#1132305 (C++23) No.3345 Reducible Sequence

提出ソース
結果

問題	No.3345 Reducible Sequence
コンテスト
ユーザー	noya2
提出日時	2025-11-12 02:04:08
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	91 ms / 2,000 ms
コード長	18,057 bytes
コンパイル時間	3,112 ms
コンパイル使用メモリ	296,128 KB
実行使用メモリ	14,176 KB
最終ジャッジ日時	2025-11-13 21:20:20
合計ジャッジ時間	5,060 ms
ジャッジサーバーID （参考情報）	judge2 / judge4
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 * 3
other	AC * 26
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ソースコード

raw source code
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/simple_queue.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/simple_queue.hpp"

namespace noya2::internal {

template <class T>
struct simple_queue {
    std::vector<T> payload;
    int pos = 0;
    void reserve(int n) { payload.reserve(n); }
    int size() const { return int(payload.size()) - pos; }
    bool empty() const { return pos == int(payload.size()); }
    void push(const T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};

} // namespace noya2::internal
#line 4 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"

#line 10 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"

namespace noya2 {

template <class Cap> struct mf_graph {
  public:
    mf_graph() : _n(0) {}
    explicit mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) {
            result.push_back(get_edge(i));
        }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto& _e = g[pos[i].first][pos[i].second];
        auto& _re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    Cap flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        std::vector<int> level(_n), iter(_n);
        internal::simple_queue<int> que;

        auto bfs = [&]() {
            std::fill(level.begin(), level.end(), -1);
            level[s] = 0;
            que.clear();
            que.push(s);
            while (!que.empty()) {
                int v = que.front();
                que.pop();
                for (auto e : g[v]) {
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return;
                    que.push(e.to);
                }
            }
        };
        auto dfs = [&](auto self, int v, Cap up) {
            if (v == s) return up;
            Cap res = 0;
            int level_v = level[v];
            for (int& i = iter[v]; i < int(g[v].size()); i++) {
                _edge& e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                Cap d =
                    self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up) return res;
            }
            level[v] = _n;
            return res;
        };

        Cap flow = 0;
        while (flow < flow_limit) {
            bfs();
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = dfs(dfs, t, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        internal::simple_queue<int> que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

  private:
    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

} // namespace noya2

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

namespace noya2::internal {

template<class E>
struct csr {
    csr () {}
    csr (int _n) : n(_n) {}
    csr (int _n, int m) : n(_n){
        start.reserve(m);
        elist.reserve(m);
    }
    // ACL style constructor (do not have to call build)
    csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
        for (auto &[i, e] : idx_elem){
            start[i + 2]++;
        }
        for (int i = 1; i < n; i++){
            start[i + 2] += start[i + 1];
        }
        for (auto &[i, e] : idx_elem){
            elist[start[i + 1]++] = e;
        }
        prepared = true;
    }
    int add(int idx, E elem){
        int eid = start.size();
        start.emplace_back(idx);
        elist.emplace_back(elem);
        return eid;
    }
    void build(){
        if (prepared) return ;
        int m = start.size();
        std::vector<E> nelist(m);
        std::vector<int> nstart(n + 2, 0);
        for (int i = 0; i < m; i++){
            nstart[start[i] + 2]++;
        }
        for (int i = 1; i < n; i++){
            nstart[i + 2] += nstart[i + 1];
        }
        for (int i = 0; i < m; i++){
            nelist[nstart[start[i] + 1]++] = elist[i];
        }
        swap(elist,nelist);
        swap(start,nstart);
        prepared = true;
    }
    const auto operator[](int idx) const {
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    auto operator[](int idx){
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    const auto operator()(int idx, int l, int r) const {
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    auto operator()(int idx, int l, int r){
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    size_t size() const {
        return n;
    }
    int n;
    std::vector<int> start;
    std::vector<E> elist;
    bool prepared = false;
};

} // namespace noya2::internal
#line 151 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"

namespace noya2 {

template<class Cap>
struct maxflow {
    struct edge {
        int from, to;
        Cap cap, flow;
    };
    maxflow() : n(0) {}
    explicit maxflow(int _n) : n(_n), g(n), degree(_n,0) {}

    int add_edge(int from, int to, Cap cap){
        assert(0 <= from && from < n);
        assert(0 <= to && to < n);
        assert(0 <= cap);

        int eid = (int)(pos.size());
        int from_id = degree[from];
        int to_id = degree[to] + (from == to ? 1 : 0);

        g.add(from, _edge{to, to_id, cap});
        degree[from]++;
        g.add(to, _edge{from, from_id, 0});
        degree[to]++;
        pos.emplace_back(from, from_id);

        return eid;
    }

    edge get_edge(int i) {
        auto e = g[pos[i].first][pos[i].second];
        auto re = g[e.to][e.rev];
        return edge{pos[i].first, e.to, e.cap + re.cap, re.cap};
    }

    Cap flow(int s, int t){
        return flow(s, t, std::numeric_limits<Cap>::max());
    }

    Cap flow(int s, int t, Cap flow_limit){
        assert(0 <= s && s < n);
        assert(0 <= t && t < n);
        assert(s != t);
        g.build();

        std::vector<int> level(n), iter(n);
        internal::simple_queue<int> que;

        auto bfs = [&]() {
            std::fill(level.begin(), level.end(), -1);
            level[s] = 0;
            que.clear();
            que.push(s);
            while (!que.empty()){
                int v = que.front(); que.pop();
                for (auto e : g[v]){
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return ;
                    que.push(e.to);
                }
            }
        };
        auto dfs = [&](auto sfs, int v, Cap up){
            if (v == s) return up;
            Cap res = 0;
            int level_v = level[v];
            for (int &i = iter[v]; i < degree[v]; i++){
                _edge &e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                Cap d = sfs(sfs, e.to, std::min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up) return res;
            }
            level[v] = n;
            return res;
        };

        Cap flow = 0;
        while (flow < flow_limit){
            bfs();
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = dfs(dfs, t, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s){
        std::vector<bool> visited(n);
        internal::simple_queue<int> que;
        que.push(s);
        visited[s] = true;
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto e : g[v]){
                if (e.cap && !visited[e.to]){
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

  private:
    int n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    internal::csr<_edge> g;
    std::vector<int> degree;
};

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp"

namespace noya2{

struct prime_sieve {
    static std::vector<int> primes, factor, mu;
    prime_sieve (int n = 1024){
        build(n);
    }
    static void reserve(int n){
        int sz = size();
        if (sz == 0){
            build(n);
            return ;
        }
        if (n <= sz) return ;
        while (sz < n) sz <<= 1;
        build(sz);
    }
    // n in [1, size()] is available
    static int size(){
        return (int)factor.size() - 1;
    }
  private:
    static void build(int n){
        primes.clear();
        factor.assign(n + 1, 0);
        mu.assign(n + 1, 1);
        for (int x = 2; x <= n; x++){
            if (factor[x] == 0){
                primes.emplace_back(x);
                factor[x] = x;
                mu[x] = -1;
            }
            for (int p : primes){
                if (x * p > n || p > factor[x]) break;
                factor[x * p] = p;
                mu[x * p] = (p == factor[x] ? 0 : -mu[x]);
            }
        }
    }
} sieve;
std::vector<int> prime_sieve::primes;
std::vector<int> prime_sieve::factor;
std::vector<int> prime_sieve::mu;

void reserve_sieve(int n){
    sieve.reserve(n);
}

int mobius_sieve(int n){
    assert(1 <= n && n <= sieve.size());
    return sieve.mu[n];
}

bool is_prime_sieve(int n){
    if (n <= 2) return n == 2;
    assert(n <= sieve.size());
    return sieve.factor[n] == n;
}

// pair(prime, exponent)
std::vector<std::pair<int, int>> factorize_sieve(int n){
    assert(1 <= n && n <= sieve.size());
    std::vector<std::pair<int, int>> ret;
    int pre = 0;
    while (n > 1){
        int p = sieve.factor[n];
        if (pre != p){
            ret.emplace_back(p, 1);
        }
        else {
            ret.back().second += 1;
        }
        pre = p;
        n /= p;
    }
    return ret;
}

std::vector<int> divisors_sieve(int n){
    assert(1 <= n && n <= sieve.size());
    std::vector<int> ret = {1};
    int pre = 0, w = 1;
    while (n > 1){
        int p = sieve.factor[n];
        int sz = ret.size();
        if (pre != p){
            w = ret.size();
        }
        ret.reserve(sz + w);
        for (int i = 0; i < w; i++){
            ret.emplace_back(ret[sz - w + i] * p);
        }
        pre = p;
        n /= p;
    }
    return ret;
}

} // namespace noya2
#line 5 "c.cpp"

void solve(){
    int n; in(n);
    vector<int> a(n); in(a);
    reserve_sieve(5050);
    int le = 1, ri = n+1;
    while (ri - le > 1){
        int md = (le + ri) / 2;
        int s = n+md, t = s+1;
        mf_graph<int> g(t+1);
        rep(i,n){
            g.add_edge(s,i,1);
            for (int d : divisors_sieve(a[i])){
                if (d <= md){
                    g.add_edge(i,n+d-1,1);
                }
            }
        }
        rep(i,md){
            g.add_edge(n+i,t,1);
        }
        int f = g.flow(s,t);
        if (f == md){
            le = md;
        }
        else {
            ri = md;
        }
    }
    out(le);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
yukicoder

結果

ソースコード
