Jolly Jumpers..~

Problem Statement
     
A string X is an ordered superstring of the vector <string> words if
Each element of words is a substring of X.
There exists a sequence of indices x_1 <= x_2 <= ... <= x_n, where n is the number of elements in words. For each element k of words, where k is a 1-based index, there is an occurrence of words[k] that starts at the x_k-th letter of X.
For example "abca" is an ordered superstring of {"abc", "ca"}, but "cabc" is not.
Given a vector <string> words, return the length of its shortest ordered superstring.
Definition
   
Class:
OrderedSuperString
Method:
getLength
Parameters:
vector <string>
Returns:
int
Method signature:
int getLength(vector <string> words)
(be sure your method is public)
   
 
Constraints
-
words will contain between 1 and 50 elements, inclusive.
-
Each element of words will contain between 1 and 50 lowercase letters ('a'-'z'), inclusive.
Examples
0)
 
   
{"abc","ca"}
Returns: 4
This is the example from the problem statement. The shortest ordered superstring is "abca". The sequence of indices is {0, 2}. There is an occurrence of "abc" starting at character 0 of "abca", and there is an occurrence of "ca" starting at character 2 of "abca".
1)
 
   
{"a","a","b","a"}
Returns: 3
Although the given words are all substrings of "ab", they do not appear in the proper order. The shortest ordered superstring is "aba".
2)
 
   
{"abcdef", "ab","bc", "de","ef"}
Returns: 6
 
3)
 
   
{"ab","bc", "de","ef","abcdef"}
Returns: 12
 
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.

Problem Statement
     
Once upon a time, there lived a powerful wizard who created spheresCount magical spheres. These spheres, when connected together, were a source of unimaginable power. To prevent anyone else from using them, the wizard created fakeSpheresCount spheres that are indistinguishable from the real ones, but don't hold any magical power.
You are determined to find out which spheres are real, and use them to rule the world. To accomplish this, you want to gather a team of gnomes to try every combination of spheresCount spheres out of (spheresCount + fakeSpheresCount) spheres, even if it takes centuries. You will assign combinations to each gnome beforehand, and you will not test any combination more than once. Unfortunately, the gnomes have a labor union that won't allow some gnomes to have more work than others. Therefore, you must select a team size that will allow you to assign an equal number of combinations to each gnome.
Return the maximum possible team size less than or equal to gnomesAvailable that allows even distribution of the work.
Definition
   
Class:
MagicalSpheres
Method:
divideWork
Parameters:
int, int, int
Returns:
int
Method signature:
int divideWork(int spheresCount, int fakeSpheresCount, int gnomesAvailable)
(be sure your method is public)
   
 
Constraints
-
spheresCount will be between 1 and 1,000,000,000, inclusive.
-
fakeSpheresCount will be between 1 and 1,000,000,000, inclusive.
-
availableGnomes will be between 1 and 100000, inclusive.
Examples
0)
 
   
3
1
3
Returns: 2
We have a total of four spheres, lets call them {a,b,c,d}. We need to check all triplets to find which of them are real. The different triplets are: {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}. Since there are four possibilities to check, we can divide it between two gnomes, by assigning two to each of them.
1)
 
   
3
3
50
Returns: 20
With three fake spheres, there are 20 triplets to check. You can use 20 gnomes and assign one of the triplets to each of them.
2)
 
   
4
3
4
Returns: 1
 
3)
 
   
15634
456
5000
Returns: 4990
 
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.

Problem Statement
     
Given a rectangular grid where all the cells are initially white, you perform the following procedure K times:
Select a cell from the grid at random, and call it A
Select a cell from the grid at random, and call it B
Color all the cells in the rectangle bounded by A and B
Each cell is selected at random, with uniform distribution, and each selection is independent from the other selections. It's possible that A and B correspond to the same cell.
For example, the image below shows a 5x7 grid where the selected pairs could have been (row, column):
(0,1); (3,2)
(3,6); (4,0)
(0,6); (0,5)
Resulting in a grid with 22 colored cells and 13 white cells.