[POJ 2406] Power Strings【KMP】
Problem:
| Time Limit: 3000MS | Memory Limit: 65536K |
Description
Given two strings a and b we define a*b to be their concatenation. For example, if a = "abc" and b = "def" then a*b = "abcdef". If we think of concatenation as multiplication, exponentiation by a non-negative integer is defined in the normal way: a^0 = "" (the empty string) and a^(n+1) = a*(a^n).
Input
Each test case is a line of input representing s, a string of printable characters. The length of s will be at least 1 and will not exceed 1 million characters. A line containing a period follows the last test case.
Output
For each s you should print the largest n such that s = a^n for some string a.
Sample Input
abcd aaaa ababab .
Sample Output
1 4 3
Hint
This problem has huge input, use scanf instead of cin to avoid time limit exceed.
Source
Waterloo local 2002.07.01
Solution:
本题是 KMP 的变形，考查了自匹配 nxt[] 数组的性质。
设原串 s 长度为 len，令 k = len - nxt[len]，则若 k | len，我们可以得到：
- ⇒ len = c * k (c ∈ N*)，s1..(c-1)k == sk+1..ck
- ⇒ s1..k == sk+1..2k == …… == s(c-1)k+1..ck
即最大循环节数 c = len / k。否则若 k 不能整除 len，则 c = 1。
Code: O(T|s|) [5564K, 141MS]
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<algorithm>
using namespace std;
char s[1000005];
int nxt[1000005];
int main(){
while(scanf("%s", s + 1) != EOF && s[1] != '.'){
int len = strlen(s + 1);
nxt[1] = 0;
for(register int i = 2, j = 0; i <= len; i++){
while(j && s[j + 1] != s[i]) j = nxt[j];
if(s[j + 1] == s[i]) j++;
nxt[i] = j;
}
if(len % (len - nxt[len])) puts("1");
else printf("%d\n", len / (len - nxt[len]));
}
return 0;
}
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