#837222 (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	👑 rin204
提出日時	2023-02-03 22:18:02
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	852 ms / 4,000 ms
コード長	17,777 bytes
コンパイル時間	2,987 ms
コンパイル使用メモリ	237,472 KB
実行使用メモリ	25,644 KB
最終ジャッジ日時	2023-09-15 18:20:50
合計ジャッジ時間	14,583 ms
ジャッジサーバーID （参考情報）	judge15 / judge12
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	6 ms 5,344 KB
testcase_01	AC	6 ms 5,592 KB
testcase_02	AC	30 ms 5,444 KB
testcase_03	AC	30 ms 5,436 KB
testcase_04	AC	30 ms 5,620 KB
testcase_05	AC	852 ms 25,528 KB
testcase_06	AC	851 ms 24,444 KB
testcase_07	AC	841 ms 25,092 KB
testcase_08	AC	833 ms 24,612 KB
testcase_09	AC	846 ms 24,528 KB
testcase_10	AC	614 ms 25,644 KB
testcase_11	AC	621 ms 25,564 KB
testcase_12	AC	603 ms 25,332 KB
testcase_13	AC	513 ms 25,232 KB
testcase_14	AC	515 ms 24,780 KB
testcase_15	AC	520 ms 24,804 KB
testcase_16	AC	493 ms 25,116 KB
testcase_17	AC	497 ms 24,896 KB
testcase_18	AC	482 ms 24,320 KB
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ソースコード

raw source code
#line 1 "A.cpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));

#define endl "\n"
#define spa ' '
#define len(A) A.size()
#define all(A) begin(A), end(A)

#define fori1(a) for(ll _ = 0; _ < (a); _++)
#define fori2(i, a) for(ll i = 0; i < (a); i++)
#define fori3(i, a, b) for(ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for(ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

template <typename T>
vector<tuple<ll, T>> ENUMERATE(vector<T> &A, ll s = 0){
    vector<tuple<ll, T>> ret(A.size());
    for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]};
    return ret;
}

vector<tuple<ll, char>> ENUMERATE(string &A, ll s = 0){
    vector<tuple<ll, char>> ret(A.size());
    for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]};
    return ret;
}

#define enum1(A) fori(A.size())
#define enum2(a, A) for(auto a:A)
#define enum3(i, a, A) for(auto&& [i, a]: ENUMERATE(A))
#define enum4(i, a, A, s) for(auto&& [i, a]: ENUMERATE(A, s))
#define enum(...) overload4(__VA_ARGS__, enum4, enum3, enum2, enum1)(__VA_ARGS__)

template <typename T, typename S>
vector<tuple<T, S>> ZIP(vector<T> &A, vector<S> &B){
    int n = min(A.size(), B.size());
    vector<tuple<T, S>> ret(n);
    for(int i = 0; i < n; i++) ret[i] = {A[i], B[i]};
    return ret;
}

template <typename T, typename S>
vector<tuple<ll, T, S>> ENUMZIP(vector<T> &A, vector<S> &B, ll s = 0){
    int n = min(A.size(), B.size());
    vector<tuple<ll, T, S>> ret(n);
    for(int i = 0; i < n; i++) ret[i] = {i + s, A[i], B[i]};
    return ret;
}

#define zip4(a, b, A, B) for(auto&& [a, b]: ZIP(A, B))
#define enumzip5(i, a, b, A, B) for(auto&& [i, a, b]: ENUMZIP(A, B))
#define enumzip6(i, a, b, A, B, s) for(auto&& [i, a, b]: ENUMZIP(A, B, s))
#define overload6(a, b, c, d, e, f, g, ...) g
#define zip(...) overload6(__VA_ARGS__, enumzip6, enumzip5, zip4, _, _, _)(__VA_ARGS__)

vector<char> stoc(string &S){
    int n = S.size();
    vector<char> ret(n);
    for(int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}

#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);

const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;

template<class T> auto min(const T& a){
    return *min_element(all(a));
}
template<class T> auto max(const T& a){
    return *max_element(all(a));
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

void FLUSH(){cout << flush;}
void print(){cout << endl;}
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(forward<Tail>(tail)...);
}
template<typename T>
void print(vector<T> &A){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << spa;
    }
}
template<typename T>
void print(vector<vector<T>> &A){
    for(auto &row: A) print(row);
}
template<typename T, typename S>
void print(pair<T, S> &A){
    cout << A.first << spa << A.second << endl;
}
template<typename T, typename S>
void print(vector<pair<T, S>> &A){
    for(auto &row: A) print(row);
}
template<typename T, typename S>
void prisep(vector<T> &A, S sep){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << sep;
    }
}
template<typename T, typename S>
void priend(T A, S end){
    cout << A << end;
}
template<typename T>
void priend(T A){
    priend(A, spa);
}
template<class... T>
void inp(T&... a){
    (cin >> ... >> a);
}
template<typename T>
void inp(vector<T> &A){
    for(auto &a:A) cin >> a;
}
template<typename T>
void inp(vector<vector<T>> &A){
    for(auto &row:A) inp(row);
}
template<typename T, typename S>
void inp(pair<T, S> &A){
    inp(A.first, A.second);
}
template<typename T, typename S>
void inp(vector<pair<T, S>> &A){
    for(auto &row: A) inp(row.first, row.second);
}

template<typename T>
T sum(vector<T> &A){
    T tot = 0;
    for(auto a:A) tot += a;
    return tot;
}

template<typename T>
pair<vector<T>, map<T, int>> compression(vector<T> X){
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    map<T, int> mp;
    for(int i = 0; i < X.size(); i++) mp[X[i]] = i;
    return {X, mp};
}

#line 2 "Library/C++/other/Modint.hpp"

template<int MOD>
struct Modint{
    int x;
    Modint() : x(0){}
    Modint(int64_t y){
        if(y >= 0) x = y % MOD;
        else x = (y % MOD + MOD) % MOD;
    }

    Modint &operator+=(const Modint &p){
        x += p.x;
        if(x >= MOD) x -= MOD;
        return *this;
    }

    Modint &operator-=(const Modint &p){
        x -= p.x;
        if(x < 0) x += MOD;
        return *this;
    }

    Modint &operator*=(const Modint &p){
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Modint &operator/=(const Modint &p){
        *this *= p.inverse();
        return *this;
    }

    Modint &operator%=(const Modint &p){
        assert(p.x == 0);
        return *this;
    }

    Modint operator-() const{
        return Modint(-x);
    }

    Modint& operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Modint& operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Modint operator++(int) {
        Modint result = *this;
        ++*this;
        return result;
    }

    Modint operator--(int) {
        Modint result = *this;
        --*this;
        return result;
    }

    friend Modint operator+(const Modint &lhs, const Modint &rhs){
        return Modint(lhs) += rhs;
    }

    friend Modint operator-(const Modint &lhs, const Modint &rhs){
        return Modint(lhs) -= rhs;
    }

    friend Modint operator*(const Modint &lhs, const Modint &rhs){
        return Modint(lhs) *= rhs;
    }

    friend Modint operator/(const Modint &lhs, const Modint &rhs){
        return Modint(lhs) /= rhs;
    }

    friend Modint operator%(const Modint &lhs, const Modint &rhs){
        assert(rhs.x == 0);
        return Modint(lhs);
    }

    bool operator==(const Modint &p) const{
        return x == p.x;
    }

    bool operator!=(const Modint &p) const{
        return x != p.x;
    }

    bool operator<(const Modint &rhs) {
        return x < rhs.x;
    }

    bool operator<=(const Modint &rhs) {
        return x <= rhs.x;
    }

    bool operator>(const Modint &rhs) {
        return x > rhs.x;
    }

    bool operator>=(const Modint &rhs) {
        return x >= rhs.x;
    }

    Modint inverse() const{
        int a = x, b = MOD, u = 1, v = 0, t;
        while(b > 0){
            t = a / b;
            a -= t * b;
            u -= t * v;
            swap(a, b);
            swap(u, v);
        }
        return Modint(u);
    }

    Modint pow(int64_t k) const{
        Modint ret(1);
        Modint y(x);
        while(k > 0){
            if(k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Modint &p){
        return os << p.x;
    }

    friend istream &operator>>(istream &is, Modint &p){
        int64_t y;
        is >> y;
        p = Modint<MOD>(y);
        return (is);
    }

    static int get_mod(){
        return MOD;
    }
};

struct Arbitrary_Modint{
    int x;
    static int MOD;

    static void set_mod(int mod){
        MOD = mod;
    }

    Arbitrary_Modint() : x(0){}
    Arbitrary_Modint(int64_t y){
        if(y >= 0) x = y % MOD;
        else x = (y % MOD + MOD) % MOD;
    }

    Arbitrary_Modint &operator+=(const Arbitrary_Modint &p){
        x += p.x;
        if(x >= MOD) x -= MOD;
        return *this;
    }

    Arbitrary_Modint &operator-=(const Arbitrary_Modint &p){
        x -= p.x;
        if(x < 0) x += MOD;
        return *this;
    }

    Arbitrary_Modint &operator*=(const Arbitrary_Modint &p){
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Arbitrary_Modint &operator/=(const Arbitrary_Modint &p){
        *this *= p.inverse();
        return *this;
    }

    Arbitrary_Modint &operator%=(const Arbitrary_Modint &p){
        assert(p.x == 0);
        return *this;
    }

    Arbitrary_Modint operator-() const{
        return Arbitrary_Modint(-x);
    }

    Arbitrary_Modint& operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Arbitrary_Modint& operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Arbitrary_Modint operator++(int) {
        Arbitrary_Modint result = *this;
        ++*this;
        return result;
    }

    Arbitrary_Modint operator--(int) {
        Arbitrary_Modint result = *this;
        --*this;
        return result;
    }

    friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs){
        return Arbitrary_Modint(lhs) += rhs;
    }

    friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs){
        return Arbitrary_Modint(lhs) -= rhs;
    }

    friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs){
        return Arbitrary_Modint(lhs) *= rhs;
    }

    friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs){
        return Arbitrary_Modint(lhs) /= rhs;
    }

    friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs){
        assert(rhs.x == 0);
        return Arbitrary_Modint(lhs);
    }

    bool operator==(const Arbitrary_Modint &p) const{
        return x == p.x;
    }

    bool operator!=(const Arbitrary_Modint &p) const{
        return x != p.x;
    }

    bool operator<(const Arbitrary_Modint &rhs) {
        return x < rhs.x;
    }

    bool operator<=(const Arbitrary_Modint &rhs) {
        return x <= rhs.x;
    }

    bool operator>(const Arbitrary_Modint &rhs) {
        return x > rhs.x;
    }

    bool operator>=(const Arbitrary_Modint &rhs) {
        return x >= rhs.x;
    }

    Arbitrary_Modint inverse() const{
        int a = x, b = MOD, u = 1, v = 0, t;
        while(b > 0){
            t = a / b;
            a -= t * b;
            u -= t * v;
            swap(a, b);
            swap(u, v);
        }
        return Arbitrary_Modint(u);
    }

    Arbitrary_Modint pow(int64_t k) const{
        Arbitrary_Modint ret(1);
        Arbitrary_Modint y(x);
        while(k > 0){
            if(k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Arbitrary_Modint &p){
        return os << p.x;
    }

    friend istream &operator>>(istream &is, Arbitrary_Modint &p){
        int64_t y;
        is >> y;
        p = Arbitrary_Modint(y);
        return (is);
    }

    static int get_mod(){
        return MOD;
    }
};
int Arbitrary_Modint::MOD = 998244353;

using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint = Arbitrary_Modint;
#line 2 "Library/C++/math/modinv.hpp"

template<typename T>
T modinv(T a, T MOD){
    T b = MOD;
    T u = 1;
    T v = 0;
    while(b > 0){
        T t = a / b;
        a -= t * b;
        u -= t * v;
        swap(a, b);
        swap(u, v);
    }
    if(a != 1) return -1;
    if(u < 0) u += MOD;
    return u;
}
#line 3 "Library/C++/math/Combination.hpp"

template <typename T>
struct Combination{
    int N;
    vector<T> fact, invfact;
    Combination(int N) : N(N){
        fact.resize(N + 1);
        invfact.resize(N + 1);
        fact[0] = 1;
        for(int i = 1; i <= N; i++){
            fact[i] = fact[i - 1] * i;
        }
        invfact[N] = T(1) / fact[N];
        for(int i = N - 1; i >= 0; i--){
            invfact[i] = invfact[i + 1] * (i + 1);
        }
    }

    T nCk(int n, int k){
        assert(0 <= n && n <= N);
        if(k > n || k < 0) return T(0);
        return fact[n] * invfact[k] * invfact[n - k];
    }

    T nPk(int n, int k){
        assert(0 <= n && n <= N);
        if(k > n || k < 0) return T(0);
        return fact[n] * invfact[n - k];
    }

    T nHk(int n, int k){
        if(n == 0 && k == 0) return T(1);
        return nCk(n + k - 1, k);
    }
};
#line 2 "Library/C++/data_structure/UnionFind.hpp"

struct UnionFind{
    int n;
    vector<int> par;
    int group;

    UnionFind(int n) : n(n){
        par.assign(n, -1);
        group = n;
    }

    int find(int x){
        if(par[x] < 0) return x;
        par[x] = find(par[x]);
        return par[x];
    }

    bool unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return false;
        if(par[x] > par[y]) swap(x, y);
        group--;
        par[x] += par[y];
        par[y] = x;
        return true;
    }

    bool same(int x, int y){
        return find(x) == find(y);
    }

    int size(int x){
        return -par[find(x)];
    }

    vector<int> roots(){
        vector<int> ret;
        for(int i = 0; i < n; i++){
            if(i == find(i)) ret.push_back(i);
        }
        return ret;
    }

};
#line 4 "Library/C++/tree/ManhattanMST.hpp"
using namespace std;

template<typename T>
struct ManhattanEdges{
    int i;
    int j;
    T cost;
};

template<typename T>
pair<vector<ManhattanEdges<T>>, T> ManhattanMST(vector<T> X, vector<T> Y){
    assert(X.size() == Y.size());
    using ME = ManhattanEdges<T>;
    vector<ME> E;
    int n = X.size();

    vector<int> ord(n);
    iota(ord.begin(), ord.end(), 0);

    for(int s = 0; s < 2; s++){
        for(int t = 0; t < 2; t++){
            sort(ord.begin(), ord.end(), [&](int i, int j){
                return X[i] + Y[i] < X[j] + Y[j];
            });

            map<T, int> ind;
            for(auto i:ord){
                for(auto it = ind.lower_bound(-Y[i]); it != ind.end(); it = ind.erase(it)){
                    int j = (*it).second;
                    if(X[i] - X[j] < Y[i] - Y[j]) break;
                    E.push_back({i, j, abs(X[i] - X[j]) + abs(Y[i] - Y[j])});
                }
                ind[-Y[i]] = i;
            }
            swap(X, Y);
        }
        for(int i = 0; i < n; i++) X[i] *= -1;
    }

    sort(E.begin(), E.end(), [](ME &lhs, ME &rhs){
        return lhs.cost < rhs.cost;
    });

    UnionFind UF(n);
    vector<ME> ret;
    T cost = 0;
    for(auto tmp:E){
        if(UF.unite(tmp.i, tmp.j)){
            ret.push_back(tmp);
            cost += tmp.cost;
        }
    }
    return {ret, cost};
}

template<typename T>
pair<vector<ManhattanEdges<T>>, T> ManhattanMST(vector<pair<T, T>> xy){
    int n = xy.size();
    vector<T> X(n), Y(n);
    for(int i = 0; i < n; i++){
        X[i] = xy[i].first;
        Y[i] = xy[i].second;
    }
    return ManhattanMST(X, Y);
}
#line 188 "A.cpp"
using mint = modint9;

void solve(){
    INT(T);
    vec(int, N, T);
    vec(int, M, T);
    vec(int, X, T);
    vec(int, Y, T);
    fori(i, T){
        inp(N[i], M[i]);
        N[i]--;
        M[i]--;
        X[i] = N[i] + M[i];
        Y[i] = N[i] - M[i];
    }
    auto res = ManhattanMST(X, Y).first;
    vvec(int, edges, T);
    for(auto tmp:res){
        edges[tmp.i].push_back(tmp.j);
        edges[tmp.j].push_back(tmp.i);
    }

    Combination<mint> C(200020);
    vec(mint, ans, T);
    mint tot = 0;
    fori(i, M[0] + 1) tot += C.nCk(N[0], i);
    ans[0] = tot;
    mint inv2 = mint(1) / 2;

    auto calc=[&](int npos, int pos){
        mint x = ans[pos];
        int n = N[pos];
        int m = M[pos];
        int nn = N[npos];
        int mm = M[npos];
        while(n < nn){
            if(m < mm){
                x *= 2;
                x += C.nCk(n, m + 1);
                m++;
            }
            else{
                x *= 2;
                x -= C.nCk(n, m);
            }
            n++;
        }

        while(n > nn){
            if(m > mm){
                x -= C.nCk(n - 1, m);
                x *= inv2;
                m--;
            }
            else{
                x += C.nCk(n - 1, m);
                x *= inv2;
            }
            n--;
        }

        while(m < mm){
            m++;
            x += C.nCk(nn, m);
        }

        while(m > mm){
            x -= C.nCk(nn, m);
            m--;
        }
        ans[npos] = x;
    };

    auto dfs=[&](auto &&self, int pos, int bpos) -> void {
        for(auto npos:edges[pos]){
            if(npos == bpos) continue;
            calc(npos, pos);
            self(self, npos, pos);
        }
    };

    dfs(dfs, 0, -1);


    vec(mint, pow2, 200020);
    pow2[0] = 1;
    fori(i, 1, 200020) pow2[i] = pow2[i - 1] * 2;
    fori(i, T){
        ans[i] *= pow2[N[i] + 1] - 1;
    }
    prisep(ans, endl);

}

int main(){
    cin.tie(0)->sync_with_stdio(0);
    // cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while(t--) solve();
    return 0;
}
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結果

テストケース

ソースコード
