hdu2243---考研路茫茫——单词情结(AC自动机+矩阵+二分)

首先对2^64取模的话,可以直接用unsigned long long,这样溢出部分就是取模后的结果了
方法类似POJ2778传送门
只不过这里要统计长度不超过m的方案
我们先统计出长度为m的所有方案,然后减去不包含这些串的方案,剩下就是至少包含一个串的方案了
设转移矩阵为A
相当于sum = A + A^2 + … A^m
f(m) = f(m / 2) * (1 + A ^(m / 2)) + (m & 1) ? A^m : 0
二分即可求出,但是不要写成递归的,不然会爆栈

对于求总数
f(m) = 1 + 26 + … + 26^m
f(m) = f(m - 1) * 26 + 1
[f(m), 1] = [26, 1; 0 1][f(m - 1), 1];
转移即可

/************************************************************************* > File Name: hdu2243.cpp > Author: ALex > Mail: [email protected] > Created Time: 2015年03月11日 星期三 10时27分24秒 ************************************************************************/

#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#pragma comment (linker, "/STACK:1024000000, 1024000000")
using namespace std;

const double pi = acos(-1.0);
const int inf = 0x3f3f3f3f;
const double eps = 1e-15;
typedef long long LL;
typedef pair <int, int> PLL;

const int MAX_NODE = 26;
const int CHILD_NUM = 26;
struct node
{
    int k;
    unsigned long long mat[MAX_NODE][MAX_NODE];
    void clear()
    {
        memset (mat, 0, sizeof(mat));
    }
};

stack <node> st;

struct MARTIX
{
    unsigned long long mat[MAX_NODE][MAX_NODE];
}A, E;

MARTIX mul(MARTIX a, MARTIX b, int L)
{
    MARTIX c;
    for (int i = 0; i < L; ++i)
    {
        for (int j = 0; j < L; ++j)
        {
            c.mat[i][j] = 0;
            for (int k = 0; k < L; ++k)
            {
                c.mat[i][j] += a.mat[i][k] * b.mat[k][j];
            }
        }
    }
    return c;
}

MARTIX add(MARTIX a, MARTIX b, int L)
{
    for (int i = 0; i < L; ++i)
    {
        for (int j = 0; j < L; ++j)
        {
            a.mat[i][j] += b.mat[i][j];
        }
    }
    return a;
}


MARTIX martix_pow(MARTIX ret, int n, int L)
{
    MARTIX ans;
    for (int i = 0; i < L; ++i)
    {
        for (int j = 0; j < L; ++j)
        {
            ans.mat[i][j] = (i == j);
        }
    }
    while (n)
    {
        if (n & 1)
        {
            ans = mul(ans, ret, L);
        }
        n >>= 1;
        ret = mul(ret, ret, L);
    }
    return ans;
}

/*MARTIX Binsearch(int k, int L) { if (k == 1) { return A; } if (k & 1) { MARTIX a = martix_pow(A, k >> 1, L); a = add(a, E, L); MARTIX b = Binsearch(k >> 1, L); a = mul(a, b, L); MARTIX c = martix_pow(A, k, L); a = add(a, c, L); return a; } else { MARTIX a = martix_pow(A, k >> 1, L); a = add(a, E, L); MARTIX b = Binsearch(k >> 1, L); a = mul(a, b, L); return a; } }*/

MARTIX work (int k, int L)
{
    while (!st.empty())
    {
        st.pop();
    }
    int tmp = k;
    while (tmp != 1)
    {
        node x;
        x.clear();
        x.k = tmp;
        st.push(x);
        tmp >>= 1;
    }
    MARTIX ans = A;
    while (!st.empty())
    {
        node cur = st.top();
        st.pop();
        MARTIX a = martix_pow(A, cur.k / 2, L);
        a = add(a, E, L);
        ans = mul(ans, a, L);
        if (cur.k & 1)
        {
            MARTIX b = martix_pow(A, cur.k, L);
            ans = add(ans, b, L);
        }
    }
    return ans;
}

struct AC_Automation
{
    int next[MAX_NODE][CHILD_NUM];
    int fail[MAX_NODE];
    int end[MAX_NODE];
    int root, L;

    int newnode()
    {
        for (int i = 0; i < CHILD_NUM; ++i)
        {
            next[L][i] = -1;
        }
        end[L++] = 0;
        return L - 1;
    }

    void init()
    {
        L = 0;
        root = newnode();
    }

    void Build_Trie(char buf[])
    {
        int len = strlen(buf);
        int now = root;
        for (int i = 0; i < len; ++i)
        {
            if (next[now][buf[i] - 'a'] == -1)
            {
                next[now][buf[i] - 'a'] = newnode();
            }
            now = next[now][buf[i] - 'a'];
        }
        end[now] = 1;
    }

    void Build_AC()
    {
        queue <int> qu;
        fail[root] = root;
        for (int i = 0; i < CHILD_NUM; ++i)
        {
            if (next[root][i] == -1)
            {
                next[root][i] = root;
            }
            else
            {
                fail[next[root][i]] = root;
                qu.push(next[root][i]);
            }
        }
        while (!qu.empty())
        {
            int now = qu.front();
            qu.pop();
            if (end[fail[now]])
            {
                end[now] = 1;
            }
            for (int i = 0; i < CHILD_NUM; ++i)
            {
                if (next[now][i] == -1)
                {
                    next[now][i] = next[fail[now]][i];
                }
                else
                {
                    fail[next[now][i]] = next[fail[now]][i];
                    qu.push(next[now][i]);
                }

            }
        }
    }

    void solve (int n)
    {
        unsigned long long ans = 0;
        MARTIX tmp;
        tmp.mat[0][0] = 26;
        tmp.mat[0][1] = 1;
        tmp.mat[1][0] = 0;
        tmp.mat[1][1] = 1;
        tmp = martix_pow(tmp, n, 2);
        ans = tmp.mat[0][0] + tmp.mat[0][1] - 1;
        for (int i = 0; i < L; ++i)
        {
            for (int j = 0; j < L; ++j)
            {
                A.mat[i][j] = 0;
                E.mat[i][j] = (i == j);
            }
        }
        for (int i = 0; i < L; ++i)
        {
            if (end[i])
            {
                continue;
            }
            for (int j = 0; j < CHILD_NUM; ++j)
            {
                if (!end[next[i][j]])
                {
                    ++A.mat[i][next[i][j]];
                }
            }
        }
        MARTIX res = work(n, L);
        for (int i = 0; i < L; ++i)
        {
            ans -= res.mat[0][i];
        }
        printf("%llu\n", ans);
    }
}AC;

char buf[15];

int main()
{
    int m, n;
    while (~scanf("%d%d", &m, &n))
    {
        AC.init();
        for (int i = 1; i <= m; ++i)
        {
            scanf("%s", buf);
            AC.Build_Trie(buf);
        }
        AC.Build_AC();
        AC.solve(n);
    }
    return 0;
}