結果

問題 No.2990 Interval XOR
ユーザー ecottea
提出日時 2024-12-16 20:23:43
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 387 ms / 2,000 ms
コード長 14,431 bytes
コンパイル時間 5,170 ms
コンパイル使用メモリ 277,272 KB
実行使用メモリ 14,576 KB
最終ジャッジ日時 2024-12-16 20:23:58
合計ジャッジ時間 13,360 ms
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
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 37
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

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9e18int -2^31 2^31 = 2e9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<1000000007>;
//using mint = modint; // mint::set_mod(m);
string mint_to_frac(mint x, int v_max = 31595) {
repi(dnm, 1, v_max) {
int num = (x * dnm).val();
if (num == 0) {
return "0";
}
if (num <= v_max) {
if (dnm == 1) return to_string(num);
return to_string(num) + "/" + to_string(dnm);
}
if (mint::mod() - num <= v_max) {
if (dnm == 1) return "-" + to_string(mint::mod() - num);
return "-" + to_string(mint::mod() - num) + "/" + to_string(dnm);
}
}
return to_string(x.val());
}
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
#ifdef _MSC_VER
inline ostream& operator<<(ostream& os, const mint& x) { os << mint_to_frac(x); return os; }
#else
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
#endif
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(...)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//: O(2^n n)
/*
* a[0..2^n)
* A[set] = Σset2 (-1)^popcount(set ∩ set2) a[set2]
* A[0..2^n)
*/
template <class T>
void hadamard(vector<T>& a) {
// verify : https://judge.yosupo.jp/problem/bitwise_xor_convolution
//
// A[0] = a[0] + a[1] + a[2] + a[3] + a[4] + a[5] + a[6] + a[7] + ...
// A[1] = a[0] - a[1] + a[2] - a[3] + a[4] - a[5] + a[6] - a[7] + ...
// A[2] = a[0] + a[1] - a[2] - a[3] + a[4] + a[5] - a[6] - a[7] + ...
// A[3] = a[0] - a[1] - a[2] + a[3] + a[4] - a[5] - a[6] + a[7] + ...
// A[4] = a[0] + a[1] + a[2] + a[3] - a[4] - a[5] - a[6] - a[7] + ...
// A[5] = a[0] - a[1] + a[2] - a[3] - a[4] + a[5] - a[6] + a[7] + ...
// A[6] = a[0] + a[1] - a[2] - a[3] - a[4] - a[5] + a[6] + a[7] + ...
// A[7] = a[0] - a[1] - a[2] + a[3] - a[4] + a[5] + a[6] - a[7] + ...
int n = msb(sz(a));
rep(i, n) repb(set, n) {
if (!(set & (1 << i))) {
T x = a[set];
T y = a[set | (1 << i)];
a[set] = x + y;
a[set + (1 << i)] = x - y;
}
}
}
//mint: O(2^n n + log(mod))
/*
* A[0..2^n)
* A[set] = Σset2 (-1)^popcount(set ∩ set2) a[set2]
* a[0..2^n)
*
* mint 2
*
*
*/
void hadamard_inv(vm& A) {
// verify : https://atcoder.jp/contests/abc265/tasks/abc265_h
hadamard(A);
// log(mod)
mint inv = mint(sz(A)).inv();
rep(i, sz(A)) A[i] *= inv;
}
vm TLE(int n, int m, vi l, vi r) {
vm f(1LL << n, 1);
rep(j, m) {
dump("--- j:", j, "---");
dump("w:", r[j] - l[j]);
vm g(1LL << n);
repi(i, l[j], r[j] - 1) g[i]++;
dump(g);
hadamard(g);
dump(g);
rep(i, 1 << n) f[i] *= g[i];
}
dump("f:"); dump(f);
hadamard_inv(f);
return f;
}
void zikken() {
int n = 4;
int N = 1 << n;
auto dump2 = [&](vm a) {
rep(b, n) {
rep(i, N) if (lsb(i) == b) cout << right << setw(2) << a[i] << " ";
cout << "|\n"[b == n - 1];
}
};
repi(k, 0, N) {
// dump("--- k:", k, "---");
vm g(N);
rep(i, k) g[i] = 1;
// dump2(g);
hadamard(g);
dump2(g);
}
exit(0);
}
/*
r\i 1 3 5 7 9 11 13 15 | 2 6 10 14 | 4 12 | 8
0 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 0
1 1 1 1 1 1 1 1 1 | 1 1 1 1 | 1 1 | 1
2 0 0 0 0 0 0 0 0 | 2 2 2 2 | 2 2 | 2
3 1 -1 1 -1 1 -1 1 -1 | 1 1 1 1 | 3 3 | 3
4 0 0 0 0 0 0 0 0 | 0 0 0 0 | 4 4 | 4
5 1 1 -1 -1 1 1 -1 -1 | 1 -1 1 -1 | 3 3 | 5
6 0 0 0 0 0 0 0 0 | 2 -2 2 -2 | 2 2 | 6
7 1 -1 -1 1 1 -1 -1 1 | 1 -1 1 -1 | 1 1 | 7
8 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 8
9 1 1 1 1 -1 -1 -1 -1 | 1 1 -1 -1 | 1 -1 | 7
10 0 0 0 0 0 0 0 0 | 2 2 -2 -2 | 2 -2 | 6
11 1 -1 1 -1 -1 1 -1 1 | 1 1 -1 -1 | 3 -3 | 5
12 0 0 0 0 0 0 0 0 | 0 0 0 0 | 4 -4 | 4
13 1 1 -1 -1 -1 -1 1 1 | 1 -1 -1 1 | 3 -3 | 3
14 0 0 0 0 0 0 0 0 | 2 -2 -2 2 | 2 -2 | 2
15 1 -1 -1 1 -1 1 1 -1 | 1 -1 -1 1 | 1 -1 | 1
16 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 0
A_r[i] = Σj∈[0..r) (-1)^popcount(i ∩ j)
*/
void zikken2() {
int n = 4;
int N = 1 << n;
cout << "r\\i";
rep(s, n) {
rep(i, N) {
if (lsb(i) == s) {
cout << right << setw(2) << i << " ";
}
}
cout << "|\n"[s == n - 1];
}
repi(r, 0, N) {
cout << right << setw(2) << r << " ";
rep(s, n) {
rep(i, N) {
if (lsb(i) == s) {
int t = ((i >> s) - 1) / 2;
int q = r / (1 << (s + 1));
int m = r % (1 << (s + 1));
int val = (popcount(t & q) & 1 ? -1 : 1) * min(m, (1 << (s + 1)) - m);
cout << right << setw(2) << val << " ";
}
}
cout << "|\n"[s == n - 1];
}
}
exit(0);
}
/*
r\i 1 3 5 7 9 11 13 15 | 2 6 10 14 | 4 12 | 8
0 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 0
1 1 1 1 1 1 1 1 1 | 1 1 1 1 | 1 1 | 1
2 0 0 0 0 0 0 0 0 | 2 2 2 2 | 2 2 | 2
3 1 -1 1 -1 1 -1 1 -1 | 1 1 1 1 | 3 3 | 3
4 0 0 0 0 0 0 0 0 | 0 0 0 0 | 4 4 | 4
5 1 1 -1 -1 1 1 -1 -1 | 1 -1 1 -1 | 3 3 | 5
6 0 0 0 0 0 0 0 0 | 2 -2 2 -2 | 2 2 | 6
7 1 -1 -1 1 1 -1 -1 1 | 1 -1 1 -1 | 1 1 | 7
8 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 8
9 1 1 1 1 -1 -1 -1 -1 | 1 1 -1 -1 | 1 -1 | 7
10 0 0 0 0 0 0 0 0 | 2 2 -2 -2 | 2 -2 | 6
11 1 -1 1 -1 -1 1 -1 1 | 1 1 -1 -1 | 3 -3 | 5
12 0 0 0 0 0 0 0 0 | 0 0 0 0 | 4 -4 | 4
13 1 1 -1 -1 -1 -1 1 1 | 1 -1 -1 1 | 3 -3 | 3
14 0 0 0 0 0 0 0 0 | 2 -2 -2 2 | 2 -2 | 2
15 1 -1 -1 1 -1 1 1 -1 | 1 -1 -1 1 | 1 -1 | 1
16 0 0 0 0 0 0 0 0 | 0 0 0 0 | 0 0 | 0
A_r[i] = Σj∈[0..r) (-1)^popcount(i ∩ j)
i = (2t+1) 2^s, r = q 2^(s+1) + m
A_r[i] = (-1)^popcount(t ∩ q) min(m, 2^(s+1)-m)
*/
vm TLE2(int n, int m, vi l, vi r) {
int N = 1 << n;
vm res(N, 1); vm sub(N, 1);
rep(j, m) res[0] *= r[j] - l[j];
rep(s, n) {
int Ns = N >> (s + 1);
vi ql(m), A(m), qr(m), B(m);
rep(j, m) {
qr[j] = r[j] / (1 << (s + 1));
ql[j] = l[j] / (1 << (s + 1));
int mr = r[j] % (1 << (s + 1));
A[j] = min(mr, (1 << (s + 1)) - mr);
int ml = l[j] % (1 << (s + 1));
B[j] = min(ml, (1 << (s + 1)) - ml);
}
rep(t, Ns) {
int i = (2 * t + 1) << s;
rep(j, m) {
int sgnA = popcount(t & qr[j]) & 1 ? -1 : 1;
int sgnB = popcount(t & ql[j]) & 1 ? -1 : 1;
res[i] *= sgnA * A[j] - sgnB * B[j];
sub[i] *= sgnB;
}
}
}
dump(res); dump(sub);
hadamard_inv(res);
return res;
}
/*
f[i] = Π(A_r[i] - A_l[i])
i = (2t+1) 2^s, r = q 2^(s+1) + m
f[i] = Π((-1)^popcount(t ∩ qr) min(mr, 2^(s+1)-mr) - (-1)^popcount(t ∩ ql) min(ml, 2^(s+1)-ml))
*/
vm TLE3(int n, int m, vi l, vi r) {
int N = 1 << n;
vm res(N, 1);
rep(j, m) res[0] *= r[j] - l[j];
rep(s, n) {
int Ns = N >> (s + 1);
vi cnt(n - s);
rep(j, m) {
int q = r[j] >> (s + 1);
repis(b, q) cnt[b]++;
}
rep(t, Ns) {
int i = (2 * t + 1) << s;
int sum = 0;
repis(b, t) sum += cnt[b];
res[i] *= sum & 1 ? -1 : 1;
}
vi q(m), A(m), B(m);
rep(j, m) {
q[j] = (r[j] ^ l[j]) / (1 << (s + 1));
int mr = r[j] % (1 << (s + 1));
A[j] = min(mr, (1 << (s + 1)) - mr);
int ml = l[j] % (1 << (s + 1));
B[j] = min(ml, (1 << (s + 1)) - ml);
}
rep(t, Ns) {
int i = (2 * t + 1) << s;
rep(j, m) {
int sgn = popcount(t & q[j]) & 1 ? -1 : 1;
res[i] *= A[j] - sgn * B[j];
}
}
}
dump(res);
hadamard_inv(res);
return res;
}
/*
f[i] = Π(A_r[i] - A_l[i])
i = (2t+1) 2^s, r = q 2^(s+1) + m
f[i] = Π(-1)^popcount(t ∩ qr) Π(min(mr, 2^(s+1)-mr) - (-1)^popcount(t ∩ (qr XOR ql)) min(ml, 2^(s+1)-ml))
= Π(-1)^popcount(t ∩ qr) Π_j (A_j - (-1)^popcount(t ∩ q_j) B_j)
*/
//O(2^n n)
/*
* a[0..2^n)
* A[set] = Σset2 (-1)^popcount(set ∩ set2) a[set2]
* A[0..2^n)
*/
void hadamard2(vector<pair<mint, mint>>& a) {
int n = msb(sz(a));
rep(i, n) repb(set, n) {
if (!(set & (1 << i))) {
auto [xu, xv] = a[set];
auto [yu, yv] = a[set | (1 << i)];
// (log xu - log xv) + (log yu - log yv)
// = log (xu yu) - log (xv yv)
a[set] = { xu * yu, xv * yv };
// (log xu - log xv) - (log yu - log yv)
// = log (xu yv) - log (xv yu)
a[set + (1 << i)] = { xu * yv, xv * yu };
}
}
}
vm solve(int n, int m, vi l, vi r) {
int N = 1 << n;
vm res(N, 1);
rep(j, m) res[0] *= r[j] - l[j];
rep(s, n) {
int Ns = N >> (s + 1);
vi cnt(n - s);
rep(j, m) {
int q = r[j] >> (s + 1);
repis(b, q) cnt[b]++;
}
rep(t, Ns) {
int i = (2 * t + 1) << s;
int sum = 0;
repis(b, t) sum += cnt[b];
res[i] *= sum & 1 ? -1 : 1;
}
vector<pair<mint, mint>> CD(Ns, { 1, 1 });
rep(j, m) {
int q = (r[j] ^ l[j]) / (1 << (s + 1));
int mr = r[j] % (1 << (s + 1));
int A = min(mr, (1 << (s + 1)) - mr);
int ml = l[j] % (1 << (s + 1));
int B = min(ml, (1 << (s + 1)) - ml);
CD[q % Ns].first *= A - B;
CD[q % Ns].second *= A + B;
}
hadamard2(CD);
rep(t, Ns) {
int i = (2 * t + 1) << s;
res[i] *= CD[t].first;
}
}
dump(res);
hadamard_inv(res);
return res;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken2();
int n, m;
cin >> n >> m;
vi l(m), r(m);
rep(j, m) cin >> l[j] >> r[j];
++r;
dump(TLE(n, m, l, r)); dump("-----");
dump(TLE2(n, m, l, r)); dump("-----");
dump(TLE3(n, m, l, r)); dump("-----");
auto res = solve(n, m, l, r);
repb(set, n) cout << res[set] << "\n";
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0