[USACO 2011 Dec Gold] Threatening Letter后缀

Posted 2020-08-17 ciao_sora

Problem 3: Threatening Letter [J. Kuipers, 2002]

FJ has had a terrible fight with his neighbor and wants to send him
a nasty letter, but wants to remain anonymous. As so many before
him have done, he plans to cut out printed letters and paste them
onto a sheet of paper. He has an infinite number of the most recent
issue of the Moo York Times that has N (1 <= N <= 50,000) uppercase
letters laid out in a long string (though read in as a series of
shorter strings). Likewise, he has a message he‘d like to compose
that is a single long string of letters but that is read in as a
set of shorter strings.

Being lazy, he wants to make the smallest possible number of cuts.
FJ has a really great set of scissors that enables him to remove
any single-line snippet from the Moo York Times with one cut. He
notices that he can cut entire words or phrases with a single cut,
thus reducing his total number of cuts.

What is the minimum amount of cuts he has to make to construct his
letter of M (1 <= M <= 50,000) letters?

It is guaranteed that it is possible for FJ to complete his task.

Consider a 38 letter Moo York Times:

        THEQUICKBROWNFOXDO
        GJUMPSOVERTHELAZYDOG

from which FJ wants to construct a 9 letter message:

        FOXDOG
        DOG

These input lines represent a pair of strings:

        THEQUICKBROWNFOXDOGJUMPSOVERTHELAZYDOG
        FOXDOGDOG

Since "FOXDOG" exists in the newspaper, FJ can cut this piece out
and then get the last "DOG" by cutting out either instance of the
word "DOG".

Thus, he requires but two cuts.

PROBLEM NAME: letter

INPUT FORMAT:

* Line 1: Two space-separated integers: N and M

* Lines 2..?: N letters laid out on several input lines; this is the
        text of the one copy of the Moo York Times. Each line will
        have no more than 80 characters.

* Lines ?..?: M letters that are the text of FJ‘s letter. Each line
        will have no more than 80 characters.

SAMPLE INPUT (file letter.in):

38 9
THEQUICKBROWNFOXDO
GJUMPSOVERTHELAZYDOG
FOXDOG
DOG

OUTPUT FORMAT:

* Line 1: The minimum number of cuts FJ has to make to create his
        message

SAMPLE OUTPUT (file letter.out):

2

 

 

一看跟子串相关，就是后缀那一套了。想法是这样的，尽量在文本串中找到更长的子串与当前串匹配。若无法继续匹配了，则重新匹配，答案+1。这里我选择了后缀自动机，实现起来好写。

#include <cstdio>
#include <cstring>

const int maxn = 50005;

int n, m, ans, now;
int sam[maxn << 1][26], len[maxn << 1], link[maxn << 1], sz, last, p, q, cur, clone;
char ch;

int main(void) {
	freopen("letter.in", "r", stdin);
	freopen("letter.out", "w", stdout);
	scanf("%d%d", &n, &m);
	link[sz++] = -1;
	for (int i = 1; i <= n; ++i) {
		while ((ch = getchar()) < ‘A‘);
		cur = sz++;
		len[cur] = len[last] + 1;
		for (p = last; p != -1 && !sam[p][ch - ‘A‘]; p = link[p]) {
			sam[p][ch - ‘A‘] = cur;
		}
		if (p != -1) {
			q = sam[p][ch - ‘A‘];
			if (len[p] + 1 == len[q]) {
				link[cur] = q;
			}
			else {
				clone = sz++;
				memcpy(sam[clone], sam[q], sizeof sam[0]);
				link[clone] = link[q];
				len[clone] = len[p] + 1;
				for (; p != -1 && sam[p][ch - ‘A‘] == q; p = link[p]) {
					sam[p][ch - ‘A‘] = clone;
				}
				link[q] = link[cur] = clone;
			}
		}
		last = cur;
	}
	
	for (int i = 1; i <= m; ++i) {
		while ((ch = getchar()) < ‘A‘);
		now = sam[now][ch - ‘A‘];
		if (!now) {
			++ans;
			now = sam[0][ch - ‘A‘];
		}
	}
	if (now) {
		++ans;
	}
	printf("%d\n", ans);
	return 0;
}

　　这也算是SAM的模版了叭。