結果

問題 No.1661 Sum is Prime (Hard Version)
ユーザー rniyarniya
提出日時 2021-08-27 23:16:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,289 ms / 3,000 ms
コード長 7,953 bytes
コンパイル時間 2,344 ms
コンパイル使用メモリ 210,164 KB
実行使用メモリ 68,332 KB
最終ジャッジ日時 2024-11-21 05:12:26
合計ジャッジ時間 15,848 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 223 ms
41,532 KB
testcase_01 AC 218 ms
41,532 KB
testcase_02 AC 863 ms
67,948 KB
testcase_03 AC 219 ms
41,532 KB
testcase_04 AC 215 ms
41,660 KB
testcase_05 AC 217 ms
41,440 KB
testcase_06 AC 223 ms
41,536 KB
testcase_07 AC 217 ms
41,440 KB
testcase_08 AC 223 ms
41,528 KB
testcase_09 AC 219 ms
41,532 KB
testcase_10 AC 218 ms
41,660 KB
testcase_11 AC 222 ms
41,536 KB
testcase_12 AC 763 ms
67,196 KB
testcase_13 AC 768 ms
66,592 KB
testcase_14 AC 834 ms
66,836 KB
testcase_15 AC 1,058 ms
66,836 KB
testcase_16 AC 911 ms
66,492 KB
testcase_17 AC 844 ms
66,344 KB
testcase_18 AC 446 ms
50,664 KB
testcase_19 AC 645 ms
60,992 KB
testcase_20 AC 477 ms
50,192 KB
testcase_21 AC 781 ms
68,332 KB
testcase_22 AC 649 ms
62,064 KB
testcase_23 AC 1,289 ms
68,188 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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
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> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

typedef pair<int, int> P;
#define stop   \
    char nyaa; \
    cin >> nyaa;
#define rep(i, n) for (int i = 0; i < n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define Rep1(i, sta, n) for (int i = sta; i <= n; i++)
#define all(v) (v).begin(), (v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

bool isp[25000001];
vector<int> ps;

void init(int sup = 25000000) {
    fill(isp + 2, isp + sup + 1, true);
    for (int i = 2; i <= sup; i++) {
        if (!isp[i]) continue;
        ps.push_back(i);
        for (int j = 2 * i; j <= sup; j += i) {
            isp[j] = false;
        }
    }
}

ll count_prime(ll n) {
    if (n < 10) {
        ll res = 0;
        for (int i = 2; i <= n; i++)
            if (isp[i]) res++;

        return res;
    }

    ll t = 1;
    while (t * t * t <= n) {
        t++;
    }
    t--;

    int loc = 0;
    rep(i, ps.size()) if (ps[i] > t) {
        loc = i;
        break;
    }

    // cout << "! " << t <<" "<<loc<< "\n";
    vector<bool> used(t * t + 1, false);
    vector<vector<int>> ids(loc);
    rep(i, loc) {
        for (int j = ps[i]; j <= t * t; j += ps[i]) {
            if (!used[j]) {
                used[j] = true;
                ids[i].push_back(j);
            }
        }
    }

    function<ll(ll, ll)> calc = [&](ll n, ll m) -> ll {
        if (m == 0) return n;
        if (n <= t * t) {
            ll res = n;
            rep(i, m) { res -= upper_bound(all(ids[i]), n) - ids[i].begin(); }
            return res;
        } else {
            return calc(n, m - 1) - calc(n / ps[m - 1], m - 1);
        }
    };

    ll ans = calc(n, loc) + loc;
    ans--;
    int las = ps.size();
    rep(i, ps.size()) {
        if ((ll)ps[i] * ps[loc] > n) {
            las = i;
            break;
        }
    }
    while (true) {
        while (loc < las && (ll)ps[loc] * ps[las - 1] > n) {
            las--;
        }
        if (loc >= las) break;
        // cout << ps[loc] << " " << ps[las - 1] << "\n";
        ans -= las - loc;
        loc++;
    }
    return ans;
}

/**
 * @brief osa_k法
 * @docs docs/math/prime_factor_table.md
 */
vector<int> prime_factor_table(int n) {
    vector<int> res(n + 1, 0);
    for (int i = 2; i <= n; i++)
        if (!res[i]) {
            for (int j = i; j <= n; j += i) {
                if (!res[j]) res[j] = i;
            }
        }
    return res;
}

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

const int MAX_L = 1000010;

ll small(ll L, ll R) {
    auto table = prime_factor_table(MAX_L * 2);

    int ans = 0;
    for (int i = L; i <= R; i++) {
        ans += (table[i] == i);
        if (i + 1 <= R) ans += (table[i + (i + 1)] == i + (i + 1));
    }

    return ans;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    init();
    ll L, R;
    cin >> L >> R;

    if (R < MAX_L) {
        cout << small(L, R) << '\n';
        return 0;
    }

    auto calc = [&](ll n) { return count_prime(n); };  // number of primes lower than n
    ll ans = 0;
    ans += calc(R) - calc(L - 1);
    if (L + 1 <= R) ans += calc((R - 1) + R) - calc(L + (L + 1) - 1);

    cout << ans << '\n';
    return 0;
}
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