poj3415Common Substrings(好题)

Common Substrings

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 8519		Accepted: 2812

Description

A substring of a string T is defined as:

T( i, k)= T_iT_{i +1}... T_{i+k -1}, 1≤ i≤ i+k-1≤| T|.

Given two strings A, B and one integer K, we define S, a set of triples (i, j, k):

S = {( i, j, k) | k≥ K, A( i, k)= B( j, k)}.

You are to give the value of |S| for specific A, B and K.

Input

The input file contains several blocks of data. For each block, the first line contains one integer K, followed by two lines containing strings A and B, respectively. The input file is ended by K=0.

1 ≤ |A|, |B| ≤ 10⁵
1 ≤ K ≤ min{|A|, |B|}
Characters of A and B are all Latin letters.

Output

For each case, output an integer |S|.

Sample Input

2
aababaa
abaabaa
1
xx
xx
0

Sample Output

22
5

Source

POJ Monthly--2007.10.06, wintokk

论文题,
基本思路是计算 A 的所有后缀和 B 的所有后缀之间的最长公共前缀的长度，
把最长公共前缀长度不小于 k 的部分全部加起来。先将两个字符串连起来，中间
用一个没有出现过的字符隔开。按 height 值分组后，接下来的工作便是快速的
统计每组中后缀之间的最长公共前缀之和。扫描一遍，每遇到一个 B 的后缀就统
计与前面的 A 的后缀能产生多少个长度不小于 k 的公共子串， 这里 A 的后缀需要
用一个单调的栈来高效的维护。然后对 A 也这样做一次。(摘自论文)

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