結果

問題 No.2979 直角三角形の個数
ユーザー noya2
提出日時 2024-12-03 03:26:19
言語 C++17(clang)
(17.0.6 + boost 1.87.0)
結果
AC  
実行時間 2,862 ms / 4,000 ms
コード長 8,853 bytes
コンパイル時間 2,693 ms
コンパイル使用メモリ 167,112 KB
実行使用メモリ 22,772 KB
最終ジャッジ日時 2024-12-03 03:26:33
合計ジャッジ時間 12,630 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 3
other AC * 26
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 #
プレゼンテーションモードにする

#line 1 "c.cpp"
// #pragma GCC optimize("Ofast")
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#include<bits/stdc++.h>
using namespace std;
#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 4 "c.cpp"
ll naive(ll n){
    ll sq = sqrt_fast(n);
    ll ans = 0;
    n /= 2;
    for (ll p = 2; p <= sq; p++){
        for (ll q = 1; q < p && p*p + p*q <= n; q++){
            if ((p - q) % 2 == 0) continue;
            if (gcd(p,q) != 1) continue;
            // out(p,q,n/(p*p+p*q));
            ans += n / (p*p+p*q);
        }
    }
    return ans;
}
#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 21 "c.cpp"
inline ll quo(ll x, ll d){
    return double(x) / d;
}
ll fast(ll n){
    const int mx = 1001000;
    sieve.request(mx);
    n /= 2;
    ll sq = sqrt_fast(n);
    vector<ll> sml(sq+1), big(sq+1);
    auto calc = [&](ll x){
        // p*p + p*q <= x
        // p > q >= 1
        // p - q = 1 (mod 2)
        ll lim = (1 + sqrt_fast(1 + 8 * x)) / 4;
        // p <= lim --> 0 <= k <= p/2 - 1
        // p > lim --> p - 1/2 - x/(2p) <= k <= p/2 - 1
        ll last = lim/2;
        ll ret = last*(last+1);
        if (lim % 2 == 0){
            ret -= last;
        }
        ll sqx = sqrt_fast(x);
        for (ll p = lim+1; p <= sqx; p++){
            ll ri = p/2-1;
            ll le = ceil_div(2*p*p-p-x,2*p);
            ret += max(ri - le + 1, 0LL);
        }
        return ret;
    };
    for (ll x = 1; x <= sq; x++){
        sml[x] = calc(x);
        big[x] = calc(n/x);
    }
    // return 0;
    auto get = [&](ll x){
        if (x <= sq){
            return sml[x];
        }
        else {
            return big[quo(n, x)];
        }
    };
    ll ans = 0;
    for (ll d = 1; d <= sq; d += 2){
        ll lim = n / (d * d);
        ll sum = 0;
        ll g = 1;
        while (true){
            // ll v = lim / g;
            ll v = quo(lim, g);
            if (v == 0) break;
            // ll rg = lim / v; // [g, rg]
            ll rg = quo(lim, v);
            sum += get(v) * (rg - g + 1);
            g = rg + 1;
        }
        ans += sum * mobius_sieve(d);
    }
    return ans;
}
void jikken1(){
    int n; in(n);
    ld ans = 0;
    for (int i = 1; i <= n; i++){
        ans += sqrtl(i) + n / sqrtl(i);
    }
    out(ans);
}
void jikken2(){
    ll n; in(n);
    ll sq = sqrt_fast(n);
    ld ans = 0;
    for (ll d = 1; d <= sq; d += 2){
        ans += sqrtl(ld(n)/(d*d));
    }
    out(ans);
}
void solve(){
    // jikken1(); return ;
    // jikken2(); return ;
    ll n; in(n);
    // out(naive(n));
    out(fast(n));
}
int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
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