#850587 (C++17) No.2249 GCDistance

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結果

問題	No.2249 GCDistance
コンテスト
ユーザー	noya2
提出日時	2023-03-17 22:41:48
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	454 ms / 5,000 ms
コード長	10,987 bytes
コンパイル時間	3,784 ms
コンパイル使用メモリ	259,364 KB
最終ジャッジ日時	2025-02-11 13:45:50
ジャッジサーバーID （参考情報）	judge5 / judge3
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 * 1
other	AC * 10
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ソースコード

raw source code
#line 1 "c.cpp"
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for (int i = 0; i < int(n); ++i)
#define repp(i,n,m) 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 namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using PL = pair<long long, long long>;
using pdd = pair<long double, long double>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
template<class T>istream &operator>>(istream &is,vector<T> &v){for(auto &e:v)is>>e;return is;}
template<typename T>bool range(T a,T b,T x){return (a<=x&&x<b);}
template<typename T>bool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));}
template<typename T> T rev(const T& str_or_vec){T res = str_or_vec; reverse(res.begin(),res.end()); return res; }
template<typename T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}
template<typename T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<typename T>void uniq(vector<T> &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}
template<typename T1, typename T2>void print(pair<T1,T2> a);
template<typename T>void print(vector<T> v);
template<typename T>void print(vector<vector<T>> v);
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
void print(unsigned int a){ printf("%u", a); }
void print(unsigned long long a) { printf("%llu", a); }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template<typename T1,typename T2>void print(pair<T1,T2> a){print(a.first);print(),print(a.second);}
template<typename T>void print(vector<T> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}}
template<typename T>void print(vector<vector<T>> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}}
void yes(){out("Yes");}
void no (){out("No");}
void yn (bool t){if(t)yes();else no();}
void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);}
void o(){out("!?");}

namespace noya2{

const int INF = 1001001007;
const long long mod1 = 998244353;
const long long mod2 = 1000000007;
const long long inf = 2e18;
const long double pi = 3.14159265358979323;
const long double eps = 1e-7;
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";

} // namespace noya2
using namespace noya2;

using mint = modint998244353;
//using mint = modint1000000007;
//using mint = modint;
void out(mint a){out(a.val());}
void out(vector<mint> a){vector<ll> b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);}
void out(vector<vector<mint>> a){for (auto v : a) out(v);}
istream &operator>>(istream &is,vector<mint> &v){for(auto &e:v){ll _x;is>>_x;e=_x;}return is;}

#line 2 "dirichlet.hpp"

/*

https://maspypy.com/dirichlet-積と、数論関数の累積和

*/

#line 11 "dirichlet.hpp"

namespace noya2{

using namespace std;
using ll = long long;
using ld = long double;

struct Dirichlet {
    int N;
    vector<int> primes, factor, mu;
    Dirichlet (int Nmax = 1'000'000) : N(Nmax), factor(Nmax+1,0), mu(Nmax+1,1) {
        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];
            }
        }
    }
};

template<typename T> T floor_sqrt(T x){ // floor(sqrt(x))
    if (x <= T(1)) return x;
    T tmp = (T)(sqrtl((long double)(x))) + T(2);
    while (tmp--){
        if (tmp * tmp <= x) break;
    }
    return tmp;
}

// proposition 4
template<typename T>
pair<vector<T>,vector<T>> multiply_sparce(ll N, vector<T> &a, vector<T> &b, vector<T> &A, vector<T> &B){
    ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N)
    vector<T> c(K+1,0);
    for (int i = 1; i <= K; i++){
        for (int j = 1; i * j <= K; j++){
            c[i*j] += a[i] * b[j];
        }
    }
    vector<T> arui(K+1,0), brui(K+1,0);
    for (int i = 1; i <= K; i++){
        arui[i] = arui[i-1] + a[i];
        brui[i] = brui[i-1] + b[i];
    }
    ld Nd = N;
    vector<T> C(L+1,0);
    for (ll l = 1; l <= L; l++){
        ll n = Nd / ld(l);
        ll m = floor_sqrt(n);
        for (ll i = 1; i <= m; i++){
            ll il = i*l;
            if (il <= L){
                C[l] += a[i] * B[il]; // B[i] = B(N/i)
            }
            else {
                C[l] += a[i] * brui[int(Nd/ld(i*l))];
            }
        }
        for (ll j = 1; j <= m; j++){
            ll jl = j*l;
            ll r = Nd / ld(jl); // m < i <= n/j = r
            if (m >= r) continue;
            if (jl <= L){
                C[l] += b[j] * (A[jl] - arui[m]); // A[i] = A(N/i)
            }
            else {
                C[l] += b[j] * (arui[r] - arui[m]);
            }
        }
    }
    return make_pair(c,C);
}

// proposition 5
template<typename T>
pair<vector<T>,vector<T>> divide_sparce(ll N, vector<T> &a, vector<T> &c, vector<T> &A, vector<T> &C){
    ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N)
    vector<T> b = c;
    for (int i = 1; i <= K; i++){
        b[i] /= a[1];
        for (int j = 2; i * j <= K; j++){
            b[i*j] -= a[j] * b[i];
        }
    }
    vector<T> arui(K+1,0), brui(K+1,0);
    for (int i = 1; i <= K; i++){
        arui[i] = arui[i-1] + a[i];
        brui[i] = brui[i-1] + b[i];
    }
    ld Nd = N;
    vector<T> B = C;
    for (ll l = L; l >= 1; l--){
        ll n = Nd / ld(l);
        ll m = floor_sqrt(n);
        for (ll j = 1; j <= m; j++){
            ll jl = j*l;
            ll r = Nd / ld(jl);
            if (m >= r) continue;
            if (jl <= L){
                B[l] -= b[j] * (A[jl] - arui[m]);
            }
            else {
                B[l] -= b[j] * (arui[r] - arui[m]);
            }
        }
    }
    for (ll l = L; l >= 1; l--){
        ll n = Nd / ld(l);
        ll m = floor_sqrt(n);
        for (ll i = 2; i <= m; i++){
            ll il = i*l;
            if (il <= L){
                B[l] -= a[i] * B[il];
            }
            else {
                B[l] -= a[i] * brui[int(Nd/ld(il))];
            }
        }
        B[l] /= a[1];
    }
    return make_pair(b,B);
}

pair<ll,ll> KL(ll N){
    ll K = max( ceill(powl(ld(N)/logl(N),ld(2)/ld(3))) , sqrtl(N) );
    ll L = N / K + 1;
    return make_pair(K,L);
}

// usage : Totient_Sum<mint>(N) 
template<typename T>
T Totient_Sum(ll N){
    if (N <= 0){
        return T(0);
    }
    if (N == 1){
        return T(1);
    }
    ll K = max( ceill(powl(ld(N)/logl(N),ld(2)/ld(3))) , sqrtl(N) );
    ll L = N / K + 1;
    vector<T> a(K+1,0), c(K+1,0);
    for (ll n = 1; n <= K; n++){
        a[n] = 1;
        c[n] = n;
    }
    vector<T> A(L+1,0), C(L+1,0);
    for (ll n = 1; n <= L; n++){
        T m = N / n;
        A[n] = m;
        C[n] = m * (m+1) / 2;
    }
    return divide_sparce(N,a,c,A,C).second[1];
}

// prefix sum of mobius function
// n <= K ( K >= floor(sqrt(N)) ) or n = floor(N/i) ( for some i <= L )
template<typename T>
struct prefix_mu{
    ll N, K, L;
    vector<T> b, brui, B;
    prefix_mu(ll _N) : N(_N) { init(); }
    T get(ll n){
        if (N <= 0){
            return T(0);
        }
        if (n <= K){
            return brui[n];
        }
        return B[N/n];
    }
    void init(){
        if (N <= 0) return ;
        if (N == 1){
            b = {0,1};
            brui = {0,1};
            B = {0,1};
            return ;
        }
        K = max( ceill(powl(ld(N)/logl(N),ld(2)/ld(3))) , sqrtl(N) );
        L = N / K + 1;
        vector<T> a(K+1,1), c(K+1,0);
        a[0] = 0, c[1] = 1;
        vector<T> A(L+1,0), C(L+1,1);
        C[0] = 0;
        for (ll n = 1; n <= L; n++){
            ll m = N / n;
            A[n] = m;
        }
        auto bB = divide_sparce(N,a,c,A,C);
        b = bB.first, B = bB.second;
        brui.resize(K+1,0);
        for (ll n = 1; n <= K; n++){
            brui[n] = brui[n-1] + b[n];
        }
    }
};

} // namespace noya2


/*

random checker


#include"dirichlet.hpp"
#include"random_kyopro.hpp"

void solve(){
    int n = rnd(1,200000);
    vector<ll> a(n+1), b(n+1); //cin >> a >> b;
    for (int i = 1; i <= n; i++){
        a[i] = rnd(10000);
        b[i] = rnd(10000);
    }
    vector<ll> c(n+1,0);
    for (int i = 1; i <= n; i++){
        for (int j = 1; i * j <= n; j++){
            c[i*j] += a[i] * b[j];
        }
    }
    vector<ll> arui(n+1,0), brui(n+1,0), crui(n+1,0);
    rep(i,n){
        arui[i+1] = arui[i] + a[i+1];
        brui[i+1] = brui[i] + b[i+1];
        crui[i+1] = crui[i] + c[i+1];
    }
    int s = floor_sqrt(n);
    vector<ll> ap(s+1), bp(s+1);
    rep(i,s+1){
        ap[i] = a[i];
        bp[i] = b[i];
    }
    int t = n/s+2;
    vector<ll> Ap(t+1), Bp(t+1);
    repp(i,t+1,1){
        Ap[i] = arui[n/i];
        Bp[i] = brui[n/i];
    }
    auto [cp, Cp] = multiply_sparce(n,ap,bp,Ap,Bp);
    auto [bq, Bq] = divide_sparce(n,ap,cp,Ap,Cp);
    for (int i = 1; i <= s; i++){
        assert(c[i] == cp[i]);
    }
    for (int i = 1; i <= t; i++){
        assert(crui[n/i] == Cp[i]);
    }
    assert(bp == bq);
    assert(Bp == Bq);
    //out(a), out(b), out(arui), out(brui);
    //out(c), out(crui);
    //out(ap); out(Ap);
    //out(bp); out(Bp);
    //out(cp); out(Cp);
    //out(bq); out(Bq);
}

*/
#line 78 "c.cpp"

void solve(){
    const int mx = 10000000;
    Dirichlet dir(mx);
    vector<ll> phi(mx+1); phi[1] = 1;
    for (int d = 2; d <= mx; d++){
        int p = dir.factor[d];
        phi[d] = p-1;
        int cur = d;
        while (cur % p == 0){
            phi[d] *= p;
            cur /= p;
        }
        phi[d] /= p;
        phi[d] *= phi[cur];
    }
    for (int d = 2; d <= mx; d++){
        phi[d] += phi[d-1];
    }
    int t; cin >> t;
    while (t--){
        ll n; cin >> n;
        ll ans = n * (n-1) + 1;
        ans -= phi[n];
        out(ans);
    }
}

int main(){
    fast_io();
    int t = 1; //cin >> t;
    while(t--) solve();
}
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結果

ソースコード
