学步园

题目链接：uva 1399 - Puzzle

题目大意：给定K和N，表示有K种不同的字符，N个禁止串，求一个最长的串使得该串不包含任何禁止串为子串。如果存在循环或者不能构成的话，输出No。

解题思路：建立AC自动机，然后在AC自动机上做dp，所有单词结尾节点为禁止点。

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>

using namespace std;
const int maxn = 50005;
const int sigma_size = 26;

struct Aho_Corasick {
    int sz, ac[maxn][sigma_size];
    int fail[maxn], last[maxn];

    void init();
    int idx(char ch);
    void insert(char* s);
    void get_fail();
}fuck;

int K, vis[maxn], dp[maxn], jump[maxn];

int dfs (int u) {
    if (vis[u])
        return -1;

    if (dp[u] != -1)
        return dp[u];

    vis[u] = 1;
    int& ret = dp[u];
    jump[u] = -1;
    ret = 0;

    for (int i = K - 1; i >= 0; i--) {
        int v = fuck.ac[u][i];
        if (fuck.last[v] == 0) {
            int tmp = dfs(v);

            if (tmp == -1)
                return -1;

            if (tmp + 1 > ret) {
                ret = tmp + 1;
                jump[u] = i;
            }
        }
    }
    vis[u] = 0;
    return ret;
}

void put_ans (int u) {
    while (jump[u] != -1) {
        printf("%c", 'A' + jump[u]);
        u = fuck.ac[u][jump[u]];
    }
    printf("\n");
}

int main () {
    int cas, n;
    char word[55];

    scanf("%d", &cas);
    while (cas--) {
        fuck.init();
        memset(vis, 0, sizeof(vis));
        memset(dp, -1, sizeof(dp));

        scanf("%d%d", &K, &n);
        for (int i = 0; i < n; i++) {
            scanf("%s", word);
            fuck.insert(word);
        }
        fuck.get_fail();

        if (dfs(0) != -1 && dp[0])
            put_ans(0);
        else
            printf("No\n");
    }
    return 0;
}

void Aho_Corasick::init() {
    sz = 1;
    memset(ac[0], 0, sizeof(ac[0]));
}

int Aho_Corasick::idx(char ch) {
    return ch - 'A';
}

void Aho_Corasick::insert(char* s) {
    int n = strlen(s), u = 0;

    for (int i = 0; i < n; i++) {
        int v = idx(s[i]);

        if (ac[u][v] == 0) {
            memset(ac[sz], 0, sizeof(ac[sz]));
            last[sz] = 0;
            ac[u][v] = sz++;
        }
        u = ac[u][v];
    }
    last[u] = 1;
}

void Aho_Corasick::get_fail () {
    queue<int> que;
    fail[0] = 0;

    for (int i = 0; i < sigma_size; i++) {
        int u = ac[0][i];
        if (u) {
            fail[u] = 0;
            que.push(u);
        }
    }

    while (!que.empty()) {
        int r = que.front();
        que.pop();

        for (int i = 0; i < K; i++) {
            int u = ac[r][i];

            if (u == 0) {
                ac[r][i] = ac[fail[r]][i];
                continue;
            }

            que.push(u);
            int v = fail[r];

            while (v && ac[v][i] == 0)
                v = fail[v];

            fail[u] = ac[v][i];
            last[u] |= last[fail[u]];
        }
    }
}