POJ 3974 Palindrome (Manacher)

题目链接：POJ 3974

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

1
2
3

abcbabcbabcba
abacacbaaaab
END

Sample Output

1 2	Case 1: 13 Case 2: 6

Source

Seventh ACM Egyptian National Programming Contest

Solution

题意

给定一个字符串，求最长回文子串。

思路

Manacher 模板题。

有关 Manacher 算法的讲解见这里

Code

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cstdlib>
using namespace std;
const int maxn = 2000010;

string init(string s) {
    string res;
    res += '@';
    for(int i = 0; i < s.size(); ++i) {
        res += '#';
        res += s[i];
    }
    res += '#';
    res += '$';
    return res;
}

int len[maxn];

int Manacher(string s) {
    memset(len, 0, sizeof(len));
    int mx = 0, id = 0;
    int ans = 0;
    for(int i = 1; i < s.size() - 1; ++i) {
        if(mx > i) {
            len[i] = min(mx - i, len[2 * id - i]);
        } else {
            len[i] = 1;
        }
        while(s[i - len[i]] == s[i + len[i]]) {
            ++len[i];
        }
        if(i + len[i] > mx) {
            mx = i + len[i];
            id = i;
        }
        ans = max(ans, len[i]);
    }
    return ans - 1;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    string s;
    int kase = 0;
    while (cin >> s) {
        if(s == "END") break;
        string tmp = init(s);
        cout << "Case " << (++kase) << ": ";
        cout << Manacher(tmp) << endl;
    }
    return 0;
}