题目链接：uva 1076 - Password Suspects

题目大意：有一个长度为n的密码，存在m个子串，问说有多少种字符串满足，如果满足个数不大于42，按照字典序输出。

解题思路：根据子串构建AC自动机，然后记忆化搜索，dp[i][u][s]表示第i个字符，在u节点，匹配s个子串。

#include <cstdio>
#include <cstring>
#include <queue>
#include <string>
#include <vector>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;

const int maxn = 105;
const int maxs = (1<<10)+5;
const int sigma_size = 26;

struct Aho_Corasick {
    int sz, g[maxn][sigma_size];
    int val[maxn], fail[maxn];

    void init();
    int idx(char ch);
    void insert(char* str, int k);
    void get_fail();
}AC;

int N, M;
vector<string> vec;
ll dp[30][maxn][maxs];

void init () {
    AC.init();
    char str[20];

    for (int i = 0; i < M; i++) {
        cin >> str;
        AC.insert(str, i);
    }
    AC.get_fail();
    memset(dp, -1, sizeof(dp));
}

ll solve (int d, int u, int s) {

    if (d >= N)
        return s == (1<<M)-1 ? 1 : 0;

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

    ll& ret = dp[d][u][s];
    ret = 0;

    for (int i = 0; i < sigma_size; i++) {
        int v = AC.g[u][i];
        ret += solve(d + 1, v, s | AC.val[v]);
    }
    return ret;
}

void search (int d, int u, int s, string str) {

    if (d >= N) {
        if (s == (1<<M) - 1)
            vec.push_back(str);
        return;
    }

    if (dp[d][u][s] <= 0)
        return ;

    for (int i = 0; i < sigma_size; i++) {
        int v = AC.g[u][i];
        char ch = ‘a‘ + i;
        search(d + 1, v, s | AC.val[v], str + ch);
    }
}

int main () {
    int cas = 0;
    while (scanf("%d%d", &N, &M) == 2 && N + M) {
        init();
        ll ans = solve(0, 0, 0);
        //printf("Case %d: %lld suspects\n", ++cas, ans);
        cout << "Case " << ++cas << ": " << ans << " suspects" << endl;

        if (ans <= 42) {
            vec.clear();
            search(0, 0, 0, "");
            sort(vec.begin(), vec.end());
            for (int i = 0; i < vec.size(); i++)
                cout << vec[i] << endl;
        }
    }
    return 0;
}

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

int Aho_Corasick::idx(char ch) {
    return ch - ‘a‘;
}

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

    for (int i = 0; i < n; i++) {
        int v = idx(str[i]);
        if (g[u][v] == 0) {
            val[sz] = 0;
            memset(g[sz], 0, sizeof(g[sz]));
            g[u][v] = sz++;
        }
        u = g[u][v];
    }
    val[u] |= (1<<k);
}

void Aho_Corasick::get_fail() {
    queue<int> que;

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

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

        for (int i = 0; i < sigma_size; i++) {
            int u = g[r][i];

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

            que.push(u);
            int v = fail[r];
            while (v && g[v][i] == 0)
                v = fail[v];

            fail[u] = g[v][i];
            val[u] |= val[fail[u]];
        }
    }
}

uva 1076 - Password Suspects(AC自动机+记忆化搜索)