結果
問題 | No.1289 RNG and OR |
ユーザー | hitonanode |
提出日時 | 2020-11-13 21:43:36 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 101 ms / 2,000 ms |
コード長 | 10,299 bytes |
コンパイル時間 | 1,951 ms |
コンパイル使用メモリ | 207,368 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-07-22 20:36:38 |
合計ジャッジ時間 | 3,259 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
6,812 KB |
testcase_01 | AC | 2 ms
6,940 KB |
testcase_02 | AC | 2 ms
6,940 KB |
testcase_03 | AC | 1 ms
6,940 KB |
testcase_04 | AC | 2 ms
6,940 KB |
testcase_05 | AC | 2 ms
6,940 KB |
testcase_06 | AC | 2 ms
6,944 KB |
testcase_07 | AC | 1 ms
6,940 KB |
testcase_08 | AC | 2 ms
6,940 KB |
testcase_09 | AC | 1 ms
6,940 KB |
testcase_10 | AC | 1 ms
6,940 KB |
testcase_11 | AC | 2 ms
6,940 KB |
testcase_12 | AC | 2 ms
6,940 KB |
testcase_13 | AC | 2 ms
6,940 KB |
testcase_14 | AC | 3 ms
6,940 KB |
testcase_15 | AC | 5 ms
6,944 KB |
testcase_16 | AC | 8 ms
6,944 KB |
testcase_17 | AC | 14 ms
6,940 KB |
testcase_18 | AC | 26 ms
6,944 KB |
testcase_19 | AC | 51 ms
6,940 KB |
testcase_20 | AC | 101 ms
6,944 KB |
ソースコード
#include <bits/stdc++.h>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); returnvec; }template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }#if __cplusplus >= 201703Ltemplate <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); returnis; }template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);},tpl); return os; }#endiftemplate <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ',';os << '}'; return os; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os;}template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')';return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp)os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCAL#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl#else#define dbg(x) {}#endiftemplate <int mod>struct ModInt{using lint = long long;static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&](){std::set<int> fac;int v = mod - 1;for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}int val;constexpr ModInt() : val(0) {}constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }constexpr ModInt(lint v) { _setval(v % mod + mod); }explicit operator bool() const { return val != 0; }constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }constexpr bool operator==(const ModInt &x) const { return val == x.val; }constexpr bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }constexpr lint power(lint n) const {lint ans = 1, tmp = this->val;while (n) {if (n & 1) ans = ans * tmp % mod;tmp = tmp * tmp % mod;n /= 2;}return ans;}constexpr lint inv() const { return this->power(mod - 2); }constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }inline ModInt fac() const {static std::vector<ModInt> facs;int l0 = facs.size();if (l0 > this->val) return facs[this->val];facs.resize(this->val + 1);for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));return facs[this->val];}ModInt doublefac() const {lint k = (this->val + 1) / 2;if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();else return ModInt(k).fac() * ModInt(2).power(k);}ModInt nCr(const ModInt &r) const {if (this->val < r.val) return ModInt(0);return this->fac() / ((*this - r).fac() * r.fac());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (power((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.power((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.power(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, mod - x.val));}};constexpr lint MOD = 998244353;using mint = ModInt<MOD>;// Fast Walsh-Hadamard transform// Tutorials: <https://codeforces.com/blog/entry/71899>// <https://csacademy.com/blog/fast-fourier-transform-and-variations-of-it>template <typename T, typename F>void walsh_hadamard(std::vector<T>& seq, F f){const int n = seq.size();assert(__builtin_popcount(n) == 1);for (int w = 1; w < n; w *= 2) {for (int i = 0; i < n; i += w * 2) {for (int j = 0; j < w; j++) {f(seq[i + j], seq[i + j + w]);}}}}template <typename T, typename F1, typename F2>std::vector<T> walsh_hadamard_conv(std::vector<T> x, std::vector<T> y, F1 f, F2 finv){const int n = x.size();assert(__builtin_popcount(n) == 1);assert(x.size() == y.size());if (x == y) {walsh_hadamard(x, f), y = x;} else {walsh_hadamard(x, f), walsh_hadamard(y, f);}for (size_t i = 0; i < x.size(); i++) {x[i] *= y[i];}walsh_hadamard(x, finv);return x;}// bitwise or convolution// ret[i] = \sum_{(j | k) == i} x[j] * y[k]template <typename T>std::vector<T> orconv(std::vector<T> x, std::vector<T> y){return walsh_hadamard_conv(x, y, [](T& lo, T& hi) { hi += lo; }, [](T& lo, T& hi) { hi -= lo; });}int main(){int N;cin >> N;vector<mint> trans(1 << N);cin >> trans;mint S = accumulate(ALL(trans), mint(0));REP(i, 1 << N) {trans[i] /= S;trans[i] *= -1;}trans[0] += 1;using T = mint;auto conv = [](T& lo, T& hi) { hi += lo; };auto iconv = [](T& lo, T& hi) { hi -= lo; };walsh_hadamard(trans, conv);REP(i, trans.size()) {trans[i] = 1 / trans[i];}vector<mint> dp(1 << N);dp[0] = 1;walsh_hadamard(dp, conv);REP(i, dp.size()) {dp[i] *= trans[i];}walsh_hadamard(dp, iconv);cout << accumulate(ALL(dp) - 1, mint(0)) << '\n';}