POJ - 3974 Palindrome

Posted 2020-10-31 hit_yjl

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

思路：求一个字符串的最长回文子串，manacher算法或者预处理前后缀hash值二分求解。我写的manacher。

 1 #include <iostream>
 2 #include <fstream>
 3 #include <sstream>
 4 #include <cstdlib>
 5 #include <cstdio>
 6 #include <cmath>
 7 #include <string>
 8 #include <cstring>
 9 #include <algorithm>
10 #include <queue>
11 #include <stack>
12 #include <vector>
13 #include <set>
14 #include <map>
15 #include <list>
16 #include <iomanip>
17 #include <cctype>
18 #include <cassert>
19 #include <bitset>
20 #include <ctime>
21 
22 using namespace std;
23 
24 #define pau system("pause")
25 #define ll long long
26 #define pii pair<int, int>
27 #define pb push_back
28 #define mp make_pair
29 #define clr(a, x) memset(a, x, sizeof(a))
30 
31 const double pi = acos(-1.0);
32 const int INF = 0x3f3f3f3f;
33 const int MOD = 1e9 + 7;
34 const double EPS = 1e-9;
35 
36 /*
37 #include <ext/pb_ds/assoc_container.hpp>
38 #include <ext/pb_ds/tree_policy.hpp>
39 
40 using namespace __gnu_pbds;
41 tree<pli, null_type, greater<pli>, rb_tree_tag, tree_order_statistics_node_update> T;
42 */
43 
44 char s[1000015], t[2000015];
45 int ls, lt, p[2000015];
46 void get_t() {
47     t[0] = ‘@‘;
48     ls = strlen(s + 1);
49     for (int i = 1; i <= ls; ++i) {
50         t[(i << 1) - 1]  = ‘#‘;
51         t[i << 1] = s[i];
52     }
53     t[ls << 1 | 1] = ‘#‘;
54     lt = ls << 1 | 1;
55     t[lt + 1] = 0;
56 }
57 int get_maxlen() {
58     get_t();
59     int mi = 1, mx = 1, res = 0;
60     p[1] = 1;
61     for (int i = 2; i <= lt; ++i) {
62         if (i <= mx) {
63             p[i] = min(mx - i + 1, p[2 * mi - i]);
64         } else {
65             p[i] = 1;
66         }
67         while (t[i - p[i]] == t[i + p[i]]) ++p[i];
68         if (mx < i + p[i]) {
69             mi = i;
70             mx = i + p[i];
71         }
72         res = max(res, p[i] - 1);
73     }
74     return res;
75 }
76 int main() {
77     for (int ca = 1; scanf("%s", s + 1) && strcmp(s + 1, "END"); ++ca) {
78         printf("Case %d: %d\n", ca, get_maxlen());
79     }
80     return 0;
81 }

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