Jolly Jumpers..~

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Problem Statement
     
Taro and Hanako have rabbits, and they want to assign a distinct integer to each rabbit so they can easily identify them.  The rabbits have expressed their preferences to Taro and Hanako. The i-th rabbit wants an integer between 1 and maxNumber[i], inclusive. Taro and Hanako must obey the preferences of all their rabbits.  Return the number of ways they can assign numbers to their rabbits, modulo 1,000,000,007. If it's impossible to assign distinct integers to the rabbits, return 0.
Definition
   
Class:
RabbitNumbering
Method:
theCount
Parameters:
vector <int>
Returns:
int
Method signature:
int theCount(vector <int> maxNumber)
(be sure your method is public)
   
 
Constraints
-
maxNumber will contain between 1 and 50 elements, inclusive.
-
Each element of maxNumber will be between 1 and 1,000, inclusive.
Examples
0)
 
   
{5}
Returns: 5
They can assign any number between 1 and 5, inclusive, to the only rabbit.
1)
 
   
{4, 4, 4, 4}
Returns: 24
All permutations of {1, 2, 3, 4} are possible.
2)
 
   
{5, 8}
Returns: 35
 
3)
 
   
{2, 1, 2}
Returns: 0
 
4)
 
   
{25, 489, 76, 98, 704, 98, 768, 39, 697, 8, 56, 74, 36, 95, 87, 2, 968, 4, 920, 54, 873, 90}
Returns: 676780400
 
This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2003, TopCoder, Inc. All rights reserved.

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Problem Statement
     
Taro and Hanako are playing a game called Nisoku, which is played as follows. Initially, there is a pile of cards. Each card contains a real number between 1.5 and 10.0, inclusive. You are given a vector <double> cards, the i-th element of which is the number written on the i-th card.  Repeat the following step until there is only one card left in the pile: Remove any two cards from the pile, and add one new card to the pile. Write either a+b or a*b on the new card, where a and b are the numbers written on the two cards that were removed.  Return the maximal possible number written on the final card in the pile.
Definition
   
Class:
Nisoku
Method:
theMax
Parameters:
vector <double>
Returns:
double
Method signature:
double theMax(vector <double> cards)
(be sure your method is public)
   
 
Notes
-
Your return value must have an absolute or relative error less than 1e-9.
Constraints
-
cards will contain between 2 and 50 elements, inclusive.
-
Each element of cards will be between 1.5 and 10.0, inclusive.
Examples
0)
 
   
{5, 8}
Returns: 40.0
5 * 8 = 40.
1)
 
   
{1.5, 1.8}
Returns: 3.3
1.5 + 1.8 = 3.3.
2)
 
   
{8.26, 7.54, 3.2567}
Returns: 202.82857868
 
3)
 
   
{1.5, 1.7, 1.6, 1.5}
Returns: 9.920000000000002
 
4)
 
   
{10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10}
Returns: 1.0E50
The answer can be extremely big.
This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2003, TopCoder, Inc. All rights reserved.

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Problem Statement
   
NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.  Taro and Hanako are playing Rabbit Puzzle. There are three rabbits and three nests on a line. You are given a vector<long long> rabbits, where each element is the initial position of a single rabbit, and a vector<long long> nests, where each element is the position of a single nest.

They must perform the following routine exactly K times:
1. Choose two different rabbits A and B, located at points a and b, respectively.
2. A jumps over B and lands at point 2*b-a.

      The jump is not allowed if another rabbit is already at point 2*b-a.


The goal of the puzzle is to have every rabbit be in a nest after the K routines. Note that the i-th rabbit doesn't necessarily have to be in the i-th nest. Return the number of ways to solve this puzzle, modulo 1,000,000,007. Two ways are considered different if at least one jump is different. 
Definition
     
Class:
RabbitPuzzle
Method:
theCount
Parameters:
vector<long long>, vector<long long>, int
Returns:
int
Method signature:
int theCount(vector<long long> rabbits, vector<long long> nests, int K)
(be sure your method is public)
   
 
Constraints
-
rabbits will contain exactly 3 elements.
-
Each element of rabbits will be between -10^18 and 10^18, inclusive.
-
rabbits will be sorted in strictly ascending order.
-
nests will contain exactly 3 elements.
-
Each element of nests will be between -10^18 and 10^18, inclusive.
-
nests will be sorted in strictly ascending order.
-
K will be between 1 and 100, inclusive.
Examples
0)
 
   
{0, 5, 8}
{0, 8, 11}
1
Returns: 1
The only solution is moving a rabbit from 5 to 11.
1)
 
   
{0, 5, 8}
{0, 8, 11}
3
Returns: 5
 
2)
 
   
{0, 5, 8}
{0, 8, 11}
2
Returns: 0
They must use exactly 2 jumps. It's impossible to solve this puzzle.
3)
 
   
{5, 8, 58}
{13, 22, 64}
58
Returns: 0
This puzzle is also impossible.
4)
 
   
{0, 1, 2}
{1, 2, 3}
100
Returns: 0
This puzzle is also impossible.
5)
 
   
{5, 8, 58}
{20, 26, 61}
58
Returns: 537851168
 
6)
 
   
{67, 281, 2348}
{235, 1394, 3293}
83
Returns: 167142023
 
7)
 
   
{-1000000000000000000, 999999999999999998, 999999999999999999}
{-1000000000000000000, 999999999999999999, 1000000000000000000}
5
Returns: 29
 
This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2003, TopCoder, Inc. All rights reserved.

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