hdu 2825(ac自动机+状态压缩dp)

来源：互联网发布：java什么是工厂模式编辑：程序博客网时间：2024/04/29 14:20

题意：有m个模式串，问长度为n的目标串中至少出现k种模式串的种类数，可以重叠且所有的串都只包含小写字母。
题解：因为模式串最多10个，可以用状态压缩来表示每一个模式串是否出现，f[i][j][k]是长度为i的字符串，结尾节点是j且当前所用模式串状态是k的所有可能情况。状态转移方程f[i][next[j][l]][k | val[next[j][l]] = sum{ f[i - 1][j][k] }，val存的是到当前节点所得到的模式串状态。

#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#define ll long longusing namespace std;const int N = 105;const int SIGMA_SIZE = 26;const int MOD = 20090717;int Next[N][SIGMA_SIZE], fail[N], val[N], sz, n, m, p;ll f[30][N][1 << 10];int num[1050];char str[N];void init() {    memset(Next[0], 0, sizeof(Next[0]));    val[0] = 0;    sz = 1;}void insert(char *s, int v) {    int u = 0, len = strlen(s);    for (int i = 0; i < len; i++) {        int k = s[i] - 'a';        if (!Next[u][k]) {            memset(Next[sz], 0, sizeof(Next[sz]));            val[sz] = 0;            Next[u][k] = sz++;        }        u = Next[u][k];    }    val[u] |= (1 << v);}void getFail() {    queue<int> Q;    fail[0] = 0;    for (int i = 0; i < SIGMA_SIZE; i++)        if (Next[0][i]) {            fail[Next[0][i]] = 0;            Q.push(Next[0][i]);        }    while (!Q.empty()) {        int u = Q.front();        Q.pop();        val[u] |= val[fail[u]];        for (int i = 0; i < SIGMA_SIZE; i++) {            if (!Next[u][i])                Next[u][i] = Next[fail[u]][i];            else {                fail[Next[u][i]] = Next[fail[u]][i];                Q.push(Next[u][i]);            }        }    }}int main() {    for (int i = 0; i < 1024; i++) {        num[i] = 0;        for (int j = 0; j < 10; j++)            if (i & (1 << j))                num[i]++;    }    while (scanf("%d%d%d", &n, &m, &p) == 3 && n + m + p) {        init();        for (int i = 0; i < m; i++) {            scanf("%s", str);            insert(str, i);        }        getFail();        memset(f, 0, sizeof(f));        f[0][0][0] = 1;        int temp = 1 << m;        for (int i = 1; i <= n; i++)            for (int j = 0; j < sz; j++)                for (int k = 0; k < temp; k++) {                    if (f[i - 1][j][k] > 0) {                        for (int l = 0; l < SIGMA_SIZE; l++) {                            int kk = k | val[Next[j][l]];                            f[i][Next[j][l]][kk] = (f[i][Next[j][l]][kk] + f[i - 1][j][k]) % MOD;                        }                    }                }        ll res = 0;        for (int i = 0; i < temp; i++)            if (num[i] >= p) {                for (int j = 0; j < sz; j++)                    res = (res + f[n][j][i]) % MOD;            }        printf("%lld\n", res);    }    return 0;}

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