Palindromic characteristics
题目描述
Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes.
A string is 1-palindrome if and only if it reads the same backward as forward.
A string is k-palindrome (k>1) if and only if:
- Its left half equals to its right half.
- Its left and right halfs are non-empty (k-1)-palindromes.
The left half of string t is its prefix of length ⌊|t|/2⌋, and right half− the suffix of the same length. ⌊|t|/2⌋ denotes the length of string t divided by 2, rounded down.
Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.
The first line contains the string s (1≤|s|≤5000) consisting of lowercase English letters.
Print |s| integers− palindromic characteristics of string s.
abba
6 1 0 0
abacaba
12 4 1 0 0 0 0
In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.
题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 84 题。保留原作者与原赛事署名。