cp-library-cpp
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test/src/algorithm/mo/abc238_g.test.cpp
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- Last update: 2023-07-09 04:04:16+09:00
- Problem: https://atcoder.jp/contests/abc238/tasks/abc238_g
Depends on
- Mo
(library/algorithm/mo.hpp)
- Internal Eratosthenes
(library/number/internal_eratosthenes.hpp)
- エラトステネスの篩
(library/number/sieve_of_eratosthenes.hpp)
Code
#define PROBLEM "https://atcoder.jp/contests/abc238/tasks/abc238_g"
#include <iostream>
#include <atcoder/modint>
using mint = atcoder::static_modint<3>;
#include "library/number/sieve_of_eratosthenes.hpp"
#include "library/algorithm/mo.hpp"
using suisen::Sieve;
using suisen::Mo;
constexpr int M = 1000000;
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n, q;
std::cin >> n >> q;
Sieve<M> sieve;
std::vector<std::vector<std::pair<int, mint>>> factorized(n);
for (int i = 0; i < n; ++i) {
int v;
std::cin >> v;
for (auto &&[p, c] : sieve.factorize(v)) {
factorized[i].emplace_back(p, c);
}
}
std::vector<std::pair<int, int>> queries(q);
for (auto &[l, r] : queries) {
std::cin >> l >> r;
--l;
}
std::vector<mint> index_sum(M + 1, 0);
int invalid = 0;
auto answers = Mo(n, queries).solve(
// Eval
[&]{
return invalid == 0;
},
// Add
[&](int i) {
for (const auto &[p, c] : factorized[i]) {
invalid -= index_sum[p] != 0;
index_sum[p] += c;
invalid += index_sum[p] != 0;
}
},
// Del
[&](int i) {
for (const auto &[p, c] : factorized[i]) {
invalid -= index_sum[p] != 0;
index_sum[p] -= c;
invalid += index_sum[p] != 0;
}
}
);
for (bool answer : answers) {
if (answer) {
std::cout << "Yes" << '\n';
} else {
std::cout << "No" << '\n';
}
}
return 0;
}#line 1 "test/src/algorithm/mo/abc238_g.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/abc238/tasks/abc238_g"
#include <iostream>
#include <atcoder/modint>
using mint = atcoder::static_modint<3>;
#line 1 "library/number/sieve_of_eratosthenes.hpp"
#include <cassert>
#include <cmath>
#include <vector>
#line 1 "library/number/internal_eratosthenes.hpp"
#include <cstdint>
#line 6 "library/number/internal_eratosthenes.hpp"
namespace suisen::internal::sieve {
constexpr std::uint8_t K = 8;
constexpr std::uint8_t PROD = 2 * 3 * 5;
constexpr std::uint8_t RM[K] = { 1, 7, 11, 13, 17, 19, 23, 29 };
constexpr std::uint8_t DR[K] = { 6, 4, 2, 4, 2, 4, 6, 2 };
constexpr std::uint8_t DF[K][K] = {
{ 0, 0, 0, 0, 0, 0, 0, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1 },
{ 2, 2, 0, 2, 0, 2, 2, 1 }, { 3, 1, 1, 2, 1, 1, 3, 1 },
{ 3, 3, 1, 2, 1, 3, 3, 1 }, { 4, 2, 2, 2, 2, 2, 4, 1 },
{ 5, 3, 1, 4, 1, 3, 5, 1 }, { 6, 4, 2, 4, 2, 4, 6, 1 },
};
constexpr std::uint8_t DRP[K] = { 48, 32, 16, 32, 16, 32, 48, 16 };
constexpr std::uint8_t DFP[K][K] = {
{ 0, 0, 0, 0, 0, 0, 0, 8 }, { 8, 8, 8, 0, 8, 8, 8, 8 },
{ 16, 16, 0, 16, 0, 16, 16, 8 }, { 24, 8, 8, 16, 8, 8, 24, 8 },
{ 24, 24, 8, 16, 8, 24, 24, 8 }, { 32, 16, 16, 16, 16, 16, 32, 8 },
{ 40, 24, 8, 32, 8, 24, 40, 8 }, { 48, 32, 16, 32, 16, 32, 48, 8 },
};
constexpr std::uint8_t MASK[K][K] = {
{ 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80 }, { 0x02, 0x20, 0x10, 0x01, 0x80, 0x08, 0x04, 0x40 },
{ 0x04, 0x10, 0x01, 0x40, 0x02, 0x80, 0x08, 0x20 }, { 0x08, 0x01, 0x40, 0x20, 0x04, 0x02, 0x80, 0x10 },
{ 0x10, 0x80, 0x02, 0x04, 0x20, 0x40, 0x01, 0x08 }, { 0x20, 0x08, 0x80, 0x02, 0x40, 0x01, 0x10, 0x04 },
{ 0x40, 0x04, 0x08, 0x80, 0x01, 0x10, 0x20, 0x02 }, { 0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01 },
};
constexpr std::uint8_t OFFSET[K][K] = {
{ 0, 1, 2, 3, 4, 5, 6, 7, },
{ 1, 5, 4, 0, 7, 3, 2, 6, },
{ 2, 4, 0, 6, 1, 7, 3, 5, },
{ 3, 0, 6, 5, 2, 1, 7, 4, },
{ 4, 7, 1, 2, 5, 6, 0, 3, },
{ 5, 3, 7, 1, 6, 0, 4, 2, },
{ 6, 2, 3, 7, 0, 4, 5, 1, },
{ 7, 6, 5, 4, 3, 2, 1, 0, },
};
constexpr std::uint8_t mask_to_index(const std::uint8_t bits) {
switch (bits) {
case 1 << 0: return 0;
case 1 << 1: return 1;
case 1 << 2: return 2;
case 1 << 3: return 3;
case 1 << 4: return 4;
case 1 << 5: return 5;
case 1 << 6: return 6;
case 1 << 7: return 7;
default: assert(false);
}
}
} // namespace suisen::internal::sieve
#line 9 "library/number/sieve_of_eratosthenes.hpp"
namespace suisen {
template <unsigned int N>
class SimpleSieve {
private:
static constexpr unsigned int siz = N / internal::sieve::PROD + 1;
static std::uint8_t flag[siz];
public:
SimpleSieve() {
using namespace internal::sieve;
flag[0] |= 1;
unsigned int k_max = (unsigned int) std::sqrt(N + 2) / PROD;
for (unsigned int kp = 0; kp <= k_max; ++kp) {
for (std::uint8_t bits = ~flag[kp]; bits; bits &= bits - 1) {
const std::uint8_t mp = mask_to_index(bits & -bits), m = RM[mp];
unsigned int kr = kp * (PROD * kp + 2 * m) + m * m / PROD;
for (std::uint8_t mq = mp; kr < siz; kr += kp * DR[mq] + DF[mp][mq], ++mq &= 7) {
flag[kr] |= MASK[mp][mq];
}
}
}
}
std::vector<int> prime_list(unsigned int max_val = N) const {
using namespace internal::sieve;
std::vector<int> res { 2, 3, 5 };
res.reserve(max_val / 25);
for (unsigned int i = 0, offset = 0; i < siz and offset < max_val; ++i, offset += PROD) {
for (uint8_t f = ~flag[i]; f;) {
uint8_t g = f & -f;
res.push_back(offset + RM[mask_to_index(g)]);
f ^= g;
}
}
while (res.size() and (unsigned int) res.back() > max_val) res.pop_back();
return res;
}
bool is_prime(const unsigned int p) const {
using namespace internal::sieve;
switch (p) {
case 2: case 3: case 5: return true;
default:
switch (p % PROD) {
case RM[0]: return ((flag[p / PROD] >> 0) & 1) == 0;
case RM[1]: return ((flag[p / PROD] >> 1) & 1) == 0;
case RM[2]: return ((flag[p / PROD] >> 2) & 1) == 0;
case RM[3]: return ((flag[p / PROD] >> 3) & 1) == 0;
case RM[4]: return ((flag[p / PROD] >> 4) & 1) == 0;
case RM[5]: return ((flag[p / PROD] >> 5) & 1) == 0;
case RM[6]: return ((flag[p / PROD] >> 6) & 1) == 0;
case RM[7]: return ((flag[p / PROD] >> 7) & 1) == 0;
default: return false;
}
}
}
};
template <unsigned int N>
std::uint8_t SimpleSieve<N>::flag[SimpleSieve<N>::siz];
template <unsigned int N>
class Sieve {
private:
static constexpr unsigned int base_max = (N + 1) * internal::sieve::K / internal::sieve::PROD;
static unsigned int pf[base_max + internal::sieve::K];
public:
Sieve() {
using namespace internal::sieve;
pf[0] = 1;
unsigned int k_max = ((unsigned int) std::sqrt(N + 1) - 1) / PROD;
for (unsigned int kp = 0; kp <= k_max; ++kp) {
const int base_i = kp * K, base_act_i = kp * PROD;
for (int mp = 0; mp < K; ++mp) {
const int m = RM[mp], i = base_i + mp;
if (pf[i] == 0) {
unsigned int act_i = base_act_i + m;
unsigned int base_k = (kp * (PROD * kp + 2 * m) + m * m / PROD) * K;
for (std::uint8_t mq = mp; base_k <= base_max; base_k += kp * DRP[mq] + DFP[mp][mq], ++mq &= 7) {
pf[base_k + OFFSET[mp][mq]] = act_i;
}
}
}
}
}
bool is_prime(const unsigned int p) const {
using namespace internal::sieve;
switch (p) {
case 2: case 3: case 5: return true;
default:
switch (p % PROD) {
case RM[0]: return pf[p / PROD * K + 0] == 0;
case RM[1]: return pf[p / PROD * K + 1] == 0;
case RM[2]: return pf[p / PROD * K + 2] == 0;
case RM[3]: return pf[p / PROD * K + 3] == 0;
case RM[4]: return pf[p / PROD * K + 4] == 0;
case RM[5]: return pf[p / PROD * K + 5] == 0;
case RM[6]: return pf[p / PROD * K + 6] == 0;
case RM[7]: return pf[p / PROD * K + 7] == 0;
default: return false;
}
}
}
int prime_factor(const unsigned int p) const {
using namespace internal::sieve;
switch (p % PROD) {
case 0: case 2: case 4: case 6: case 8:
case 10: case 12: case 14: case 16: case 18:
case 20: case 22: case 24: case 26: case 28: return 2;
case 3: case 9: case 15: case 21: case 27: return 3;
case 5: case 25: return 5;
case RM[0]: return pf[p / PROD * K + 0] ? pf[p / PROD * K + 0] : p;
case RM[1]: return pf[p / PROD * K + 1] ? pf[p / PROD * K + 1] : p;
case RM[2]: return pf[p / PROD * K + 2] ? pf[p / PROD * K + 2] : p;
case RM[3]: return pf[p / PROD * K + 3] ? pf[p / PROD * K + 3] : p;
case RM[4]: return pf[p / PROD * K + 4] ? pf[p / PROD * K + 4] : p;
case RM[5]: return pf[p / PROD * K + 5] ? pf[p / PROD * K + 5] : p;
case RM[6]: return pf[p / PROD * K + 6] ? pf[p / PROD * K + 6] : p;
case RM[7]: return pf[p / PROD * K + 7] ? pf[p / PROD * K + 7] : p;
default: assert(false);
}
}
/**
* Returns a vector of `{ prime, index }`.
*/
std::vector<std::pair<int, int>> factorize(unsigned int n) const {
assert(0 < n and n <= N);
std::vector<std::pair<int, int>> prime_powers;
while (n > 1) {
int p = prime_factor(n), c = 0;
do { n /= p, ++c; } while (n % p == 0);
prime_powers.emplace_back(p, c);
}
return prime_powers;
}
/**
* Returns the divisors of `n`.
* It is NOT guaranteed that the returned vector is sorted.
*/
std::vector<int> divisors(unsigned int n) const {
assert(0 < n and n <= N);
std::vector<int> divs { 1 };
for (auto [prime, index] : factorize(n)) {
int sz = divs.size();
for (int i = 0; i < sz; ++i) {
int d = divs[i];
for (int j = 0; j < index; ++j) {
divs.push_back(d *= prime);
}
}
}
return divs;
}
};
template <unsigned int N>
unsigned int Sieve<N>::pf[Sieve<N>::base_max + internal::sieve::K];
} // namespace suisen
#line 1 "library/algorithm/mo.hpp"
#include <algorithm>
#line 6 "library/algorithm/mo.hpp"
#include <numeric>
#line 8 "library/algorithm/mo.hpp"
namespace suisen {
struct Mo {
Mo() = default;
Mo(const int n, const std::vector<std::pair<int, int>> &queries) : n(n), q(queries.size()), b(bucket_size(n, q)), qs(queries), ord(q) {
std::iota(ord.begin(), ord.end(), 0);
std::sort(
ord.begin(), ord.end(),
[&, this](int i, int j) {
const auto &[li, ri] = qs[i];
const auto &[lj, rj] = qs[j];
const int bi = li / b, bj = lj / b;
if (bi != bj) return bi < bj;
if (ri != rj) return bi & 1 ? ri > rj : ri < rj;
return li < lj;
}
);
}
// getter methods used in updating functions: AddL, DelL, etc.
auto get_left() const { return l; }
auto get_right() const { return r; }
auto get_range() const { return std::make_pair(l, r); }
auto get_query_id() const { return query_id; }
/**
* [Parameters]
* Eval : () -> T : return the current answer
* AddL : int -> any (discarded) : add `l` to the current range [l + 1, r)
* DelL : int -> any (discarded) : delete `l` from the current range [l, r)
* AddR : int -> any (discarded) : add `r` to the current range [l, r)
* DelR : int -> any (discarded) : delete `r` from the current range [l, r + 1)
*
* [Note]
* starting from the range [0, 0).
*/
template <typename Eval, typename AddL, typename DelL, typename AddR, typename DelR>
auto solve(Eval eval, AddL add_l, DelL del_l, AddR add_r, DelR del_r) {
l = 0, r = 0;
std::vector<decltype(eval())> res(q);
for (int qi : ord) {
const auto &[nl, nr] = qs[query_id = qi];
while (r < nr) add_r(r), ++r;
while (l > nl) --l, add_l(l);
while (r > nr) --r, del_r(r);
while (l < nl) del_l(l), ++l;
res[qi] = eval();
}
return res;
}
/**
* [Parameters]
* Eval : () -> T : return the current answer
* Add : int -> any (discarded) : add `i` to the current range [i + 1, r) or [l, i)
* Del : int -> any (discarded) : delete `i` from the current range [i, r) or [l, i + 1)
*
* [Note]
* starting from the range [0, 0).
*/
template <typename Eval, typename Add, typename Del>
auto solve(Eval eval, Add add, Del del) {
return solve(eval, add, del, add, del);
}
private:
int n, q, b;
int query_id = -1;
std::vector<std::pair<int, int>> qs;
std::vector<int> ord;
int l = 0, r = 0;
static int bucket_size(int n, int q) {
return std::max(1, int(::sqrt(3) * n / ::sqrt(std::max(1, 2 * q))));
}
};
} // namespace suisen
#line 10 "test/src/algorithm/mo/abc238_g.test.cpp"
using suisen::Sieve;
using suisen::Mo;
constexpr int M = 1000000;
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n, q;
std::cin >> n >> q;
Sieve<M> sieve;
std::vector<std::vector<std::pair<int, mint>>> factorized(n);
for (int i = 0; i < n; ++i) {
int v;
std::cin >> v;
for (auto &&[p, c] : sieve.factorize(v)) {
factorized[i].emplace_back(p, c);
}
}
std::vector<std::pair<int, int>> queries(q);
for (auto &[l, r] : queries) {
std::cin >> l >> r;
--l;
}
std::vector<mint> index_sum(M + 1, 0);
int invalid = 0;
auto answers = Mo(n, queries).solve(
// Eval
[&]{
return invalid == 0;
},
// Add
[&](int i) {
for (const auto &[p, c] : factorized[i]) {
invalid -= index_sum[p] != 0;
index_sum[p] += c;
invalid += index_sum[p] != 0;
}
},
// Del
[&](int i) {
for (const auto &[p, c] : factorized[i]) {
invalid -= index_sum[p] != 0;
index_sum[p] -= c;
invalid += index_sum[p] != 0;
}
}
);
for (bool answer : answers) {
if (answer) {
std::cout << "Yes" << '\n';
} else {
std::cout << "No" << '\n';
}
}
return 0;
}