結果

問題 No.2519 Coins in Array
ユーザー noya2noya2
提出日時 2023-10-27 22:44:47
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 69 ms / 2,000 ms
コード長 10,076 bytes
コンパイル時間 3,876 ms
コンパイル使用メモリ 274,364 KB
実行使用メモリ 10,248 KB
最終ジャッジ日時 2024-09-25 14:44:47
合計ジャッジ時間 8,196 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
sample AC * 4
other AC * 37
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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 1 "/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 << min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),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(vector<T> &v){
    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/math/sieve.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp"

namespace noya2{

struct Sieve {
    vector<int> primes, factor, mu;
    Sieve (int N = 1024){
        build(N);
    }
    void request(int N){
        int len = n_max();
        if (len >= N) return ;
        while (len < N) len <<= 1;
        build(len);
    }
    int n_max(){ return factor.size()-1; }
  private:
    void build (int N){
        primes.clear();
        factor.resize(N+1); fill(factor.begin(),factor.end(),0);
        mu.resize(N+1); fill(mu.begin(),mu.end(),1);

        for(int n = 2; n <= N; n++) {
            if (factor[n] == 0){
                primes.push_back(n);
                factor[n] = n;
                mu[n] = -1;
            }
            for (int p : primes){
                if(n * p > N || p > factor[n]) break;
                factor[n * p] = p;
                mu[n * p] = p == factor[n] ? 0 : -mu[n];
            }
        }
    }
} sieve;

int mobius_sieve(int n){
    assert(1 <= n && n <= sieve.n_max());
    return sieve.mu[n];
}
bool is_prime_sieve(int n){
    if (n <= 2) return n == 2;
    assert(n <= sieve.n_max());
    return sieve.factor[n] == n;
}

vector<pair<int,int>> prime_factorization_sieve(int n){
    assert(1 <= n && n <= sieve.n_max());
    vector<int> facts;
    while (n > 1){
        int p = sieve.factor[n];
        facts.push_back(p);
        n /= p;
    }
    vector<pair<int,int>> pes;
    int siz = facts.size();
    for (int l = 0, r = 0; l < siz; l = r){
        while (r < siz && facts[r] == facts[l]) r++;
        pes.emplace_back(facts[l],r-l);
    }
    return pes;
}

vector<int> divisor_enumeration_sieve(int n){
    auto pes = prime_factorization_sieve(n);
    vector<int> divs = {1};
    for (auto [p, e] : pes){
        vector<int> nxt; nxt.reserve(divs.size() * (e+1));
        for (auto x : divs){
            for (int tt = 0; tt <= e; tt++){
                nxt.push_back(x);
                x *= p;
            }
        }
        swap(divs,nxt);
    }
    return divs;
}

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/fenwick_tree.hpp"

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

namespace noya2{

template <class T> struct fenwick_tree {
  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += x;
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    vector<T> data;

    T sum(int r) {
        T s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

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

const ll mx = 1'000'000'000'000'000'000;

void naive(vector<ll> a){
    int n = a.size(); //out("naive"); cout << flush;
    a.resize(n+n-1);
    vector<bool> b(n+n-1,false);
    vector<pii> logs;
    ll mi = linf;
    vector<pii> ans;
    fenwick_tree<int> fen(n+n);
    auto dfs = [&](auto sfs, int nxt) -> void {
        vector<int> ids;
        rep(i,nxt) if (!b[i]) ids.emplace_back(i);
        if (nxt == n+n-1){
            if (chmin(mi,a[ids[0]])){
                ans = logs;
            }
            return ;
        }
        for (int i : ids) for (int j : ids){
            if (i >= j) continue;
            if (gcd_fast(a[i],a[j]) == 1){
                ll l = a[i]-1, r = a[j]-1;
                if (!(l <= mx/r)) continue;
            }
            b[i] = true;
            b[j] = true;
            int l = i - fen.sum(0,i);
            int r = j - fen.sum(0,j);
            logs.emplace_back(l+1,r+1);
            fen.add(i,1);
            fen.add(j,1);
            a[nxt] = (gcd_fast(a[i],a[j]) == 1 ? (a[i]-1)*(a[j]-1) : 0LL);
            sfs(sfs,nxt+1);
            b[i] = false;
            b[j] = false;
            logs.pop_back();
            fen.add(i,-1);
            fen.add(j,-1);
        }
    };
    dfs(dfs,n); //out("naive");
    out(mi);
    rep(i,n-1) out(ans[i]);
}


void solve(){
    sieve.request(200000);
    int n; in(n);
    vector<ll> a(n); in(a);
    a.resize(n+n-1);
    vector<bool> b(n+n-1,false);
    int cur = n;
    auto get = [&](int i, int j){
        if (gcd_fast(a[i],a[j]) == 1) return (a[i]-1)*(a[j]-1);
        return 0LL;
    };
    fenwick_tree<int> fen(n+n);
    auto upd = [&](int i, int j){
        assert(!b[i]);
        assert(!b[j]);
        //out(i,j); cout << flush; 
        int l = i - fen.sum(0,i);
        int r = j - fen.sum(0,j);
        out(l+1,r+1);
        a[cur++] = get(i,j);
        b[i] = true, b[j] = true;
        fen.add(i,1);
        fen.add(j,1);
    };
    auto say = [&](){ //out(cur);
        rep(i,n){
            if (cur == n+n-1) break;
            if (b[i]) continue;
            upd(i,cur-1);
        }
    };
    map<int,int> mp;
    rep(i,n){
        if (a[i] == 0){
            out(0);
            int j = (i == 0 ? 1 : i-1);
            upd(i,j);
            say();
            return ;
        }
        for (auto [p, e] : prime_factorization_sieve(a[i])){
            if (mp.contains(p)){
                out(0); //cout << flush;
                upd(i,mp[p]);
                say();
                return ;
            }
            mp[p] = i;
        }
    }
    vector<int> odds;
    rep(i,n) if (a[i] % 2 == 1) odds.emplace_back(i);
    if ((int)(odds.size()) >= 4){
        out(0);
        upd(odds[0],odds[1]);
        upd(odds[2],odds[3]);
        upd(n,n+1);
        say();
        return ;
    }
    assert(n <= 4);
    a.resize(n);
    naive(a);
}

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