結果
| 問題 |
No.3269 Leq-K Partition
|
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-09-12 23:44:28 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 19,969 bytes |
| コンパイル時間 | 3,412 ms |
| コンパイル使用メモリ | 259,432 KB |
| 実行使用メモリ | 13,696 KB |
| 最終ジャッジ日時 | 2025-09-12 23:48:08 |
| 合計ジャッジ時間 | 71,299 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 26 TLE * 1 |
ソースコード
#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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <algorithm>
#include <bit>
#include <cassert>
#include <cstdint>
#include <optional>
#include <vector>
template <class Int> class wavelet_matrix {
class bit_vector {
static constexpr int WSIZE = 64;
int n = 0;
int cnt0 = 0;
std::vector<uint64_t> bits;
std::vector<int> count_cumsum; // need build()
public:
bit_vector(int n_) : n(n_), cnt0(n_) {
assert(n >= 0);
bits.assign((n + WSIZE - 1) / WSIZE, 0);
}
int size() const { return n; }
void set(int i) {
assert(0 <= i and i < n);
bits[i / WSIZE] |= (1ULL << (i % WSIZE));
}
void reset(int i) {
assert(0 <= i and i < n);
bits[i / WSIZE] &= ~(1ULL << (i % WSIZE));
}
void build() {
cnt0 = n;
for (int i = 0; i < (int)bits.size(); ++i) cnt0 -= std::popcount(bits[i]);
count_cumsum.assign(bits.size(), 0);
for (int i = 1; i < (int)bits.size(); ++i) {
count_cumsum[i] = count_cumsum[i - 1] + std::popcount(bits[i - 1]);
}
}
int count0() const { return cnt0; }
int count1() const { return n - cnt0; }
// get i-th bit
bool access(int i) const {
assert(0 <= i and i < n);
return bits[i / WSIZE] & (1ULL << (i % WSIZE));
}
// count of 0s in [0, i)
int rank0(int i) const {
assert(0 <= i and i <= n);
return i - rank1(i);
}
// count of 1s in [0, i)
int rank1(int i) const {
assert(0 <= i and i <= n);
if (i == n) return count1();
return count_cumsum[i / WSIZE] +
std::popcount(bits[i / WSIZE] & ((1ULL << (i % WSIZE)) - 1));
}
// get the position of i-th element after stable sort
int sorted_pos(int i) const { return access(i) ? (rank1(i) + count0()) : rank0(i); }
template <class OStream> friend OStream &operator<<(OStream &os, const bit_vector &bv) {
os << "bit_vector[" << bv.n << "]: ";
for (int i = 0; i < bv.n; ++i) {
os << (bv.bits[i / WSIZE] & (1ULL << (i % WSIZE)) ? '1' : '0');
}
os << " (cnt0: " << bv.cnt0 << ")";
return os;
}
};
std::vector<bit_vector> bits;
std::vector<std::pair<Int, Int>> points;
std::vector<Int> distinct_ys;
int to_index_x(Int x) const {
return std::lower_bound(points.cbegin(), points.cend(), std::make_pair(x, Int{}),
[](const auto &l, const auto &r) { return l.first < r.first; }) -
points.cbegin();
}
int to_index_y(Int y) const {
return std::lower_bound(distinct_ys.cbegin(), distinct_ys.cend(), y) - distinct_ys.cbegin();
}
bool is_built() const { return !bits.empty(); }
public:
wavelet_matrix() = default;
wavelet_matrix(const std::vector<Int> &ys) {
for (int x = 0; x < (int)ys.size(); ++x) {
assert(ys[x] >= 0);
add_point(x, ys[x]);
}
build();
}
void add_point(Int x, Int y) {
assert(bits.empty()); // confirm that build() is not called yet
points.emplace_back(x, y);
distinct_ys.emplace_back(y);
}
void build() {
std::sort(points.begin(), points.end());
points.erase(std::unique(points.begin(), points.end()), points.end());
std::sort(distinct_ys.begin(), distinct_ys.end());
distinct_ys.erase(std::unique(distinct_ys.begin(), distinct_ys.end()), distinct_ys.end());
int d = 1;
while ((1 << d) < (int)distinct_ys.size()) ++d;
bits.assign(d, bit_vector(N()));
std::vector<int> a;
for (auto p : points) a.push_back(to_index_y(p.second));
auto nxt = a;
for (int d = D() - 1; d >= 0; --d) {
for (int i = 0; i < N(); ++i) {
if ((a[i] >> d) & 1) bits[d].set(i);
}
bits[d].build();
for (int i = 0; i < N(); ++i) nxt[bits[d].sorted_pos(i)] = a[i];
std::swap(a, nxt);
}
}
int N() const { return points.size(); }
int D() const { return bits.size(); }
// get v_i
int index_access(int i) const {
assert(0 <= i and i < N());
assert(is_built());
int ret = 0;
for (int d = D() - 1; d >= 0; --d) {
ret |= (int)bits[d].access(i) << d;
i = bits[d].sorted_pos(i);
}
return ret;
}
Int access(int i) const {
assert(0 <= i and i < N());
assert(is_built());
return distinct_ys.at(index_access(i));
}
// callback(d, i) means "update d-th segment's i-th element"
void index_apply(int i, auto callback) const {
assert(0 <= i and i < N());
assert(is_built());
for (int d = D() - 1; d >= 0; --d) {
i = bits[d].sorted_pos(i);
callback(d, i);
}
}
// Update weight associated to point (x, y)
// callback(d, i) means "update d-th segment's i-th element"
void apply(Int x, Int y, auto callback) const {
const int i = std::lower_bound(points.cbegin(), points.cend(), std::make_pair(x, y)) -
points.cbegin();
assert(i < N() and points[i] == std::make_pair(x, y));
index_apply(i, callback);
}
void index_prod(int l, int r, int yr, auto callback) const {
assert(0 <= l and l <= r and r <= N());
assert(0 <= yr and yr <= (int)distinct_ys.size());
assert(is_built());
if (yr & (1 << D())) {
const int d = D() - 1;
const int l0 = bits[d].rank0(l), r0 = bits[d].rank0(r);
callback(d, l0, r0);
const int l1 = bits[d].rank1(l) + bits[d].count0();
const int r1 = bits[d].rank1(r) + bits[d].count0();
callback(d, l1, r1);
return;
}
for (int d = D() - 1; d >= 0; --d) {
if (l == r) break;
const int l0 = bits[d].rank0(l), r0 = bits[d].rank0(r);
if ((yr >> d) & 1) {
callback(d, l0, r0);
// l = bits[d].rank1(l) + bits[d].count0();
l += bits[d].count0() - l0;
// r = bits[d].rank1(r) + bits[d].count0();
r += bits[d].count0() - r0;
} else {
l = l0, r = r0;
}
}
}
// Get product of weights associated to elements in [xl, xr) * [-inf, yr)
// callback(d, l, r) means "use d-th segment's [l, r) elements"
void prod(Int xl, Int xr, Int yr, auto callback) const {
index_prod(to_index_x(xl), to_index_x(xr), to_index_y(yr), callback);
}
// Get k-th smallest v_i, i in [l, r) (0-indexed, duplicates are counted)]
int index_kth_smallest(int l, int r, int k) const {
assert(0 <= l and l <= r and r <= N());
assert(0 <= k and k < r - l);
assert(is_built());
int ret = 0;
for (int d = D() - 1; d >= 0; --d) {
const int l0 = bits[d].rank0(l), r0 = bits[d].rank0(r);
if (k < r0 - l0) {
l = l0, r = r0;
} else {
k -= r0 - l0;
ret |= 1 << d;
l = bits[d].rank1(l) + bits[d].count0();
r = bits[d].rank1(r) + bits[d].count0();
}
}
return ret;
}
// Get k-th largest v_i, i in [l, r) (0-indexed, duplicates are counted)
int index_kth_largest(int l, int r, int k) const {
assert(0 <= l and l <= r and r <= N());
assert(0 <= k and k < r - l);
return index_kth_smallest(l, r, (r - l - 1) - k);
}
// count i s.t. i in [l, r) and v_i < upper_bound
int index_range_freq(int l, int r, int upper_bound) const {
assert(0 <= l and l <= r and r <= N());
assert(is_built());
if (upper_bound <= 0) return 0;
if (upper_bound >= (int)distinct_ys.size()) return r - l;
int ret = 0;
for (int d = D() - 1; d >= 0; --d) {
const int l0 = bits[d].rank0(l), r0 = bits[d].rank0(r);
if ((upper_bound >> d) & 1) {
ret += r0 - l0;
l = bits[d].rank1(l) + bits[d].count0();
r = bits[d].rank1(r) + bits[d].count0();
} else {
l = l0, r = r0;
}
}
return ret;
}
// Get k-th smallest y in [xl, xr) (0-indexed, duplicates are counted)
std::optional<Int> kth_smallest(Int xl, Int xr, int k) const {
const int l = to_index_x(xl), r = to_index_x(xr);
if (k < 0 or k >= r - l) return std::nullopt;
return distinct_ys.at(index_kth_smallest(l, r, k));
}
// Get k-th largest y in [xl, xr) (0-indexed, duplicates are counted)
std::optional<Int> kth_largest(Int xl, Int xr, int k) const {
const int l = to_index_x(xl), r = to_index_x(xr);
if (k < 0 or k >= r - l) return std::nullopt;
return distinct_ys.at(index_kth_largest(l, r, k));
}
// count points in [xl, xr) * [-inf, yr)
int range_freq(Int xl, Int xr, Int yr) const {
return index_range_freq(to_index_x(xl), to_index_x(xr), to_index_y(yr));
}
// max v_i s.t. i in [l, r), v_i < upper_bound
std::optional<int> index_prev_value(int l, int r, int upper_bound) const {
assert(0 <= l and l <= r and r <= N());
assert(is_built());
if (upper_bound <= 0) return std::nullopt;
const int n = index_range_freq(l, r, upper_bound);
return n == 0 ? std::nullopt : index_kth_smallest(l, r, n - 1);
}
// max y s.t. x in [xl, xr), y < yr
std::optional<Int> prev_value(Int xl, Int xr, Int yr) const {
const int l = to_index_x(xl), r = to_index_x(xr), ub = to_index_y(yr);
const auto idx = index_prev_value(l, r, ub);
return idx ? distinct_ys.at(*idx) : std::nullopt;
}
// min v_i s.t. i in [l, r), v_i >= lower_bound
std::optional<int> index_next_value(int l, int r, int lower_bound) const {
assert(0 <= l and l <= r and r <= N());
assert(is_built());
if (lower_bound >= (int)distinct_ys.size()) return std::nullopt;
const int n = index_range_freq(l, r, lower_bound);
return n >= (r - l) ? std::nullopt : index_kth_smallest(l, r, n);
}
// min y s.t. x in [xl, xr), y >= yl
std::optional<Int> next_value(Int l, Int r, Int yl) const {
const int xl = to_index_x(l), xr = to_index_x(r), yl_idx = to_index_y(yl);
const auto idx = index_next_value(xl, xr, yl_idx);
return idx ? distinct_ys.at(*idx) : std::nullopt;
}
};
/* Sample usage:
wavelet_matrix<int> wm;
wm.build();
vector tmp(wm.D(), vector<BIT<T>>(wm.N()));
wm.apply(i, j, [&](int d, int idx) { tmp[d].add(idx, wx); }); // point add
T ret{};
wm.prod(l, r, u, [&](int d, int l0, int r0) { ret += tmp[d].sum(l0, r0); }); // range sum
*/
#include <chrono>
#include <random>
struct rand_int_ {
using lint = long long;
std::mt19937 mt;
// rand_int_() : mt(42) {}
rand_int_() : mt(std::chrono::steady_clock::now().time_since_epoch().count()) {}
lint operator()(lint x) { return this->operator()(0, x); } // [0, x)
lint operator()(lint l, lint r) {
std::uniform_int_distribution<lint> d(l, r - 1);
return d(mt);
}
} rnd;
int main() {
int N;
cin >> N;
vector<int> A(N);
cin >> A;
// N = 100000;
// A.resize(N);
// for (auto &a : A) a = rnd(1, 10000);
vector<int> nxt(N, N);
{
map<int, int> mp;
IREP(i, N) {
if (mp.count(A.at(i))) {
nxt.at(i) = mp.at(A.at(i));
}
mp[A.at(i)] = i;
}
}
wavelet_matrix<int> wm(nxt);
vector cs(wm.D(), vector<int>(wm.N() + 1));
REP(i, N) {
wm.apply(i, nxt.at(i), [&](int d, int idx) { cs.at(d).at(idx)++; });
}
for (auto &v : cs) { FOR(i, 1, v.size()) v.at(i) += v.at(i - 1); }
constexpr int B = 20;
for (int k = 1; k <= min(B, N); ++k) {
int ret = 0;
for (int l = 0; l < N;) {
++ret;
vector<int> vs;
while (true) {
if (vs.size() < k or count(ALL(vs), A.at(l))) {
if (!count(ALL(vs), A.at(l))) {
vs.push_back(A.at(l));
}
++l;
} else {
break;
}
if (l == N) break;
}
}
cout << ret << '\n';
}
for (int k = B + 1; k <= N; ++k) {
int ans = 0;
int now = 0;
while (now < N) {
int lo = now + k, hi = N + 1;
while (hi - lo > 1) {
const int mid = (lo + hi) / 2;
int cnt = mid - now;
wm.prod(now, mid, mid,
[&](int d, int l0, int r0) { cnt -= cs.at(d).at(r0) - cs.at(d).at(l0); });
if (cnt > k) {
hi = mid;
} else {
lo = mid;
}
}
++ans;
now = lo;
}
cout << ans << '\n';
}
}