QOJ.ac
QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#507946 | #7634. Cards | pandapythoner | AC ✓ | 8331ms | 291648kb | C++23 | 14.8kb | 2024-08-07 00:31:49 | 2024-08-07 00:31:49 |
Judging History
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?
详细
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