#672864 (C++17) No.1567 Integer Coefficient Equation

提出ソース

結果

問題	No.1567 Integer Coefficient Equation
ユーザー	hitonanode
提出日時	2021-07-03 14:35:41
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	127 ms / 2,000 ms
コード長	9,870 bytes
コンパイル時間	1,762 ms
コンパイル使用メモリ	149,248 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-30 06:19:58
合計ジャッジ時間	10,288 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	90 ms 6,812 KB
testcase_01	AC	93 ms 6,944 KB
testcase_02	AC	116 ms 6,940 KB
testcase_03	AC	113 ms 6,940 KB
testcase_04	AC	113 ms 6,944 KB
testcase_05	AC	113 ms 6,940 KB
testcase_06	AC	112 ms 6,940 KB
testcase_07	AC	90 ms 6,944 KB
testcase_08	AC	89 ms 6,940 KB
testcase_09	AC	90 ms 6,944 KB
testcase_10	AC	90 ms 6,940 KB
testcase_11	AC	90 ms 6,944 KB
testcase_12	AC	91 ms 6,940 KB
testcase_13	AC	90 ms 6,940 KB
testcase_14	AC	90 ms 6,944 KB
testcase_15	AC	91 ms 6,944 KB
testcase_16	AC	91 ms 6,940 KB
testcase_17	AC	124 ms 6,940 KB
testcase_18	AC	123 ms 6,940 KB
testcase_19	AC	125 ms 6,940 KB
testcase_20	AC	126 ms 6,944 KB
testcase_21	AC	127 ms 6,944 KB
testcase_22	AC	125 ms 6,944 KB
testcase_23	AC	125 ms 6,944 KB
testcase_24	AC	124 ms 6,944 KB
testcase_25	AC	126 ms 6,940 KB
testcase_26	AC	124 ms 6,944 KB
testcase_27	AC	125 ms 6,940 KB
testcase_28	AC	123 ms 6,940 KB
testcase_29	AC	123 ms 6,944 KB
testcase_30	AC	123 ms 6,940 KB
testcase_31	AC	122 ms 6,944 KB
testcase_32	AC	123 ms 6,944 KB
testcase_33	AC	123 ms 6,944 KB
testcase_34	AC	126 ms 6,944 KB
testcase_35	AC	124 ms 6,944 KB
testcase_36	AC	123 ms 6,940 KB
testcase_37	AC	124 ms 6,940 KB
testcase_38	AC	122 ms 6,940 KB
testcase_39	AC	121 ms 6,940 KB

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ソースコード

raw source code

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

// Linear sieve algorithm for fast prime factorization
// Complexity: O(N) time, O(N) space:
// - MAXN = 10^7:  ~44 MB,  80~100 ms (Codeforces / AtCoder GCC, C++17)
// - MAXN = 10^8: ~435 MB, 810~980 ms (Codeforces / AtCoder GCC, C++17)
// Reference:
// [1] D. Gries, J. Misra, "A Linear Sieve Algorithm for Finding Prime Numbers,"
//     Communications of the ACM, 21(12), 999-1003, 1978.
// - https://cp-algorithms.com/algebra/prime-sieve-linear.html
// - https://37zigen.com/linear-sieve/
struct Sieve {
    std::vector<int> min_factor;
    std::vector<int> primes;
    Sieve(int MAXN) : min_factor(MAXN + 1) {
        for (int d = 2; d <= MAXN; d++) {
            if (!min_factor[d]) {
                min_factor[d] = d;
                primes.emplace_back(d);
            }
            for (const auto &p : primes) {
                if (p > min_factor[d] or d * p > MAXN) break;
                min_factor[d * p] = p;
            }
        }
    }
    // Prime factorization for 1 <= x <= MAXN^2
    // Complexity: O(log x)           (x <= MAXN)
    //             O(MAXN / log MAXN) (MAXN < x <= MAXN^2)
    template <typename T> std::map<T, int> factorize(T x) {
        std::map<T, int> ret;
        assert(x > 0 and x <= ((long long)min_factor.size() - 1) * ((long long)min_factor.size() - 1));
        for (const auto &p : primes) {
            if (x < T(min_factor.size())) break;
            while (!(x % p)) x /= p, ret[p]++;
        }
        if (x >= T(min_factor.size())) ret[x]++, x = 1;
        while (x > 1) ret[min_factor[x]]++, x /= min_factor[x];
        return ret;
    }
    // Enumerate divisors of 1 <= x <= MAXN^2
    // Be careful of highly composite numbers https://oeis.org/A002182/list https://gist.github.com/dario2994/fb4713f252ca86c1254d#file-list-txt
    // (n, (# of div. of n)): 45360->100, 735134400(<1e9)->1344, 963761198400(<1e12)->6720
    template <typename T> std::vector<T> divisors(T x) {
        std::vector<T> ret{1};
        for (const auto p : factorize(x)) {
            int n = ret.size();
            for (int i = 0; i < n; i++) {
                for (T a = 1, d = 1; d <= p.second; d++) {
                    a *= p.first;
                    ret.push_back(ret[i] * a);
                }
            }
        }
        return ret; // NOT sorted
    }
    // Moebius function Table, (-1)^{# of different prime factors} for square-free x
    // return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] https://oeis.org/A008683
    std::vector<int> GenerateMoebiusFunctionTable() {
        std::vector<int> ret(min_factor.size());
        for (unsigned i = 1; i < min_factor.size(); i++) {
            if (i == 1)
                ret[i] = 1;
            else if ((i / min_factor[i]) % min_factor[i] == 0)
                ret[i] = 0;
            else
                ret[i] = -ret[i / min_factor[i]];
        }
        return ret;
    }
    // Calculate [0^K, 1^K, ..., nmax^K] in O(nmax)
    // Note: **0^0 == 1**
    template <typename MODINT> std::vector<MODINT> enumerate_kth_pows(long long K, int nmax) {
        assert(nmax < int(min_factor.size()));
        assert(K >= 0);
        if (K == 0) return std::vector<MODINT>(nmax + 1, 1);
        std::vector<MODINT> ret(nmax + 1);
        ret[0] = 0, ret[1] = 1;
        for (int n = 2; n <= nmax; n++) {
            if (min_factor[n] == n) {
                ret[n] = MODINT(n).pow(K);
            } else {
                ret[n] = ret[n / min_factor[n]] * ret[min_factor[n]];
            }
        }
        return ret;
    }
};
Sieve sieve(400000);  // (can factorize n <= 10^9)

vector<int> precalc;

int solve() {
    int P, L, R;
    cin >> P >> L >> R;
    L -= P, R -= P;
    int ret = 0;
    dbg(pint(L, R));
    if (L < 0) {
        ret += precalc[abs(L)] - precalc[max(-R - 1, 0)];
    }
    dbg(ret);
    if (R >= 0) {
        ret += precalc[R] - precalc[max(L - 1, 0)];
    }
    dbg(ret);
    if (L <= 0 and 0 <= R) ret++;
    dbg(ret);
    return ret;
}

int main() {
    precalc.resize(400001);
    FOR(x, 2, precalc.size()) {
        auto f = sieve.factorize(x);
        vector<int> degs;
        for (auto [p, d] : f) degs.push_back(d);
        if (f.size() >= 3) precalc[x] = 1;
        if (f.size() == 1) {
            if (degs[0] >= 4) precalc[x] = 1;
        }
        if (f.size() == 2) {
            if (degs[0] >= 2 or degs[1] >= 2) precalc[x] = 1;
        }
    }
    FOR(i, 1, precalc.size()) if (precalc[i]) {
        for (int j = i * 2; j < int(precalc.size()); j += i) precalc[j] = 1;
    }
    FOR(i, 1, precalc.size()) precalc[i] += precalc[i - 1];

    int T;
    cin >> T;
    while (T--) cout << solve() << '\n';
}

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結果

テストケース

ソースコード