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
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.
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 ENDSample Output
Case 1: 13 Case 2: 6
马拉车模板题 主要为了怕自己以后忘记怎么写了 还要重新理解 里面详细解释
代码 :
#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> using namespace std; const int maxn=2000010; char beginn[maxn],endd[maxn]; int len[maxn]; int tralation() { int gg=strlen(beginn); int noww=0; endd[0]='&'; for(int i=0;i<gg;i++) { endd[++noww]='#'; endd[++noww]=beginn[i]; } endd[++noww]='#'; return noww; } int Manacher(int total) { int maxx = 0; int mx = 0,id = 0; //id表示的最大回文的中心点是哪一个 而mx表示的是最大回文的中心点的最远的边界是哪一个 for(int i =1;i<=total;i++) { if(i<mx) //如果此刻 i的点比mx还要小的话说明 在mx-i处这边是回文 然后在比较一下 len[i] = min(mx - i,len[2*id-i]); //因为2*id - i 和 i 他们是相对于id对称的 所以说吧 就是要比较mx-i和len[2*id-i] ; else len[i] = 1; //如果此刻i的点比边界还要大的话 那就需要从一开始加了 while(endd[i+len[i]]==endd[i-len[i]]) len[i]++; if(i+len[i]>mx) { mx = i+len[i]; id = i; } maxx = max(maxx,len[i]); } return maxx-1; } int main() { int t=0; while(scanf("%s",beginn)!=EOF) { if(strcmp("END",beginn)==0)break; int total = tralation(); int ans = Manacher(total); cout << "Case "<<++t<<": "<<ans << endl; } return 0; }