POJ3974Palindrome
1969+

Description

Andy the smart computer science student was attending an algorithms class when the professor asked the students a simple question, “Can you propose an efficient algorithm to find the length of the largest palindrome in a string?”

A string is said to be a palindrome if it reads the same both forwards and backwards, for example “madam” is a palindrome while “acm” is not.

The students recognized that this is a classical problem but couldn’t come up with a solution better than iterating over all substrings and checking whether they are palindrome or not, obviously this algorithm is not efficient at all, after a while Andy raised his hand and said “Okay, I’ve a better algorithm” and before he starts to explain his idea he stopped for a moment and then said “Well, I’ve an even better algorithm!”.

If you think you know Andy’s final solution then prove it! Given a string of at most 1000000 characters find and print the length of the largest palindrome inside this string.

Input

Your program will be tested on at most 30 test cases, each test case is given as a string of at most 1000000 lowercase characters on a line by itself. The input is terminated by a line that starts with the string “END” (quotes for clarity).

Output

For each test case in the input print the test case number and the length of the largest palindrome.

Sample Input

abcbabcbabcba
abacacbaaaab
END

Sample Output

Case 1: 13
Case 2: 6

解题思路

Manacher算法是这样的，从左到右依次计算以每个字符为对称中心的最长回文长度，如果下一个字符包含在前一个回文串中，那么由对称性可知其在回文区域内的最长回文长度。如对称中心是i，回文向右扩展的长度是c[i]（包括s[i]），如果j在[i, i+c[i])范围内，那么cspan style="color: #ff0000;">j = cstrong>i*2-j或者c[j] = i+c[i] – j，即要么是跟前面一样多，要么是超出回文区域被截取了。当然，这只是至少的情况，后面还需要继续扩展，当s[i+c[i == s[i-c[i时，回文区域就会扩大。由于回文区域右边界最大就扩展到n，区域内的可以根据对称性O(1)求出回文长度，因此整体复杂度是O(n)。