TopCoder problem "PalindromfulString" used in SRM 496 (Division II Level Three)



Problem Statement

    A palindrome is a string that is the same whether it is read from left to right or from right to left.



Consider a string of length N which contains only uppercase letters. Write down all of its contiguous substrings of length M (a separate substring must be written down for each starting position, even if some of these substrings are the same strings). If at least K of the substrings you have written down are palindromes, we call the string palindromful.



Return the number of different palindromful strings of length N.
 

Definition

    
Class:PalindromfulString
Method:count
Parameters:int, int, int
Returns:long
Method signature:long count(int N, int M, int K)
(be sure your method is public)
    
 

Constraints

-N will be between 2 and 11, inclusive.
-M will be between 2 and N, inclusive.
-K will be between 0 and 11, inclusive.
 

Examples

0)
    
2
2
1
Returns: 26
For a string of length 2, the only substring of length 2 is the string itself. Therefore, in this case we need to count palindromes of length 2, which are "AA", "BB", ..., "ZZ".
1)
    
2
2
0
Returns: 676
This time there can be no palindrome among the substrings, so any string of length 2 will do.
2)
    
3
2
1
Returns: 1326
Either the first two or the last two characters of the string should be equal, with no restrictions on the remaining one. This gives us 2*26*26=1352 variants, of which 26 are strings consisting entirely of the same character and therefore duplicated.
3)
    
4
4
1
Returns: 676
We're looking for palindromes of length 4.
4)
    
7
3
3
Returns: 4310176

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11296

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14425&pm=11296

Writer:

gojira_tc

Testers:

PabloGilberto , ivan_metelsky , it4.kp

Problem categories:

Brute Force, Recursion, Simple Math