#1029719 (C++23) No.2979 直角三角形の個数

提出ソース

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 03:11:57
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	TLE
実行時間	-
コード長	8,624 bytes
コンパイル時間	3,436 ms
コンパイル使用メモリ	259,596 KB
実行使用メモリ	33,140 KB
最終ジャッジ日時	2024-12-03 03:12:19
合計ジャッジ時間	21,905 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

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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	19 ms 33,140 KB
testcase_01	AC	15 ms 17,280 KB
testcase_02	AC	16 ms 17,408 KB
testcase_03	AC	15 ms 12,032 KB
testcase_04	AC	15 ms 11,904 KB
testcase_05	AC	15 ms 11,776 KB
testcase_06	AC	15 ms 11,904 KB
testcase_07	AC	16 ms 11,904 KB
testcase_08	AC	14 ms 11,776 KB
testcase_09	AC	15 ms 12,032 KB
testcase_10	AC	14 ms 11,904 KB
testcase_11	AC	14 ms 11,904 KB
testcase_12	AC	15 ms 11,904 KB
testcase_13	AC	15 ms 11,904 KB
testcase_14	AC	19 ms 11,904 KB
testcase_15	AC	20 ms 11,776 KB
testcase_16	AC	30 ms 11,904 KB
testcase_17	AC	53 ms 12,144 KB
testcase_18	AC	133 ms 12,536 KB
testcase_19	AC	180 ms 12,660 KB
testcase_20	AC	556 ms 13,684 KB
testcase_21	AC	817 ms 14,452 KB
testcase_22	TLE	-
testcase_23	TLE	-
testcase_24	AC	16 ms 11,776 KB
testcase_25	AC	16 ms 12,032 KB
testcase_26	AC	17 ms 12,032 KB
testcase_27	AC	17 ms 11,904 KB
testcase_28	TLE	-

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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"

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 19 "c.cpp"

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;
        }
        for (ll p = lim+1; p*p+p <= x; 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);
    }
    auto get = [&](ll x){
        if (x <= sq){
            return sml[x];
        }
        else {
            return big[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;
            if (v == 0) break;
            ll rg = lim / v; // [g, rg]
            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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結果

テストケース

ソースコード