結果

問題 No.1710 Minimum OR is X
ユーザー keijak
提出日時 2021-10-16 01:56:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 41 ms / 2,000 ms
コード長 4,626 bytes
コンパイル時間 3,891 ms
コンパイル使用メモリ 383,912 KB
最終ジャッジ日時 2025-01-25 01:29:17
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#define REP_(i, a_, b_, a, b, ...) \
for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using i64 = long long;
#include <atcoder/modint>
using Mint = atcoder::modint998244353;
std::ostream &operator<<(std::ostream &os, const Mint &m) {
return os << m.val();
}
#include <boost/multiprecision/cpp_int.hpp>
using Int = boost::multiprecision::checked_cpp_int;
namespace multip = boost::multiprecision;
template<typename T, typename U>
inline bool chmax(T &a, U b) {
return a < b and ((a = std::move(b)), true);
}
template<typename T, typename U>
inline bool chmin(T &a, U b) {
return a > b and ((a = std::move(b)), true);
}
template<typename T>
inline int ssize(const T &a) {
return (int) a.size();
}
template<class T>
inline std::ostream &print_one(const T &x, char endc) {
if constexpr (std::is_same_v<T, bool>) {
return std::cout << (x ? "Yes" : "No") << endc;
} else {
return std::cout << x << endc;
}
}
template<class T>
inline std::ostream &print(const T &x) { return print_one(x, '\n'); }
template<typename T, typename... Ts>
std::ostream &print(const T &head, Ts... tail) {
return print_one(head, ' '), print(tail...);
}
inline std::ostream &print() { return std::cout << '\n'; }
template<typename Container>
std::ostream &print_seq(const Container &a, std::string_view sep = " ",
std::string_view ends = "\n",
std::ostream &os = std::cout) {
auto b = std::begin(a), e = std::end(a);
for (auto it = std::begin(a); it != e; ++it) {
if (it != b) os << sep;
os << *it;
}
return os << ends;
}
template<typename T, typename = void>
struct is_iterable : std::false_type {};
template<typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
decltype(std::end(std::declval<T>()))>>
: std::true_type {
};
template<typename T, typename = std::enable_if_t<
is_iterable<T>::value && !std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
return print_seq(a, ", ", "", (os << "{")) << "}";
}
struct VersatileInput {
template<typename T>
operator T() const {
T x;
std::cin >> x;
return x;
}
struct Sized {
std::size_t n;
template<typename T>
operator T() const {
T x(n);
for (auto &e: x) std::cin >> e;
return x;
}
};
Sized operator()(std::size_t n) const { return {n}; }
} const in;
inline void check(bool cond, const char *message = "!ERROR!") {
if (not cond) throw std::runtime_error(message);
}
#ifdef MY_DEBUG
#include "debug_dump.hpp"
#else
#define DUMP(...)
#define cerr if(false)std::cerr
#endif
using namespace std;
template<class T = Mint>
struct Factorials {
// factorials and inverse factorials.
std::vector<T> fact, ifact;
// n: max cached value.
Factorials(int n) : fact(n + 1), ifact(n + 1) {
assert(n >= 0);
assert(n < T::mod());
fact[0] = 1;
for (int i = 1; i <= n; ++i) {
fact[i] = fact[i - 1] * i;
}
ifact[n] = fact[n].inv();
for (int i = n; i >= 1; --i) {
ifact[i - 1] = ifact[i] * i;
}
}
// Combination (nCk)
T C(int n, int k) const {
if (k < 0 || k > n) return 0;
return fact[n] * ifact[k] * ifact[n - k];
}
};
template<typename T>
std::vector<T> pow_seq(int n, int base = 2) {
assert(n >= 0 and base > 0);
std::vector<T> p(n + 1);
p[0] = 1;
for (int i = 0; i < n; ++i) {
p[i + 1] = p[i] * base;
}
return p;
}
auto solve() {
const int n = in, m = in, K = in;
string X = in;
Factorials fs(n);
auto dp = vector(2, vector(n + 1, Mint(0)));
dp[0][n] = 1;
auto pow2 = pow_seq<Mint>(n);
REP(i, m) {
if (X[i] == '1') {
REP(j, K, n + 1) {
if (dp[0][j].val() == 0) continue;
Mint q = 0;
REP(t, K) q += fs.C(j, t);
if (q.val() == 0) continue;
dp[1][j] += dp[0][j] * pow2[n - j] * q;
}
} else {
REP(j, K, n + 1) {
if (dp[0][j].val() == 0) continue;
auto q = dp[0][j] * pow2[n - j];
for (int j2 = j; j2 >= K; --j2) {
dp[1][j2] += q * fs.C(j, j2);
}
}
}
dp[0].swap(dp[1]);
dp[1].assign(n + 1, 0);
}
Mint ans;
for (int i = K; i <= n; ++i) {
ans += dp[0][i];
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false), cin.tie(nullptr);
cout << std::fixed << std::setprecision(18);
const int T = 1;//in;
REP(t, T) {
auto ans = solve();
print(ans);
}
}
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