結果
問題 | No.2483 Yet Another Increasing XOR Problem |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 23 |
ソースコード
#ifndef HIDDEN_IN_VS // 折りたたみ用// 警告の抑制#define _CRT_SECURE_NO_WARNINGS// ライブラリの読み込み#include <bits/stdc++.h>using namespace std;// 型名の短縮using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -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;// 定数の定義const double PI = acos(-1);const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左)const vi DY = { 0, 1, 0, -1 };int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;double EPS = 1e-15;// 入出力高速化struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;// 汎用マクロの定義#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 から n-1 まで昇順#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順#define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能)#define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能)#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順)#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順)#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定// 汎用関数の定義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; } // 最大値を更新(更新されたら trueを返す)template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら trueを返す)template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }// 演算子オーバーロード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 // 折りたたみ用#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 // 手元環境(Visual Studio)#include "local.hpp"#else // 提出用(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//【任意数列の列挙(要素ごと上限指定)】O(Πub[0..n))/** 数列 a[0..n) で,∀i, a[i] ∈ [0..ub[i]) を満たすもの全てを格納したリストを返す.*/vvi enumerate_all_sequences(const vi& ub) {// verify : https://atcoder.jp/contests/arc104/tasks/arc104_eint n = sz(ub);vvi seqs;vi seq; // 作成途中の列int i = 0; // 列の長さfunction<void()> rf = [&]() {// 完成していれば記録する.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 - 12 3 = 2^2 - 13 94 15 = 2^4 - 15 556 997 1698 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 : 12 : 1 23 : 1 2 64 : 1 2 6 65 : 1 2 6 6 406 : 1 2 6 6 40 447 : 1 2 6 6 40 44 708 : 1 2 6 6 40 44 70 86*///【狭義単調増加列の列挙】O(bin(m, n))/** 0 ≦ a[0] < a[1] < ... < a[n-1] < m なる列 a[0..n) を格納したリストを返す.*/vvi enumerate_strongly_increase_sequences(int n, int m) {// verify : https://atcoder.jp/contests/abc263/tasks/abc263_cvi a(n);vvi seqs;// len : 列の長さfunction<void(int)> rf = [&](int len) {// 列の長さが n の場合if (len == n) {// 完成しているので記録seqs.push_back(a);return;}// i0 : 直前の数の大きさint i0 = (len > 0 ? a[len - 1] : -1);// 直前の数 i0 より大きい数が選べる.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}}*///【上から桁 DP,未満フラグ,数え上げ】O(n b)(の改変)/** b=10 進数で n 桁の数 num 以下の非負の整数の個数を返す.*/mint count_digit(int B, ll s) {dump(B, s);// dp[i][f] : 以下の条件を満たす数の個数:// i : 上からの桁 d[0..i) まで決まっている.// f : d[0..i) < num[0..i) なら 1,さもなくば 0(未満フラグ)vvm dp(B + 1, vm(1LL << 1));dp[0][0] = 1;mint inv2 = mint(2).inv();// 上の桁から順に配る DPrep(b, B) {// x : num の上から i 桁目の数int x = (int)get(s, B - 1 - b);repb(f, 1) {int smaller = (f >> 0) & 1;// d_max : d[i] のとれる値の最大値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;}