結果

問題 No.2979 直角三角形の個数
ユーザー tko919tko919
提出日時 2024-12-07 05:12:47
言語 C++23(gcc13)
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 1,130 ms / 4,000 ms
コード長 13,562 bytes
コンパイル時間 4,484 ms
コンパイル使用メモリ 310,340 KB
実行使用メモリ 14,220 KB
最終ジャッジ日時 2024-12-07 05:12:57
合計ジャッジ時間 9,754 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 16 ms
13,836 KB
testcase_01 AC 16 ms
13,708 KB
testcase_02 AC 16 ms
13,964 KB
testcase_03 AC 15 ms
14,092 KB
testcase_04 AC 16 ms
14,128 KB
testcase_05 AC 16 ms
14,092 KB
testcase_06 AC 17 ms
13,964 KB
testcase_07 AC 20 ms
14,216 KB
testcase_08 AC 16 ms
14,092 KB
testcase_09 AC 16 ms
14,092 KB
testcase_10 AC 16 ms
13,968 KB
testcase_11 AC 16 ms
13,840 KB
testcase_12 AC 16 ms
14,092 KB
testcase_13 AC 17 ms
14,088 KB
testcase_14 AC 19 ms
13,964 KB
testcase_15 AC 19 ms
14,220 KB
testcase_16 AC 24 ms
14,112 KB
testcase_17 AC 35 ms
14,092 KB
testcase_18 AC 60 ms
14,092 KB
testcase_19 AC 73 ms
13,964 KB
testcase_20 AC 157 ms
14,092 KB
testcase_21 AC 223 ms
13,968 KB
testcase_22 AC 931 ms
13,836 KB
testcase_23 AC 948 ms
14,092 KB
testcase_24 AC 16 ms
13,712 KB
testcase_25 AC 16 ms
14,096 KB
testcase_26 AC 16 ms
13,840 KB
testcase_27 AC 17 ms
14,088 KB
testcase_28 AC 1,130 ms
14,100 KB
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 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio

using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
    print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/sieve.hpp"

template<int L=50101010>vector<int> sieve(int N){
    bitset<L> isp;
    int n,sq=ceil(sqrt(N));
    for(int z=1;z<=5;z+=4){
        for(int y=z;y<=sq;y+=6){
            for(int x=1;x<=sq and (n=4*x*x+y*y)<=N;++x){
                isp[n].flip();
            }
            for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
                isp[n].flip();
            }
        }
    }
    for(int z=2;z<=4;z+=2){
        for(int y=z;y<=sq;y+=6){
            for (int x=1;x<=sq and (n=3*x*x+y*y)<=N;x+=2){
                isp[n].flip();
            }
            for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
                isp[n].flip();
            }
        }
    }
    for(int y=3;y<=sq;y+=6){
        for(int z=1;z<=2;++z){
            for(int x=z;x<=sq and (n=4*x*x+y*y)<=N;x+=3){
                isp[n].flip();
            }
        }
    }
    for(int n=5;n<=sq;++n)if(isp[n]){
        for(int k=n*n;k<=N;k+=n*n){
            isp[k]=false;
        }
    }
    isp[2]=isp[3]=true;

    vector<int> ret;
    for(int i=2;i<=N;i++)if(isp[i]){
        ret.push_back(i);
    }
    return ret;
}

/**
 * @brief Prime Sieve
 */
#line 5 "sol.cpp"

ll subtask(ll n) { // 2(m+s)(2m+s)<=n
    if (n <= 50) {
        ll SQ = sqrtl(n), ret = 0;
        rep(m, 1, SQ + 3) {
            if (ll(m + 1) * (m * 2 + 1) * 2 > n)
                break;
            rep(s, 1, SQ + 1) {
                if (ll(m + s) * (m * 2 + s) * 2 > n)
                    break;
                ret++;
            }
        }
        return ret;
    }
    using P = pair<ll, ll>;
    ll CB = cbrtl(n);
    auto inside = [&](ll x, ll y) {
        return x >= 0 and y >= 0 and (x + y) * (x * 2 + y) * 2 > n;
    };
    auto cut = [&](ll x, ll y, P p) {
        return (i128(x) * 4 + y * 3) * p.first <=
               (i128(x) * 3 + y * 2) * p.second;
    };

    ll x = 0, y = sqrtl(n / 2);
    while (!inside(x, y))
        y++;
    ll ret = 0;
    stack<P> sbt({{1, 0}, {0, 1}});

    for (;;) {
        auto [dx1, dy1] = sbt.top();
        sbt.pop();
        while (inside(x + dx1, y - dy1)) {
            if (y <= dy1)
                break;
            ret += x * dy1 + (dy1 + 1) * (dx1 - 1) / 2;
            x += dx1, y -= dy1;
        }
        if (y <= dy1)
            break;
        ll dx2 = dx1, dy2 = dy1;
        while (!sbt.empty()) {
            tie(dx1, dy1) = sbt.top();
            if (inside(x + dx1, y - dy1))
                break;
            sbt.pop();
            dx2 = dx1, dy2 = dy1;
        }
        if (sbt.empty())
            break;

        for (;;) {
            ll mx = dx1 + dx2, my = dy1 + dy2;
            if (inside(x + mx, y - my)) {
                sbt.push({dx1 = mx, dy1 = my});
            } else {
                if (cut(x + mx, y - my, P{dx1, dy1}))
                    break;
                dx2 = mx, dy2 = my;
            }
        }
    }
    rep(i, 1, y) {
        ll add = (-3 * i + sqrtl(ll(i) * i + n * 4)) / 4 + 3;
        while (inside(add, i))
            add--;
        ret += add;
    }

    return ret;
}

const int N = 1010101;
int mu[N];

ll G(ll L) {
    if (L < 12)
        return 0;
    ll ret = 0;

    ll SQ = sqrtl(L);
    ll border = pow(L, .65);
    ll pre = 0;
    {
        rep(m, 1, SQ + 3) {
            if (ll(m + 1) * (m * 2 + 1) * 2 > border)
                break;
            rep(s, 1, SQ + 1) {
                if (ll(m + s) * (m * 2 + s) * 2 > border)
                    break;
                ret += L / (ll(m + s) * (m * 2 + s) * 2);
                pre++;
            }
        }
    }

    rrep(i, 1, ceil(L, border) + 3) {
        if (border >= L / i)
            continue;
        // (border,L/i]
        ll cnt = subtask(L / i);
        ret += (cnt - pre) * i;
        pre = cnt;
    }
    return ret;
}

int main() {
    {
        auto ps = sieve(N);
        rep(i, 1, N) mu[i] = 1;
        for (auto &p : ps) {
            for (int x = p; x < N; x += p)
                mu[x] *= -1;
            if (ll(p) * p >= N)
                continue;
            for (int x = p * p; x < N; x += p * p)
                mu[x] = 0;
        }
    }

    ll L;
    read(L);
    ll ret = 0;
    rep(d, 1, sqrtl(L) + 5) if (d & 1) {
        if (ll(d) * d > L)
            break;
        if (mu[d] != 0)
            ret += (G(L / d / d) - G(L / d / d / 2)) * mu[d];
    }
    print(ret);
    return 0;
}
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