QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#507946#7634. CardspandapythonerAC ✓8331ms291648kbC++2314.8kb2024-08-07 00:31:492024-08-07 00:31:49

Judging History

你现在查看的是最新测评结果

  • [2024-08-07 00:31:49]
  • 评测
  • 测评结果:AC
  • 用时:8331ms
  • 内存:291648kb
  • [2024-08-07 00:31:49]
  • 提交

answer

#include <bits/stdc++.h>

using namespace std;


using ll = long long;

#define flt double
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define rep(i, n) for(int i = 0; i < n; i += 1)
#define len(a) ((int)(a).size())


const ll inf = 1e18;
mt19937 rnd(234);


const ll mod = 998244353;

ll bin_pow(ll x, ll n) {
    ll rs = 1;
    for (ll i = 1, a = x; i <= n; i *= 2, a = a * a % mod)
        if (n & i) rs = rs * a % mod;
    return rs;
}

ll inv(ll x) {
    return bin_pow(x, mod - 2);
}

namespace fft {
    int mxpw;
    int mxn;
    ll w;

    void build_w() {
        ll phi = mod - 1;
        ll f = phi;
        vector<ll> p;
        for (ll i = 2; i * i <= f; i += 1) {
            if (f % i == 0) {
                p.push_back(i);
                while (f % i == 0) {
                    f /= i;
                }
            }
        }
        if (f > 1) {
            p.push_back(f);
        }
        for (int i = 1; i < mod; i += 1) {
            bool ok = true;
            for (auto q : p) {
                if (bin_pow(i, phi / q) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                w = bin_pow(i, phi / (1 << mxpw));
                break;
            }
        }
    }

    vector<ll> rvx;

    void build_rvx(int n) {
        rvx.resize(n + 1);
        for (int i = 1; i <= n; i += 1) {
            rvx[i] = inv(i);
        }
    }

    vector<ll> rvi, wpws;

    void build(int _mxpw) {
        mxpw = _mxpw;
        mxn = (1 << mxpw);
        build_w();
        int n = (1 << mxpw);
        rvi.resize(n);
        rvi[0] = 0;
        for (int i = 1; i < n; i += 1) {
            rvi[i] = (rvi[i >> 1] >> 1);
            if (i & 1) {
                rvi[i] += (1 << (mxpw - 1));
            }
        }
        wpws.resize(n + 1);
        wpws[0] = 1;
        for (int i = 1; i <= n; i += 1) {
            wpws[i] = (wpws[i - 1] * w) % mod;
        }
        build_rvx(mxn);
    }

    void fft(vector<ll>& a, int nk) {
        int n = (1 << nk);
        for (int i = 0; i < n; i += 1) {
            int mrv = (rvi[i] >> (mxpw - nk));
            if (mrv < i) {
                swap(a[mrv], a[i]);
            }
        }
        for (int ln = 1; ln < n; ln *= 2) {
            int ln2 = ln + ln;
            for (int i = 0; i < n; i += ln2) {
                for (int j = 0; j < ln; j += 1) {
                    ll mw = wpws[mxn / ln2 * j];
                    int u = i + j;
                    int v = u + ln;
                    ll y = a[v] * mw % mod;
                    a[v] = a[u] - y;
                    if (a[v] < 0) {
                        a[v] += mod;
                    }
                    a[u] += y;
                    if (a[u] >= mod) {
                        a[u] -= mod;
                    }
                }
            }
        }
    }

    void rev_fft(vector<ll>& a, int nk) {
        int n = (1 << nk);
        fft(a, nk);
        ll rvn = inv(n);
        reverse(a.begin() + 1, a.end());
        for (int i = 0; i < n; i += 1) {
            a[i] = (a[i] * rvn) % mod;
        }
    }

    vector<ll> square(vector<ll> a) {
        int nk = 0;
        while ((1 << nk) < (int)a.size() + (int)a.size() - 1) {
            nk += 1;
        }
        int n = (1 << nk);
        a.resize(n, 0);
        fft(a, nk);
        for (int i = 0; i < n; i += 1) {
            a[i] = (a[i] * a[i]) % mod;
        }
        rev_fft(a, nk);
        while (!a.empty() && a.back() == 0) {
            a.pop_back();
        }
        return a;
    }

    vector<ll> mul(vector<ll> a, vector<ll> b) {
        int nk = 0;
        while ((1 << nk) < (int)a.size() + (int)b.size() - 1) {
            nk += 1;
        }
        int n = (1 << nk);
        a.resize(n, 0);
        b.resize(n, 0);
        fft(a, nk);
        fft(b, nk);
        for (int i = 0; i < n; i += 1) {
            a[i] = (a[i] * b[i]) % mod;
        }
        rev_fft(a, nk);
        while (!a.empty() && a.back() == 0) {
            a.pop_back();
        }
        return a;
    }

    void add_inplace(vector<ll>& a, const vector<ll>& b, ll k = 1) {
        a.resize(max(a.size(), b.size()), 0);
        for (int i = 0; i < (int)b.size(); i += 1) {
            a[i] = (a[i] + b[i] * k) % mod;
        }
    }

    vector<ll> add(vector<ll> a, const vector<ll>& b, ll k = 1) {
        a.resize(max(a.size(), b.size()), 0);
        for (int i = 0; i < (int)b.size(); i += 1) {
            a[i] = (a[i] + b[i] * k) % mod;
        }
        return a;
    }

    vector<ll> sub(vector<ll> a, const vector<ll>& b, ll k = 1) {
        a.resize(max(a.size(), b.size()), 0);
        for (int i = 0; i < (int)b.size(); i += 1) {
            a[i] = (a[i] + mod - b[i] * k % mod) % mod;
        }
        return a;
    }

    vector<ll> replace_x_slow(vector<ll>& a, const vector<ll>& b) {
        vector<ll> rs = {};
        vector<ll> bpw = { 1 };
        for (int i = 0; i < (int)a.size(); i += 1) {
            if (i > 0) {
                bpw = mul(bpw, b);
            }
            add_inplace(rs, bpw, a[i]);
        }
        return rs;
    }

    vector<ll> replace_x(vector<ll>& a, const vector<ll>& b) {
        vector<ll> rs = {};
        vector<ll> bpw = b;
        int n = a.size();
        vector<vector<ll>> d(n);
        for (int i = 0; i < n; i += 1) {
            d[i] = { a[i] };
        }
        while (n > 1) {
            int m = (n + 1) / 2;
            vector<vector<ll>> nd(m);
            for (int i = 0; i < n; i += 1) {
                if (i % 2 == 0) {
                    nd[i / 2] = d[i];
                } else {
                    add_inplace(nd[i / 2], mul(d[i], bpw));
                }
            }
            n = m;
            d.swap(nd);
            if (n != 1) {
                bpw = square(bpw);
            }
        }
        return d[0];
    }

    vector<ll> shift_x(vector<ll> a, ll t) {
        if (a.empty()) {
            return {};
        }
        int n = (int)a.size() - 1;
        vector<ll> f(n + 1), rf(n + 1);
        f[0] = rf[0] = 1;
        for (int i = 1; i <= n; i += 1) {
            f[i] = (f[i - 1] * i) % mod;
            rf[i] = inv(f[i]);
        }
        vector<ll> b(n + 1), c(n + 1);
        ll tpw = 1;
        for (int i = 0; i <= n; i += 1) {
            b[i] = (a[i] * tpw % mod * f[i] % mod);
            tpw = (tpw * t) % mod;
        }
        for (int i = 0; i <= n; i += 1) {
            c[n - i] = rf[i];
        }
        a = mul(b, c);
        vector<ll> d(n + 1);
        ll rvt = inv(t);
        ll rvt_pw = 1;
        for (int i = 0; i <= n; i += 1) {
            d[i] = rvt_pw * rf[i] % mod * a[i + n] % mod;
            rvt_pw = (rvt_pw * rvt) % mod;
        }
        return d;
    }

    vector<ll> rev_polynom(const vector<ll>& a, int n) {
        int sz = a.size();
        vector<ll> b = { inv(a[0]) };
        int m = 1;
        int mk = 0;
        while (m < n) {
            int m2 = m + m;
            int m4 = m2 + m2;
            b.resize(m4);
            fft(b, mk + 2);
            vector<ll> nb(m4);
            for (int i = 0; i < sz && i < m2; i += 1) {
                nb[i] = a[i];
            }
            fft(nb, mk + 2);
            for (int i = 0; i < m4; i += 1) {
                nb[i] = (2 * b[i] - nb[i] * b[i] % mod * b[i]) % mod;
                if (nb[i] < 0) {
                    nb[i] += mod;
                }
            }
            rev_fft(nb, mk + 2);
            nb.resize(m2);
            b.swap(nb);
            m = m2;
            mk += 1;
        }
        b.resize(n);
        return b;
    }

    vector<ll> square_root(const vector<ll>& a, int n) {
        ll sz = a.size();
        ll rv2 = inv(2);
        vector<ll> b = { 1 };
        int m = 1;
        while (m < n) {
            ll m2 = m + m;
            vector<ll> rvb = rev_polynom(b, m2);
            vector<ll> ab(m2);
            for (int i = 0; i < m2 && i < sz; i += 1) {
                ab[i] = a[i];
            }
            ab = mul(ab, rvb);
            ab.resize(m2);
            b.resize(m2);
            for (int i = 0; i < m2; i += 1) {
                b[i] = (rv2 * ((b[i] + ab[i]) % mod)) % mod;
            }
            m = m2;
        }
        b.resize(n);
        return b;
    }

    vector<ll> derivative(vector<ll> a) {
        int n = a.size();
        if (n == 0) {
            return {};
        }
        for (int i = 0; i + 1 < n; i += 1) {
            a[i] = (a[i + 1] * (i + 1)) % mod;
        }
        a.resize(n - 1);
        return a;
    }

    vector<ll> integrate(vector<ll> a) {
        int n = a.size();
        a.resize(n + 1);
        for (int i = n; i > 0; i -= 1) {
            a[i] = (a[i - 1] * rvx[i]) % mod;
        }
        a[0] = 0;
        return a;
    }

    vector<ll> sin_polynomial(int n) {
        vector<ll> a(n, 0);
        ll fct = 1;
        for (int i = 0; i < n; i += 1) {
            if (i != 0) {
                fct = (fct * i) % mod;
            }
            if (i % 2 == 1) {
                int sign = 1;
                if ((i / 2) % 2 == 1) {
                    sign = -1;
                }
                a[i] = (mod + sign * inv(fct)) % mod;
            }
        }
        return a;
    }

    vector<ll> cos_polynomial(int n) {
        vector<ll> a(n, 0);
        ll fct = 1;
        for (int i = 0; i < n; i += 1) {
            if (i != 0) {
                fct = (fct * i) % mod;
            }
            if (i % 2 == 0) {
                int sign = 1;
                if ((i / 2) % 2 == 1) {
                    sign = -1;
                }
                a[i] = (mod + sign * inv(fct)) % mod;
            }
        }
        return a;
    }

    vector<ll> super_cos_polynomial(int n, int k) {
        vector<ll> a(n, 0);
        ll fct = 1;
        for (int i = 0; i < n; i += 1) {
            if (i != 0) {
                fct = (fct * i) % mod;
            }
            if (i % k == 0) {
                int sign = 1;
                if ((i / k) % 2 == 1) {
                    sign = -1;
                }
                a[i] = (mod + sign * inv(fct)) % mod;
            }
        }
        return a;
    }

    vector<ll> logarithm(const vector<ll>& a, int n) {
        if (n == 0) {
            return {};
        }
        vector<ll> b = integrate(mul(derivative(a), rev_polynom(a, n)));
        b.resize(n);
        return b;
    }

    vector<ll> exponent(const vector<ll>& a, int n) {
        vector<ll> b = { 1 };
        int m = 1;
        while (m < n) {
            int m2 = m + m;
            vector<ll> t = logarithm(b, m2);
            for (int i = 0; i < m2 && i < (int)a.size(); i += 1) {
                t[i] = (t[i] - a[i]);
                if (t[i] < 0) {
                    t[i] += mod;
                }
            }
            vector<ll> q = fft::mul(t, b);
            q.resize(m2);
            b.resize(m2);
            for (int i = 0; i < m2; i += 1) {
                b[i] -= q[i];
                if (b[i] < 0) {
                    b[i] += mod;
                }
            }
            m = m2;
        }
        b.resize(n);
        return b;
    }

    vector<ll> solve_differential(const vector<ll>& a, const vector<ll>& b, int n) {
        vector<ll> e = exponent(integrate(a), n);
        vector<ll> result = mul(e, integrate(mul(b, rev_polynom(e, n))));
        result.resize(n);
        return result;
    }

    vector<ll> pure_exponent(int n, ll k = 1) {
        if (n == 0) {
            return {};
        }
        k %= mod;
        if (k < 0) {
            k += mod;
        }
        vector<ll> rs(n);
        rs[0] = 1;
        ll rv_fct = 1;
        for (int i = 1; i < n; i += 1) {
            rv_fct = (rv_fct * rvx[i]) % mod * k % mod;
            rs[i] = rv_fct;
        }
        return rs;
    }
}  // namespace fft



vector<ll> bin_pow(vector<ll> a, ll n) {
    if (n == 0) {
        return { 1 };
    }
    if (n == 1) {
        return a;
    }
    auto x = bin_pow(a, n / 2);
    x = fft::mul(x, x);
    if (n & 1) {
        x = fft::mul(x, a);
    }
    return x;
}


const int block_len = 200;
int dp[2 * block_len + 1][block_len + 1][4 * block_len + 1];


int32_t main() {
    fft::build(20);
    cerr << sizeof(dp) / 1e6 << "\n";
    memset(dp, 0, sizeof(dp));
    if (1) {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout.tie(0);
    }
    int n, m;
    cin >> n >> m;
    vector<ll> a(5);
    rep(i, 5) cin >> a[i];
    ll sum = 0;
    rep(i, 5) sum += a[i];
    sum %= mod;
    rep(i, 5) a[i] = a[i] * inv(sum) % mod;
    rep(start, 2 * block_len + 1) {
        dp[start][0][start] = 1;
        rep(i, block_len) {
            int l = max(0, start - 2 * i);
            int r = min(4 * block_len, start + 2 * i);
            for (int old_val = l; old_val <= r; old_val += 1) {
                rep(t, 5) {
                    if (old_val + (t - 2) >= 0)
                        dp[start][i + 1][old_val + (t - 2)] = (dp[start][i + 1][old_val + (t - 2)] + dp[start][i][old_val] * ll(a[t])) % mod;
                }
            }
        }
    }
    vector<ll> cur(n + 1, 0);
    cur[n] = 1;
    ll result = 0;
    for (int l = 0; l < m; l += block_len) {
        int r = min(m - 1, l + block_len - 1);
        int len = (r - l + 1);
        vector<ll> ncur(4 * len + 1, 0);
        vector<ll> poly;
        for (int i = 2 * len; i < len(cur); i += 1) {
            poly.push_back(cur[i]);
        }
        if (!poly.empty()) {
            auto apw = bin_pow(a, len);
            vector<ll> new_poly = fft::mul(poly, apw);
            ncur.resize(max(len(ncur), len(new_poly)));
            rep(i, len(new_poly)) {
                ncur[i] += new_poly[i];
                if (ncur[i] >= mod) {
                    ncur[i] -= mod;
                }
            }
        }
        rep(start, min(2 * len, len(cur))) {
            int tl = max(0, start - 2 * len);
            int tr = min(4 * len, start + 2 * len);
            for (int i = tl; i <= tr; i += 1) {
                ncur[i] = (ncur[i] + dp[start][len][i] * cur[start]) % mod;
            }
        }

        cur.swap(ncur);
        int dist = m - (r + 1);
        while (!cur.empty() and len(cur) - 1 - 2 * dist >= 0) {
            result += cur.back();
            if (result >= mod) result -= mod;
            cur.pop_back();
        }
        while (!cur.empty() and cur.back() == 0) {
            cur.pop_back();
        }
    }
    rep(i, len(cur)) {
        result += cur[i];
        if (result >= mod) {
            result -= mod;
        }
    }
    cout << result << "\n";
    return 0;
}

这程序好像有点Bug,我给组数据试试?

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 336ms
memory: 280064kb

input:

1 1
1 1 1 1 1

output:

399297742

result:

ok 1 number(s): "399297742"

Test #2:

score: 0
Accepted
time: 7892ms
memory: 291648kb

input:

100000 100000
1234 4567 7890 4321 54321

output:

348074135

result:

ok 1 number(s): "348074135"

Test #3:

score: 0
Accepted
time: 8309ms
memory: 291452kb

input:

100000 100000
1 2 3 4 5

output:

639188342

result:

ok 1 number(s): "639188342"

Test #4:

score: 0
Accepted
time: 8306ms
memory: 291360kb

input:

100000 100000
5 4 3 2 1

output:

211669278

result:

ok 1 number(s): "211669278"

Test #5:

score: 0
Accepted
time: 339ms
memory: 280028kb

input:

0 0
1 1 1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #6:

score: 0
Accepted
time: 1429ms
memory: 282968kb

input:

1 50000
1 1 1 1 1

output:

548880636

result:

ok 1 number(s): "548880636"

Test #7:

score: 0
Accepted
time: 356ms
memory: 282032kb

input:

50000 1
1 1 1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #8:

score: 0
Accepted
time: 7003ms
memory: 289628kb

input:

100000 100000
234 666 7655 12234 0

output:

45268602

result:

ok 1 number(s): "45268602"

Test #9:

score: 0
Accepted
time: 8331ms
memory: 291452kb

input:

99999 99999
12345 54332 12345 65432 34444

output:

360543661

result:

ok 1 number(s): "360543661"

Test #10:

score: 0
Accepted
time: 7945ms
memory: 291564kb

input:

99998 99998
1 1 1 1 1

output:

602326230

result:

ok 1 number(s): "602326230"

Test #11:

score: 0
Accepted
time: 8230ms
memory: 291428kb

input:

99998 99997
1 1 1 1 1

output:

159752985

result:

ok 1 number(s): "159752985"

Test #12:

score: 0
Accepted
time: 7921ms
memory: 291572kb

input:

99997 100000
1 2 3 4 5

output:

139603712

result:

ok 1 number(s): "139603712"

Test #13:

score: 0
Accepted
time: 8314ms
memory: 291492kb

input:

100000 99997
1 2 2 1 3232323

output:

363030953

result:

ok 1 number(s): "363030953"

Test #14:

score: 0
Accepted
time: 337ms
memory: 280308kb

input:

0 0
0 0 1 0 0

output:

1

result:

ok 1 number(s): "1"

Test #15:

score: 0
Accepted
time: 412ms
memory: 281228kb

input:

10000 10000
91095828 93770094 5303328 491263 50290308

output:

135900098

result:

ok 1 number(s): "135900098"

Test #16:

score: 0
Accepted
time: 408ms
memory: 281192kb

input:

9226 9995
62366139 253808 1929312 491263 4375669

output:

812662634

result:

ok 1 number(s): "812662634"

Test #17:

score: 0
Accepted
time: 438ms
memory: 281552kb

input:

18641 10000
1061 4359 1330 13764 16043

output:

112339046

result:

ok 1 number(s): "112339046"

Extra Test:

score: 0
Extra Test Passed