4, 0, 1, 2, 3, 4, -1 }

Returns: 1.0
{1, 0, -1 }

Returns: 1.0
{-1, 0, 1, 9, 48, 2, 3, 8, 2, 5, -1, 0, 1, 9, 48, 2, 3, 7, 2, 5, -1, 0, 1, 9, 48, 2, 3, 7, 2, 5, -1, 0, 1, 9, 48, 2, 3, 7, 2, 5, -1, 0, 1, 9, 48, 2, 3, 7, 2 }

Returns: 8.846825396825398
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

Returns: 0.0
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 30, -1, -1, -1, 31, -1, -1, 20, 20 }

Returns: 32.16666666666667
{2, 0, 1, 2, 5, -1 }

Returns: 1.5
{-1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -1, -1, -1, 2, 3, 4, 5, 6, 7, 8 }

Returns: 28.16666666666667
{49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 9, 8, 7, 6, 5, 4, 3, 2, 1, -1 }

Returns: 1.5
{-1, -1, 1, 1, 2, 3, -1, -1, -1, -1, -1, -1, -1, 8, 7, 3 }

Returns: 11.499999999999998
{-1, 0, 1, 2, 3, 1, 2, 3, 2, 1, 3, 2, 3, 5, 4, 3, 2, 1, 5, 4, 2, 6, 5, 4, 3, 5 }

Returns: 2.645833333333333
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, -1 }

Returns: 1.718281828459045
{1, 2, 3, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 8, 8, 7, 9, 8, 7, 8, 7, 9, -1, -1, -1, -1, -1, -1, -1, 20, 21, 20, 20, 36, 35, 36, 35, -1, -1, -1, 5, 5, -1, 5, 48 }

Returns: 31.218055555555566
{-1, -1, 0, 2, -1, 0 }

Returns: 4.166666666666666
{-1, 0, 1, 2, 3, 4 }

Returns: 1.7180555555555557
{-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 }

Returns: 1.7182818284590455
{2, 0, 1, 1, -1, -1 }

Returns: 2.0
{2, 2, 1 }

Returns: 0.0
{1, 0, 1, 6, 6, 4, 3, 5, 3, 6, 8, 9, 3, 4, 6, 4, 3, 4, 5, 6, 7, 0, 7, 6, 5, 4, 3, 2, 1, 4, 5, 6, 7, 8, 23, 3, 4, 5, 6, 7, 8, 9, 0, -1, 1, 2, 3, 4 }

Returns: 1.0

Statistics

Problem Statement for "PrinceXToastbook"

Problem Statement

Definition

Notes

Constraints

Examples