hdu 2243 考研路茫茫——单词情结(AC自动机+矩阵快速幂)

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题目链接：hdu 2243 考研路茫茫——单词情结

题目大意：略。

解题思路：和poj 2778 DNA Sequence类似的做法，不同的是这道题目是要求小于长度L的，所以要多加一个维护总

和，做过矩阵快速幂的人肯定都会这个。然后我们肯定是先算出不包含词根的，用总的减掉就是要求的答案，所以我又

加了两个用来维护总的，长度为i时，总的可能串有26i，累加。题目要求取模264，直接用unsigned long long，注意

hdu输出long long型不能用printf。

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

using namespace std;

typedef unsigned long long ll;

const int maxn = 50;
const int sigma_size = 26;

struct Mat {
    int r, c;
    ll s[maxn][maxn];
    Mat(int r = 0, int c = 0) { init(r, c);}
    void init(int r, int c) {
        this->r = r;
        this->c = c;
        memset(s, 0, sizeof(s));
    }
    Mat operator * (const Mat& a) {
        Mat ret(r, a.c);
        for (int k = 0; k < c; k++) {
            for (int i = 0; i < r; i++)
                for (int j = 0; j < a.c; j++)
                    ret.s[i][j] += s[i][k] * a.s[k][j];
        }
        return ret;
    }
};

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

    void init();
    int idx(char ch);
    void insert(char* str, int k);
    void getFail();
    void match(char* str);
    void put(int x, int y);
    Mat solve();
}A;

int N;
ll L;

void put (Mat x) {
    for (int i = 0; i < x.r; i++) {
        for (int j = 0; j < x.c; j++)
            printf("%llu ", x.s[i][j]);
        printf("\n");
    }
}

ll pow_mat (Mat x, ll n) {

    Mat ret(x.r, 1);
    ret.s[0][0] = ret.s[A.sz+1][0] = 1;

    while (n) {
        if (n&1)
            ret = x * ret;
        x = x * x;
        n >>= 1;
    }
    int p = ret.r;
    return ret.s[p-1][0] - ret.s[p-3][0];
}

int main () {
    //while (scanf("%d%llu", &N, &L) == 2) {
    while (cin >> N >> L) {
        A.init();
        char w[20];
        for (int i = 1; i <= N; i++) {
            cin >> w;
            A.insert(w, i);
        }
        Mat X = A.solve();
        //printf("%llu\n", pow_mat(X, L + 1));
        cout << pow_mat(X, L + 1) << endl;
    }
    return 0;
}

Mat Aho_Corasick::solve() {
    getFail();
    Mat ret(sz + 3, sz + 3);

    for (int i = 0; i < sz; i++) {
        if (tag[i] || last[i])
            continue;

        for (int v = 0; v < sigma_size; v++) {
            int u = i;
            while (u && g[u][v] == 0)
                u = fail[u];

            u = g[u][v];
            ret.s[u][i]++;
        }
        ret.s[sz][i]++;
    }
    ret.s[sz][sz] = 1;
    ret.s[sz+1][sz+1] = 26;
    ret.s[sz+2][sz+1] = ret.s[sz+2][sz+2] = 1;
    return ret;
}

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

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

void Aho_Corasick::put(int x, int y) {
}

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) {
            tag[sz] = 0;
            memset(g[sz], 0, sizeof(g[sz]));
            g[u][v] = sz++;
        }
        u = g[u][v];
    }
    tag[u] = k;
}

void Aho_Corasick::match(char* str) {
    int n = strlen(str), u = 0;
    for (int i = 0; i < n; i++) {
        int v = idx(str[i]);
        while (u && g[u][v] == 0)
            u = fail[u];

        u = g[u][v];

        if (tag[u])
            put(i, u);
        else if (last[u])
            put(i, last[u]);
    }
}

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

    for (int i  = 0; i < sigma_size; i++) {
        int u = g[0][i];
        if (u) {
            fail[u] = last[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];
            last[u] = tag[fail[u]] ? fail[u] : last[fail[u]];
        }
    }
}

hdu 2243 考研路茫茫——单词情结(AC自动机+矩阵快速幂)

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原文地址：http://blog.csdn.net/keshuai19940722/article/details/40948237