#591275 (C++17) No.1322 Totient Bound

提出ソース

結果

問題	No.1322 Totient Bound
ユーザー	noimi
提出日時	2020-12-09 19:11:18
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,113 ms / 5,000 ms
コード長	15,994 bytes
コンパイル時間	3,876 ms
コンパイル使用メモリ	235,276 KB
実行使用メモリ	151,308 KB
最終ジャッジ日時	2023-10-19 05:51:38
合計ジャッジ時間	23,129 ms
ジャッジサーバーID （参考情報）	judge11 / judge12

このコードへのチャレンジ
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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	47 ms 84,772 KB
testcase_01	AC	48 ms 84,828 KB
testcase_02	AC	47 ms 84,828 KB
testcase_03	AC	47 ms 84,828 KB
testcase_04	AC	47 ms 84,828 KB
testcase_05	AC	48 ms 84,828 KB
testcase_06	AC	47 ms 84,828 KB
testcase_07	AC	48 ms 84,828 KB
testcase_08	AC	48 ms 84,828 KB
testcase_09	AC	48 ms 84,828 KB
testcase_10	AC	47 ms 84,828 KB
testcase_11	AC	48 ms 84,828 KB
testcase_12	AC	48 ms 84,828 KB
testcase_13	AC	48 ms 85,092 KB
testcase_14	AC	49 ms 85,092 KB
testcase_15	AC	48 ms 84,828 KB
testcase_16	AC	48 ms 84,828 KB
testcase_17	AC	48 ms 84,828 KB
testcase_18	AC	216 ms 99,900 KB
testcase_19	AC	326 ms 106,896 KB
testcase_20	AC	826 ms 136,132 KB
testcase_21	AC	905 ms 141,008 KB
testcase_22	AC	919 ms 141,820 KB
testcase_23	AC	1,113 ms 151,308 KB
testcase_24	AC	1,092 ms 151,308 KB
testcase_25	AC	1,090 ms 151,308 KB
testcase_26	AC	1,105 ms 151,308 KB
testcase_27	AC	1,097 ms 151,308 KB
testcase_28	AC	1,107 ms 151,308 KB
testcase_29	AC	1,087 ms 151,308 KB
testcase_30	AC	53 ms 84,828 KB
testcase_31	AC	48 ms 84,828 KB
testcase_32	AC	47 ms 84,828 KB
testcase_33	AC	1,093 ms 151,308 KB
testcase_34	AC	1,091 ms 150,772 KB
testcase_35	AC	1,110 ms 151,308 KB
testcase_36	AC	1,109 ms 150,772 KB
testcase_37	AC	1,102 ms 150,500 KB
testcase_38	AC	1,113 ms 151,308 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

raw source code

#pragma region Macros
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define rep2(i, a, b) for(ll i = a; i <= b; ++i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep3(i, a, b) for(ll i = a; i >= b; --i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                                                                                                  \
    vector<type> name(size);                                                                                                                                   \
    IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                                                                                                   \
    vector<vector<type>> name(h, vector<type>(w));                                                                                                             \
    IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)                                                                                                                         \
    vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define mt make_tuple

#define fi first
#define se second
#define all(c) begin(c), end(c)
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void yes(bool t = 1) { cout << yesno[t] << endl; }
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define si(c) (int)(c).size()
#define INT(...)                                                                                                                                               \
    int __VA_ARGS__;                                                                                                                                           \
    IN(__VA_ARGS__)
#define LL(...)                                                                                                                                                \
    ll __VA_ARGS__;                                                                                                                                            \
    IN(__VA_ARGS__)
#define STR(...)                                                                                                                                               \
    string __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
#define CHR(...)                                                                                                                                               \
    char __VA_ARGS__;                                                                                                                                          \
    IN(__VA_ARGS__)
#define DBL(...)                                                                                                                                               \
    double __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
    for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &... tail) {
    scan(head);
    IN(tail...);
}
template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
vi iota(int n) {
    vi a(n);
    iota(all(a), 0);
    return a;
}
template <typename T> vi iota(vector<T> &a, bool greater = false) {
    vi res(a.size());
    iota(all(res), 0);
    sort(all(res), [&](int i, int j) {
        if(greater) return a[i] > a[j];
        return a[i] < a[j];
    });
    return res;
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
template <class T> T POW(T x, int n) {
    T res = 1;
    for(; n; n >>= 1, x *= x)
        if(n & 1) res *= x;
    return res;
}
vector<pll> factor(ll x) {
    vector<pll> ans;
    for(ll i = 2; i * i <= x; i++)
        if(x % i == 0) {
            ans.push_back({i, 1});
            while((x /= i) % i == 0) ans.back().second++;
        }
    if(x != 1) ans.push_back({x, 1});
    return ans;
}
template <class T> vector<T> divisor(T x) {
    vector<T> ans;
    for(T i = 1; i * i <= x; i++)
        if(x % i == 0) {
            ans.pb(i);
            if(i * i != x) ans.pb(x / i);
        }
    return ans;
}
template <typename T> void zip(vector<T> &x) {
    vector<T> y = x;
    sort(all(y));
    for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int allbit(int n) { return (1 << n) - 1; }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

int in() {
    int x;
    cin >> x;
    return x;
}
ll lin() {
    unsigned long long x;
    cin >> x;
    return x;
}

template <class T> pair<T, T> operator-(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi - y.fi, x.se - y.se); }
template <class T> pair<T, T> operator+(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi + y.fi, x.se + y.se); }
template <class T> ll operator*(const pair<T, T> &x, const pair<T, T> &y) { return (ll)x.fi * y.fi + (ll)x.se * y.se; }

template <typename T> struct edge {
    int from, to;
    T cost;
    int id;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
    edge &operator=(const int &x) {
        to = x;
        return *this;
    }
    operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;

using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
    Tree res(n);
    if(m == -1) m = n - 1;
    while(m--) {
        int a, b;
        cin >> a >> b;
        a -= margin, b -= margin;
        res[a].emplace_back(b);
        if(!directed) res[b].emplace_back(a);
    }
    return move(res);
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
    Wgraph<T> res(n);
    if(m == -1) m = n - 1;
    while(m--) {
        int a, b;
        T c;
        cin >> a >> b >> c;
        a -= margin, b -= margin;
        res[a].emplace_back(b, c);
        if(!directed) res[b].emplace_back(a, c);
    }
    return move(res);
}

#define i128 __int128_t
#define ull unsigned long long int
#define TEST                                                                                                                                                   \
    INT(testcases);                                                                                                                                            \
    while(testcases--)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
    for(auto it = begin(v); it != end(v); ++it) {
        if(it == begin(v))
            os << *it;
        else
            os << " " << *it;
    }
    return os;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <class S, class T> string to_string(pair<S, T> p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; }
template <class A> string to_string(A v) {
    if(v.empty()) return "{}";
    string ret = "{";
    for(auto &x : v) ret += to_string(x) + ",";
    ret.back() = '}';
    return ret;
}

void dump() { cerr << endl; }
template <class Head, class... Tail> void dump(Head head, Tail... tail) {
    cerr << to_string(head) << " ";
    dump(tail...);
}
#define endl '\n'
#ifdef _LOCAL
#undef endl
#define debug(x)                                                                                                                                               \
    cout << #x << ": ";                                                                                                                                        \
    dump(x)
#else
#define debug(x)
#endif

template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(15);
    }
} setup_io;
#define drop(s) cout << #s << endl, exit(0)
#pragma endregion

// from https://judge.yosupo.jp/submission/5147
vector<int> prime_sieve(const int N, const int Q = 17, const int L = 1 << 15) {
    using u8 = unsigned char;
    static const int rs[] = {1, 7, 11, 13, 17, 19, 23, 29};
    struct P {
        P(int p) : p(p) {}
        int p;
        int pos[8];
    };
    auto approx_prime_count = [](const int N) -> int { return N > 60184 ? N / (log(N) - 1.1) : max(1., N / (log(N) - 1.11)) + 1; };

    const int v = sqrt(N), vv = sqrt(v);
    vector<bool> isp(v + 1, true);
    for(int i = 2; i <= vv; ++i)
        if(isp[i]) {
            for(int j = i * i; j <= v; j += i) isp[j] = false;
        }

    const int rsize = approx_prime_count(N + 30);
    vector<int> primes = {2, 3, 5};
    int psize = 3;
    primes.resize(rsize);

    vector<P> sprimes;
    size_t pbeg = 0;
    int prod = 1;
    for(int p = 7; p <= v; ++p) {
        if(!isp[p]) continue;
        if(p <= Q) prod *= p, ++pbeg, primes[psize++] = p;
        auto pp = P(p);
        for(int t = 0; t < 8; ++t) {
            int j = (p <= Q) ? p : p * p;
            while(j % 30 != rs[t]) j += p << 1;
            pp.pos[t] = j / 30;
        }
        sprimes.push_back(pp);
    }

    vector<u8> pre(prod, 0xFF);
    for(size_t pi = 0; pi < pbeg; ++pi) {
        auto pp = sprimes[pi];
        const int p = pp.p;
        for(int t = 0; t < 8; ++t) {
            const u8 m = ~(1 << t);
            for(int i = pp.pos[t]; i < prod; i += p) pre[i] &= m;
        }
    }

    const int block_size = (L + prod - 1) / prod * prod;
    vector<u8> block(block_size);
    u8 *pblock = block.data();
    const int M = (N + 29) / 30;

    for(int beg = 0; beg < M; beg += block_size, pblock -= block_size) {
        int end = min(M, beg + block_size);
        for(int i = beg; i < end; i += prod) { copy(pre.begin(), pre.end(), pblock + i); }
        if(beg == 0) pblock[0] &= 0xFE;
        for(size_t pi = pbeg; pi < sprimes.size(); ++pi) {
            auto &pp = sprimes[pi];
            const int p = pp.p;
            for(int t = 0; t < 8; ++t) {
                int i = pp.pos[t];
                const u8 m = ~(1 << t);
                for(; i < end; i += p) pblock[i] &= m;
                pp.pos[t] = i;
            }
        }
        for(int i = beg; i < end; ++i) {
            for(int m = pblock[i]; m > 0; m &= m - 1) { primes[psize++] = i * 30 + rs[__builtin_ctz(m)]; }
        }
    }
    assert(psize <= rsize);
    while(psize > 0 && primes[psize - 1] > N) --psize;
    primes.resize(psize);
    return primes;
}

ll prime_pi(const ll n) {
    if(n <= 1) return 0;
    if(n == 2) return 1;
    const int sq = sqrtl(n);
    int s = 1 + sq >> 1;
    vector<int> smalls(s);
    for(int i = 1; i < s; ++i) smalls[i] = i;
    vector<int> roughs(s);
    for(int i = 0; i < s; ++i) roughs[i] = i << 1 | 1;
    vector<ll> larges(s);
    for(int i = 0; i < s; ++i) larges[i] = (n / (i << 1 | 1) - 1) >> 1;
    vector<bool> skip(sq + 1);
    const auto divide = [](ll n, ll d) -> int { return (long double)n / d; };
    const auto half = [](int n) -> int { return (n - 1) >> 1; };
    int pc = 0;
    for(int p = 3; p <= sq; p += 2)
        if(!skip[p]) {
            int q = p * p;
            if((ll)q * q > n) break;
            skip[p] = true;
            for(int i = q; i <= sq; i += p << 1) skip[i] = true;
            int ns = 0;
            for(int k = 0; k < s; ++k) {
                int i = roughs[k];
                if(skip[i]) continue;
                ll d = (ll)i * p;
                larges[ns] = larges[k] - (d <= sq ? larges[smalls[d >> 1] - pc] : smalls[half(divide(n, d))]) + pc;
                roughs[ns++] = i;
            }
            s = ns;
            for(int i = half(sq), j = ((sq / p) - 1) | 1; j >= p; j -= 2) {
                int c = smalls[j >> 1] - pc;
                for(int e = (j * p) >> 1; i >= e; --i) smalls[i] -= c;
            }
            ++pc;
        }
    larges[0] += (ll)(s + 2 * (pc - 1)) * (s - 1) / 2;
    for(int k = 1; k < s; ++k) larges[0] -= larges[k];
    for(int l = 1; l < s; ++l) {
        int q = roughs[l];
        ll m = n / q;
        int e = smalls[half(m / q)] - pc;
        if(e < l + 1) break;
        ll t = 0;
        for(int k = l + 1; k <= e; ++k) t += smalls[half(divide(m, roughs[k]))];
        larges[0] += t - (ll)(e - l) * (pc + l - 1);
    }
    return larges[0] + 1;
}

int main() {
    LL(n);
    ll ans = 0;
    const int N = 10000000, M = 110000;
    auto P = prime_sieve(N);
    vector<ll> cnt(N + 1);
    for(auto e : P) cnt[e] = 1;
    rep(i, N) cnt[i + 1] += cnt[i];

    unordered_map<ll, ll> mem;
    auto prime_count = [&](ll x) -> ll {
        if(x > N) {
            if(mem.count(x)) return mem[x];
            return mem[x] = prime_pi(x);
        }
        return cnt[x];
    };

    auto primes = prime_sieve(M);
    vector<unordered_map<ll, ll>> dp(si(primes));
    auto rec = [&](auto &&self, int i, ll x) -> ll {
        if(dp[i].count(x)) return dp[i][x];
        auto &res = dp[i][x];

        if((ll)primes[i] * (primes[i] - 1) > x) {
            res = prime_count(x + 1) - i + 1;
            chmax(res, 1);
            return res;
        } else {
            res = self(self, i + 1, x);
            x /= primes[i] - 1;
            while(x) {
                res += self(self, i + 1, x);
                x /= primes[i];
            }
            return res;
        }
    };

    cout << rec(rec, 0, n) << endl;
}

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結果

テストケース

ソースコード