[The problem appeared in TopCoder SRM 594 (Div-2, Level-1)]
Problem link: http://community.topcoder.com/stat?c=problem_statement&pm=12811
Fox Ciel is now in high school. The seats in her classroom are arranged into an n by m matrix. The rows are numbered from 0 to n-1 (front to back) and the columns from 0 to m-1 (left to right).
At the beginning, Ciel can choose any of the seats. Then, at the end of each week Ciel will shift one row to the back and one column to the right, wrapping around whenever necessary. Formally, if her current seat is in row r and column c, then her seat next week will be the one in row ((r+1) modulo n) and column ((c+1) modulo m).
Fox Ciel now wonders whether she can sit in all the seats in the classroom if she follows the above procedure. As we already mentioned, she can start in any of the seats. Also, she can attend the school for as many weeks as she wants to. Return “Possible” if she can sit in all the seats and “Impossible” otherwise.
[The problem appeared in TopCoder SRM 592 (Div-2, Level-1)]
Problem link: http://community.topcoder.com/stat?c=problem_statement&pm=12112
Little Elephant from the Zoo of Lviv has a bunch of books. You are given a int pages. Each element of pages is the number of pages in one of those books. There are no two books with the same number of pages.
You are also given a int number. As a homework from the teacher, Little Elephant must read exactly number of his books during the summer. (Little Elephant has strictly more than number books.)
All other elephants in the school also got the exact same homework. Little Elephant knows that the other elephants are lazy: they will simply pick the shortest number books, so that they have to read the smallest possible total number of pages. Little Elephant wants to be a good student and read a bit more than the other elephants. He wants to pick the subset of books with the second smallest number of pages. In other words, he wants to pick a subset of books with the following properties:
1. There are exactly number books in the chosen subset.
2. The total number of pages of those books is greater than the smallest possible total number of pages.
3. The total number of pages of those books is as small as possible (given the above conditions).
Return the total number of pages Little Elephant will have to read.
[The problem appeared in TopCoder SRM 279 (Div-2, Level-1) and SRM 279 (Div-1, Level-1)]
Problem link: http://community.topcoder.com/stat?c=problem_statement&pm=5950&rd=8076
A sentence is called dancing if its first letter is uppercase and the case of each subsequent letter is the opposite of the previous letter. Spaces should be ignored when determining the case of a letter. For example, “A b Cd” is a dancing sentence because the first letter (‘A’) is uppercase, the next letter (‘b’) is lowercase, the next letter (‘C’) is uppercase, and the next letter (‘d’) is lowercase.
You will be given a String sentence. Turn the sentence into a dancing sentence by changing the cases of the letters where necessary. All spaces in the original sentence must be preserved.