Problem Statement | | |
A palindrome is a word that reads the same forwards and backwards.
For example, "Z", "ABBA", "RACECAR", and "XXXXXX" are all palindromes.
You are given a String S.
A sequence of integers L is called a consecutive palindromic sequence for S if it has the following properties:
- L is a strictly increasing sequence.
- All elements of L lie between 0 and length(S)-1, inclusive.
- L contains a subsequence of two or more consecutive integers (a, a+1, ..., b) such that the string S[a]S[a+1]...S[b] is a palindrome.
For example, for S = "TOPPAPPOT" the following sequences are some of the consecutive palindromic sequences:
(2, 3), (0, 5, 6), (3, 4, 5), and (0, 1, 2, 3, 4, 5, 6, 7, 8).
The sequences (0, 8) and (0, 1) are not consecutive palindromic sequences: they do not have the third property.
Let C be the number of consecutive palindromic sequences for the given string S.
Compute and return the value (C modulo 10^9+7).
| | | Definition | | | | Class: | ConsecutivePalindromes | | Method: | countStrings | | Parameters: | String | | Returns: | int | | Method signature: | int countStrings(String S) | | (be sure your method is public) |
| | | | | | Constraints | | - | S will contain between 1 and 2,000 characters, inclusive. | | - | S will contain only uppercase English letters ('A' - 'Z'). | | | Examples | | 0) | | | | | Returns: 3 |
The three consecutive palindromic sequences are the sequences (0, 1), (1, 2), and (0, 1, 2).
For example, the entire sequence (0, 1) corresponds to the palindrome S[0]S[1] = "AA".
Note that the sequence (0, 2) is not a consecutive palindromic sequence: it does not contain any subsequence of two or more consecutive integers at all.
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| | 1) | | | | | | 2) | | | | | Returns: 7 |
The seven consecutive palindromic sequences: (0, 1), (0, 1, 2), (0, 1, 3), (0, 1, 2, 3), (0, 2, 3), (1, 2, 3), and (2, 3).
For example, (0, 2, 3) is a consecutive palindromic sequence because it contains the subsequence (2, 3): two consecutive integers with the property that S[2]S[3] = "AA" is a palindrome.
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| | 3) | | | | | | 4) | | | | | | 5) | | | | "AYUEOPPOLAKIKIKIUYOPZOOLPPPPKMOPOLIURKMQOAPLFKTURIWOOWWWPLOLWWWOPSLAA" |
| Returns: 216072426 | |
| | 6) | | | | |
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