結果

問題 No.2483 Yet Another Increasing XOR Problem
ユーザー ecotteaecottea
提出日時 2023-09-23 16:22:36
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 10,887 bytes
コンパイル時間 3,834 ms
コンパイル使用メモリ 263,484 KB
最終ジャッジ日時 2025-02-17 01:45:32
ジャッジサーバーID
(参考情報)
judge4 / judge3
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 * 2
other AC * 23
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ソースコード

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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; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
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; using ull = unsigned long long;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;
double EPS = 1e-15;
//
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 < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#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 pow(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 get(T set, int i) { return (set >> i) & T(1); }
//
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 = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>;
#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) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
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; }
inline int msb(__int128 n) { return (n >> 64) != 0 ? (127 - __builtin_clzll((ll)(n >> 64))) : n != 0 ? (63 - __builtin_clzll((ll)(n))) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
//O(Πub[0..n))
/*
* a[0..n) ∀i, a[i] ∈ [0..ub[i])
*/
vvi enumerate_all_sequences(const vi& ub) {
// verify : https://atcoder.jp/contests/arc104/tasks/arc104_e
int n = sz(ub);
vvi seqs;
vi seq; //
int i = 0; //
function<void()> rf = [&]() {
//
if (i == n) {
seqs.push_back(seq);
return;
}
rep(x, ub[i]) {
seq.push_back(x); i++;
rf();
seq.pop_back(); i--;
}
};
rf();
return seqs;
}
mint naive(ll m) {
mint res = 0;
int n_max = 1 << (msb(m - 1) + 1);
dump(n_max);
repi(n, 1, n_max) {
vi ub(n, (int)m);
auto seqs = enumerate_all_sequences(ub);
repe(a, seqs) {
vi b(n);
b[0] = a[0];
repi(i, 1, n - 1) b[i] = b[i - 1] ^ a[i];
bool ok = true;
rep(i, n - 1) if (b[i] >= b[i + 1]) {
ok = false;
break;
}
if (ok) res++;
}
}
return res;
}
void zikken() {
repi(m, 1, 8) {
dump(m, naive(m));
}
exit(0);
}
/*
1 1 = 2^1 - 1
2 3 = 2^2 - 1
3 9
4 15 = 2^4 - 1
5 55
6 99
7 169
8 255 = 2^8 - 1
*/
void zikken2() {
repi(m, 1, 8) {
vm cnt(m);
int n_max = 1 << (msb(m - 1) + 1);
// dump(n_max);
repi(n, 1, n_max) {
vi ub(n, (int)m);
auto seqs = enumerate_all_sequences(ub);
repe(a, seqs) {
vi b(n);
b[0] = a[0];
repi(i, 1, n - 1) b[i] = b[i - 1] ^ a[i];
bool ok = true;
rep(i, n - 1) if (b[i] >= b[i + 1]) {
ok = false;
break;
}
if (ok) cnt[*max_element(all(a))]++;
}
}
dump(m, ":", cnt);
}
exit(0);
}
/*
1 : 1
2 : 1 2
3 : 1 2 6
4 : 1 2 6 6
5 : 1 2 6 6 40
6 : 1 2 6 6 40 44
7 : 1 2 6 6 40 44 70
8 : 1 2 6 6 40 44 70 86
*/
//調O(bin(m, n))
/*
* 0 ≦ a[0] < a[1] < ... < a[n-1] < m a[0..n)
*/
vvi enumerate_strongly_increase_sequences(int n, int m) {
// verify : https://atcoder.jp/contests/abc263/tasks/abc263_c
vi a(n);
vvi seqs;
// len :
function<void(int)> rf = [&](int len) {
// n
if (len == n) {
//
seqs.push_back(a);
return;
}
// i0 :
int i0 = (len > 0 ? a[len - 1] : -1);
// i0
repi(i, i0 + 1, m - 1) {
a[len++] = i;
rf(len);
len--;
}
};
rf(0);
return seqs;
}
void zikken3() {
int m = 16;
vm cnt(m);
int n_max = 1 << (msb(m - 1) + 1);
repi(n, 1, n_max) {
vi ub(n, (int)m);
auto seqs = enumerate_strongly_increase_sequences(n, n_max);
repe(b, seqs) {
vi a(n);
a[0] = b[0];
repi(i, 1, n - 1) a[i] = b[i - 1] ^ b[i];
int a_max = *max_element(all(a));
if (a_max < m) cnt[a_max]++;
}
}
dump_list(cnt);
exit(0);
}
/*
{1, 2, 6, 6, 40, 44, 70, 86, 1152, 1344, 2208, 2736, 8232, 10284, 17478, 21846}
*/
void zikken4() {
int m = 16;
vvm cnt(m, vm(m));
int n_max = 1 << (msb(m - 1) + 1);
repi(n, 1, n_max) {
vi ub(n, (int)m);
auto seqs = enumerate_strongly_increase_sequences(n, n_max);
repe(b, seqs) {
vi a(n);
a[0] = b[0];
repi(i, 1, n - 1) a[i] = b[i - 1] ^ b[i];
int a_max = *max_element(all(a));
int a_min = *min_element(all(a));
if (a_max < m) cnt[a_min][a_max]++;
}
}
dump_mat(cnt);
exit(0);
}
/*
{{1,1,3,3,20,22,35,43,576,672,1104,1368,4116,5142,8739,10923},
{0,1,2,2,15,17,28,36,495,591,981,1245,3787,4813,8192,10376},
{0,0,1,0,2,2,4,4,44,44,82,82,214,214,404,404},
{0,0,0,1,2,2,2,2,28,28,32,32,94,94,122,122},
{0,0,0,0,1,0,0,0,2,2,2,2,8,8,8,8},
{0,0,0,0,0,1,0,0,2,2,2,2,6,6,6,6},
{0,0,0,0,0,0,1,0,2,2,2,2,4,4,4,4},
{0,0,0,0,0,0,0,1,2,2,2,2,2,2,2,2},
{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
*/
// DPO(n b)
/*
* b=10 n num
*/
mint count_digit(int B, ll s) {
dump(B, s);
// dp[i][f] :
// i : d[0..i)
// f : d[0..i) < num[0..i) 1 0
vvm dp(B + 1, vm(1LL << 1));
dp[0][0] = 1;
mint inv2 = mint(2).inv();
// DP
rep(b, B) {
// x : num i
int x = (int)get(s, B - 1 - b);
repb(f, 1) {
int smaller = (f >> 0) & 1;
// d_max : d[i]
int k_max = (smaller ? 1 : x);
// d : d[i]
repi(k, 0, k_max) {
repi(i, 0, 1) {
int n_smaller = (int)(smaller || (k < k_max));
int nf = (n_smaller << 0);
int e = i - (i ^ k);
mint mul = 1;
if (e == 1) mul = mint(2).pow(1LL << (B - 1 - b));
else if (e == -1) mul = inv2.pow(1LL << (B - 1 - b));
dp[b + 1][nf] += dp[b][f] * mul;
}
}
}
//dump("----", i + 1, "----");
//repb(f, 1) dump("(smaller) =", bitset<1>(f), ":", dp[i + 1][f]);
}
mint res = 0;
repb(f, 1) res += dp[B][f];
return res;
}
mint solve(ll m) {
if (m == 1) return 1;
int B = msb(m - 1);
dump(B);
ll k_max = m - 1 - (1LL << B);
auto res = count_digit(B, k_max);
res *= mint(2).pow((1LL << B) - 1);
res += mint(2).pow((1LL << B) + 1);
res -= mint(2).pow((1LL << (B + 1)) - m);
res--;
return res;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken4();
ll m;
cin >> m;
// dump(naive(m)); dump("----");
cout << solve(m) << endl;
}
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