結果
| 問題 | No.1933 ABC String |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2022-05-07 12:05:18 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 102 ms / 2,000 ms |
| コード長 | 10,356 bytes |
| コンパイル時間 | 2,370 ms |
| コンパイル使用メモリ | 208,492 KB |
| 最終ジャッジ日時 | 2025-01-29 04:43:15 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 36 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int &p) const { return x == p.x; }
bool operator!=(const Mod_Int &p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
using mint = Mod_Int<MOD>;
template <typename T>
struct Combination {
static vector<T> _fac, _ifac;
Combination() {}
static void init(int n) {
_fac.resize(n + 1), _ifac.resize(n + 1);
_fac[0] = 1;
for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
_ifac[n] = _fac[n].inverse();
for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
}
static T fac(int k) { return _fac[k]; }
static T ifac(int k) { return _ifac[k]; }
static T inv(int k) { return fac(k - 1) * ifac(k); }
static T P(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k);
}
static T C(int n, int k) {
if (n == -1 && (k == 0 || k == -1)) return 1;
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k) * ifac(k);
}
static T H(int n, int k) { // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
static T second_stirling_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数
T ret = 0;
for (int i = 0; i <= k; i++) {
T tmp = C(k, i) * T(i).pow(n);
ret += ((k - i) & 1) ? -tmp : tmp;
}
return ret * ifac(k);
}
static T bell_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数
if (n == 0) return 1;
k = min(k, n);
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1) {
pref[i] = pref[i - 1] - ifac(i);
} else {
pref[i] = pref[i - 1] + ifac(i);
}
}
T ret = 0;
for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
return ret;
}
};
template <typename T>
vector<T> Combination<T>::_fac = vector<T>();
template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();
using comb = Combination<mint>;
template <typename T>
struct Number_Theoretic_Transform {
static int max_base;
static T root;
static vector<T> r, ir;
Number_Theoretic_Transform() {}
static void init() {
if (!r.empty()) return;
int mod = T::get_mod();
int tmp = mod - 1;
root = 2;
while (root.pow(tmp >> 1) == 1) root++;
max_base = 0;
while (tmp % 2 == 0) tmp >>= 1, max_base++;
r.resize(max_base), ir.resize(max_base);
for (int i = 0; i < max_base; i++) {
r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根
ir[i] = r[i].inverse(); // ir[i] := 1/r[i]
}
}
static void ntt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = n; k >>= 1;) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = w * a[j];
a[i] = x + y, a[j] = x - y;
}
w *= r[__builtin_ctz(++t)];
}
}
}
static void intt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = 1; k < n; k <<= 1) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = a[j];
a[i] = x + y, a[j] = w * (x - y);
}
w *= ir[__builtin_ctz(++t)];
}
}
T inv = T(n).inverse();
for (auto &e : a) e *= inv;
}
static vector<T> convolve(vector<T> a, vector<T> b) {
if (a.empty() || b.empty()) return {};
int k = (int)a.size() + (int)b.size() - 1, n = 1;
while (n < k) n <<= 1;
a.resize(n), b.resize(n);
ntt(a), ntt(b);
for (int i = 0; i < n; i++) a[i] *= b[i];
intt(a), a.resize(k);
return a;
}
};
template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;
template <typename T>
T Number_Theoretic_Transform<T>::root = T();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();
using NTT = Number_Theoretic_Transform<mint>;
int main() {
string S;
cin >> S;
vector<int> a(3, 0), b(3, 0);
rep(i, 3) cin >> a[i];
each(e, S) b[e - 'a']++;
comb::init(1000000);
vector<vector<mint>> f(2);
rep(i, 2) {
f[i].assign(a[i] - b[i] + 1, 0);
rep(j, a[i] - b[i] + 1) f[i][j] = comb::ifac(a[i] - b[i] - j) * comb::C(b[i ^ 1] + j - 1, j);
// print(f[i]);
}
auto g = NTT::convolve(f[0], f[1]);
int K = sz(g);
// print(g);
int N = a[0] + a[1];
mint ans = 0;
vector<mint> s(N + 1, 0);
rep(i, N + 1) s[i] = comb::C(b[2] + i - 1, i) * comb::C(a[2] - b[2] + N - i, N - i);
rep2(i, 1, N) s[i] += s[i - 1];
rep(i, K) {
int L = b[0] + b[1] + i, R = a[0] + a[1] - L;
g[i] *= comb::fac(R);
// rep2(j, b[2], a[2]) {
// mint tmp = comb::C(R + j, j) * comb::C(L - 1 + a[2] - j, a[2] - j);
// ans += tmp * g[i];
// }
ans += s[R] * g[i];
}
cout << ans << '\n';
}