#837531 (C++17) No.2206 Popcount Sum 2

提出ソース
結果

問題	No.2206 Popcount Sum 2
ユーザー	poyon
提出日時	2023-02-04 12:05:53
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	619 ms / 4,000 ms
コード長	11,842 bytes
コンパイル時間	2,754 ms
コンパイル使用メモリ	219,376 KB
実行使用メモリ	12,800 KB
最終ジャッジ日時	2024-07-03 10:22:10
合計ジャッジ時間	10,877 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
このコードへのチャレンジ
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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	8 ms 6,400 KB
testcase_01	AC	8 ms 6,400 KB
testcase_02	AC	40 ms 6,528 KB
testcase_03	AC	40 ms 6,528 KB
testcase_04	AC	41 ms 6,400 KB
testcase_05	AC	619 ms 12,668 KB
testcase_06	AC	614 ms 12,796 KB
testcase_07	AC	612 ms 12,668 KB
testcase_08	AC	612 ms 12,792 KB
testcase_09	AC	610 ms 12,668 KB
testcase_10	AC	329 ms 12,668 KB
testcase_11	AC	327 ms 12,672 KB
testcase_12	AC	326 ms 12,800 KB
testcase_13	AC	282 ms 12,752 KB
testcase_14	AC	281 ms 12,672 KB
testcase_15	AC	281 ms 12,668 KB
testcase_16	AC	196 ms 12,796 KB
testcase_17	AC	195 ms 12,796 KB
testcase_18	AC	193 ms 12,800 KB
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ソースコード

raw source code
// clang-format off
#ifdef _LOCAL
    #include <pch.hpp>
#else
    #include <bits/stdc++.h>
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(...)
    #define debug2(vv)
    #define debug3(vvv)
#endif

using namespace std;
using ll = long long;
using ld = long double;
using str = string;
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(c) (c).begin(), (c).end()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define SZ(c) ((ll)(c).size())
#define len(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) ((ll)__builtin_popcountll(b))
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0)
#define END(...) do { print(__VA_ARGS__); exit(0); } while (0)
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class P1, class P2> void print(const pair<P1, P2>& a) { cout << a.first << " " << a.second << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> void print(const vector<T>& a) { cout_line(a, 0, a.size()); }
template<class T> bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = false) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
template<class T> string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; }
template<class F> ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class F> double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class T> using PQ_max = priority_queue<T>;
template<class T> using PQ_min = priority_queue<T, vector<T>, greater<T>>;
template<class T> T pick(stack<T>& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; }
template<class T> T pick(queue<T>& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; }
template<class T> T pick_front(deque<T>& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; }
template<class T> T pick_back(deque<T>& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; }
template<class T> T pick(PQ_min<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(PQ_max<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(vector<T>& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); }
ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); }
int a2i(const char& c) { assert(islower(c)); return (c - 'a'); }
int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); }
int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); }
char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); }
char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); }
char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); }
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VC = vector<char>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VLD = vector<ld>;
using VVLD = vector<VLD>;
using VVVLD = vector<VVLD>;
const ld EPS = 1e-10;
const ld PI  = acosl(-1.0);
constexpr int inf = (1 << 30) - 1;   // 1073741824 - 1
constexpr ll INF = (1LL << 62) - 1;  // 4611686018427387904 - 1
// --------------------------------------------------------

#include <atcoder/modint>
using namespace atcoder;

// constexpr ll MOD = 1000003;
// using mint = modint;
// mint::set_mod(MOD);  // write in main()

// using mint = modint1000000007;
using mint = modint998244353;

using VM = vector<mint>;
using VVM = vector<VM>;
using VVVM = vector<VVM>;
using VVVVM = vector<VVVM>;

template<int M> istream &operator>>(istream &is, static_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> istream &operator>>(istream &is, dynamic_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> ostream &operator<<(ostream &os, const static_modint<M> &m) { return os << m.val(); }
template<int M> ostream &operator<<(ostream &os, const dynamic_modint<M> &m) { return os << m.val(); }

// It is assumed that M (= mod) is prime number
struct combination {
  public:
    combination() : combination(1) {}
    combination(int n) : N(1), fact_(2,0), ifact_(2,0), inv_(2,0) {
        M = mint().mod();
        assert(0 < n && n < M);

        fact_[0] = fact_[1] = 1;
        ifact_[0] = ifact_[1] = 1;
        inv_[1] = 1;

        if (N < n) { build(n); }
    }

    mint P(int n, int k) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return fact_[n] * ifact_[n-k];
    }
    mint C(int n, int k) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return fact_[n] * ifact_[n-k] * ifact_[k];
    }
    mint H(int n, int k) {
        if (n == 0 && k == 0) { return 1; }
        if (n < 0 || k < 0) { return 0; }
        return C(n + k - 1, k);
    }
    mint fact(int n) {
        if (N < n) { build(n); }
        if (n < 0) { return 0; }
        return fact_[n];
    }
    mint ifact(int n) {
        if (N < n) { build(n); }
        if (n < 0) { return 0; }
        return ifact_[n];
    }
    mint inv(int n) {
        if (N < n) { build(n); }
        if (n < 0) { return 0; }
        return inv_[n];
    }
    mint P_naive(ll n, int k) const noexcept {
        if (n < 0 || k < 0 || n < k) { return 0; }
        mint res = 1;
        for (int i = 1; i <= k; i++) { res *= (n - i + 1); }
        return res;
    }
    mint C_naive(ll n, int k) const noexcept {
        if (n < 0 || k < 0 || n < k) { return 0; }
        if (k > n - k) { k = n - k; }
        mint nume = 1, deno = 1;
        for (int i = 1; i <= k; i++) { nume *= (n - i + 1); deno *= i; }
        return nume / deno;
    }
    mint H_naive(ll n, int k) const noexcept {
        if (n == 0 && k == 0) { return 1; }
        if (n < 0 || k < 0) { return 0; }
        return C_naive(n + k - 1, k);
    }

  private:
    int N;
    int M;  // mod
    vector<mint> fact_, ifact_, inv_;

    void build(int N_new) {
        assert(N < N_new);
        fact_.resize(N_new + 1);
        ifact_.resize(N_new + 1);
        inv_.resize(N_new + 1);
        for (int i = N + 1; i <= N_new; i++) {
            fact_[i] = fact_[i - 1] * i;
            inv_[i] = -inv_[M % i] * (M / i);
            ifact_[i] = ifact_[i - 1] * inv_[i];
        }
        N = N_new;
    }
};


// References:
//   <https://codeforces.com/blog/entry/7383>
//   <https://snuke.hatenablog.com/entry/2016/07/01/000000>
//   <https://ei1333.hateblo.jp/entry/2017/09/11/211011>
//   <https://ei1333.github.io/library/other/mo.cpp>
//   <https://cp-algorithms.com/data_structures/sqrt_decomposition.html#toc-tgt-4>
//   <https://blog.hamayanhamayan.com/entry/2017/04/18/012937>

// Mo's algorithm
struct Mo {
  public:
    Mo(int N) : N(N) {}

    // クエリ [l, r) を追加する : O(1)
    void add_query(int l, int r) {
        assert(0 <= l && l <= r && r <= N);
        L.push_back(l);
        R.push_back(r);
    }

    // Mo's algorithm を実行する : O(QlogQ + f(N)N√Q)
    // → O(f(N)) は区間の伸縮に必要な計算量
    template<class AL, class AR, class DL, class DR, class O>
    void solve(const AL& add_L, const AR& add_R, const DL& del_L, const DR& del_R, const O& out) {
        int Q = L.size();
        int B = max(1, (int)(N / sqrt(Q)));  // ブロックサイズ

        // クエリ順をソート
        vector<int> ord(Q);
        iota(ord.begin(), ord.end(), 0);
        sort(ord.begin(), ord.end(), [&](const int& i1, const int& i2) {
            int B1 = L[i1] / B;
            int B2 = L[i2] / B;
            if (B1 != B2) {
                return B1 < B2;
            } else {
                // 偶奇で r の大小関係を反転させて定数倍高速化を狙う
                return (B1 % 2 == 0 ? R[i1] < R[i2] : R[i1] > R[i2]);
            }
        });

        // クエリの処理
        int l = 0, r = 0;  // [l, r)  現在の区間
        for (const auto& i : ord) {
            while (L[i] < l) { add_L(--l); }
            while (r < R[i]) { add_R(r++); }
            while (l < L[i]) { del_L(l++); }
            while (R[i] < r) { del_R(--r); }
            out(i);
        }
    }

  private:
    int N;
    vector<int> L, R;
};

// clang-format on
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll Q;
    input(Q);
    VLL N(Q), M(Q);
    REP (i, Q) { input(N[i], M[i]); }

    int K = 2e5;
    Mo mo(K + 1);
    REP (i, Q) {
        mo.add_query(M[i] - 1, N[i] - 1);
    }

    combination Z(K);
    VM pow2(K + 1, 1);
    FOR (i, 1, K + 1) pow2[i] = pow2[i - 1] * 2;
    mint f = 1;

    VM ans(Q);
    int n = 0, m = 0;
    auto add_L = [&]([[maybe_unused]] int i) -> void { f = f - Z.C(n, m--); };
    auto add_R = [&]([[maybe_unused]] int i) -> void { f = f * 2 - Z.C(n++, m); };
    auto del_L = [&]([[maybe_unused]] int i) -> void { f = f + Z.C(n, ++m); };
    auto del_R = [&]([[maybe_unused]] int i) -> void { f = (f + Z.C(--n, m)) * Z.inv(2); };
    auto out = [&](int i) -> void { ans[i] = (pow2[N[i]] - 1) * f; };

    mo.solve(add_L, add_R, del_L, del_R, out);
    REP (i, Q) cout << ans[i] << '\n';

    return 0;
}
yukicoder

結果

テストケース

ソースコード
