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模板 - BM算法

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN = 3e5 + 51, MOD = 998244353, G = 3, INVG = 332748118;
int exponent, fd, cnt = 1, limit = -1, rres, ptr;
int rev[MAXN], f[MAXN], g[MAXN], tmp[MAXN], tmp2[MAXN], tmp3[MAXN], tbm[MAXN];
int res[MAXN], base[MAXN], fail[MAXN];
ll delta[MAXN];

inline int read() {
    int num = 0;
    bool neg = false;
    char ch = getchar();
    while(!isdigit(ch) && ch != '-')
        ch = getchar();
    if(ch == '-')
        neg = true, ch = getchar();
    while(isdigit(ch))
        num = (num << 3) + (num << 1) + (ch - '0'), ch = getchar();
    return neg ? -num : num;
}

inline int qpow(ll x, int n) {
    ll res = 1;
    for(; n; x = x * x % MOD, n >>= 1)
        if(n & 1)
            res = res * x % MOD;
    return res;
}

inline void NTT(int *cp, int cnt, int inv) {
    int cur = 0, res = 0;
    for(int i = 0; i < cnt; i++)
        if(i < rev[i])
            swap(cp[i], cp[rev[i]]);

    for(int i = 2; i <= cnt; i <<= 1) {
        cur = i >> 1, res = qpow(inv == 1 ? G : INVG, (MOD - 1) / i);
        for(int *p = cp; p != cp + cnt; p += i) {
            ll w = 1;
            for(int j = 0; j < cur; j++) {
                int t = w * p[j + cur] % MOD, t2 = p[j];
                p[j + cur] = (t2 - t + MOD) % MOD, p[j] = (t2 + t) % MOD;
                w = w * res % MOD;
            }
        }
    }

    if(inv == -1) {
        int invl = qpow(cnt, MOD - 2);
        for(int i = 0; i <= cnt; i++)
            cp[i] = (ll) cp[i] * invl % MOD;
    }
}

inline void inv(int fd, int *f, int *res) {
    static int tmp[MAXN];
    if(fd == 1) {
        res[0] = qpow(f[0], MOD - 2);
        return;
    }
    inv((fd + 1) >> 1, f, res);
    int cnt = 1, limit = -1;
    while(cnt < (fd << 1))
        cnt <<= 1, limit++;
    for(int i = 0; i < cnt; i++) {
        tmp[i] = i < fd ? f[i] : 0;
        rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << limit);
    }
    NTT(tmp, cnt, 1), NTT(res, cnt, 1);
    for(int i = 0; i < cnt; i++)
        res[i] = 1ll * (2 - 1ll * tmp[i] * res[i] % MOD + MOD) % MOD * res[i] % MOD;
    NTT(res, cnt, -1);
    for(int i = fd; i < cnt; i++)
        res[i] = 0;
}

inline void mod(int *f) {
    static int tmp[MAXN], q[MAXN];
    int deg = fd << 1;
    while(!f[--deg]);
    if(deg < fd)
        return;

    for(int i = 0; i < cnt; i++)
        tmp[i] = i <= deg ? f[i] : 0;
    reverse(tmp, tmp + 1 + deg);
    for(int i = deg + 1 - fd; i <= deg; tmp[i] = 0, i++);
    NTT(tmp, cnt, 1);
    for(int i = 0; i < cnt; q[i] = (ll)tmp[i] * tmp3[i] % MOD, i++);
    NTT(q, cnt, -1);
    for(int i = 0; i < cnt; tmp[i] = 0, q[i] = i <= deg - fd ? q[i] : 0, i++);
    reverse(q, q + 1 + deg - fd), NTT(q, cnt, 1);
    for(int i = 0; i < cnt; tmp[i] = (ll)q[i] * g[i] % MOD, i++);
    NTT(tmp, cnt, -1);
    for(int i = 0; i < fd; f[i] = (f[i] - tmp[i] + MOD) % MOD, i++);
    for(int i = 0; i < cnt; q[i] = tmp[i] = 0, f[i] = i < fd ? f[i] : 0, i++);
}

vector<ll>bmf[MAXN];
inline void BerlekampMassey(int length, int *base, int *res) {
    int cur = 0;
    for(int i = 1; i <= length; i++) {
        ll curr = base[i];
        for(int j = 0; j < bmf[cur].size(); j++) {
            curr = (curr - (ll)base[i - j - 1] * bmf[cur][j] % MOD) % MOD;
        }
        delta[i] = curr;
        if(!delta[i]) {
            continue;
        }
        fail[cur] = i;
        if(!cur) {
            bmf[++cur].resize(i), delta[i] = base[i];
            continue;
        }
        int id = cur - 1, x = bmf[id].size() - fail[id] + i;
        for(int j = 0; j < cur; j++) {
            if(i - fail[j] + bmf[j].size() < x) {
                id = j, x = i - fail[j] + bmf[j].size();
            }
        }
        bmf[cur + 1] = bmf[cur], cur++;
        while(bmf[cur].size() < x) {
            bmf[cur].push_back(0);
        }
        ll mul = (ll)delta[i] * qpow(delta[fail[id]], MOD - 2) % MOD;
        bmf[cur][i - fail[id] - 1] = (ll)(bmf[cur][i - fail[id] - 1] + mul) % MOD;
        for(int j = 0; j < bmf[id].size(); j++) {
            int t = (ll)mul * bmf[id][j] % MOD;
            bmf[cur][i - fail[id] + j] = (bmf[cur][i - fail[id] + j] - t + MOD) % MOD;
        }
    }
    ptr = cur;
    for(int i = 0; i < bmf[cur].size(); i++) {
        res[i + 1] = (bmf[cur][i] % MOD + MOD) % MOD;
    }
}
int main() {
#ifdef Yinku
    freopen("Yinku.in", "r", stdin);
#endif // Yinku
    fd = read(), exponent = read();
    for(int i = 0; i < fd; i++)
        tbm[i + 1] = f[i] = (read() + MOD) % MOD;

    BerlekampMassey(fd, tbm, tmp);
    for(int i = 1, ci = bmf[ptr].size(); i <= ci; i++)
        printf("%d%c", tmp[i], " \n"[i == ci]);

    for(int i = 1; i <= fd; g[fd - i] = MOD - tmp[i], i++);
    g[fd] = 1;
    for(int i = 0; i <= fd; i++)
        tmp2[i] = g[i];

    reverse(tmp2, tmp2 + 1 + fd), inv(fd << 1, tmp2, tmp3);
    for(int i = 0; i <= fd; i++)
        tmp2[i] = 0;

    while(cnt < (fd << 2))
        cnt <<= 1, limit++;

    for(int i = 0; i < cnt; i++)
        rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << limit);

    NTT(g, cnt, 1), NTT(tmp3, cnt, 1), base[1] = res[0] = 1;
    while(exponent) {
        if(exponent & 1) {
            NTT(res, cnt, 1), NTT(base, cnt, 1);
            for(int i = 0; i < cnt; i++)
                res[i] = (ll)res[i] * base[i] % MOD;
            NTT(res, cnt, -1), NTT(base, cnt, -1), mod(res);
        }
        NTT(base, cnt, 1);
        for(int i = 0; i < cnt; i++)
            base[i] = (ll)base[i] * base[i] % MOD;
        NTT(base, cnt, -1), mod(base), exponent >>= 1;
    }
    for(int i = 0; i < fd; i++)
        rres = (rres + (ll)res[i] * f[i] % MOD) % MOD;
    printf("%d\n", rres);
}
posted @ 2019-10-27 16:16  Inko  阅读(...)  评论(...编辑  收藏