結果
| 問題 |
No.1720 Division Permutation
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-10-24 11:52:24 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 179 ms / 4,000 ms |
| コード長 | 12,529 bytes |
| コンパイル時間 | 2,875 ms |
| コンパイル使用メモリ | 197,964 KB |
| 実行使用メモリ | 26,264 KB |
| 最終ジャッジ日時 | 2024-10-01 23:03:07 |
| 合計ジャッジ時間 | 11,060 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 60 |
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 <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;
#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> 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
// StarrySkyTree: segment tree for Range Minimum Query & Range Add Query
// Complexity: (N)$ (construction), (\log N)$ (add / get / prod)
// - RangeAddRangeMin(std::vector<Tp> data_init) : Initialize array x by data_init.
// - add(int begin, int end, Tp vadd) : Update x[i] <- x[i] + vadd for all begin <= i < end.
// - get(int pos) : Get x[pos].
// - prod(int begin, int end) : Get min(x[begin], ..., x[end - 1]).
template <typename Tp, Tp defaultT = std::numeric_limits<Tp>::max() / 2> struct RangeAddRangeMin {
int N, head;
std::vector<Tp> range_min, range_add;
static inline Tp f(Tp x, Tp y) noexcept { return std::min(x, y); }
inline void _merge(int pos) {
range_min[pos] = f(range_min[pos * 2] + range_add[pos * 2], range_min[pos * 2 + 1] + range_add[pos * 2 + 1]);
}
void initialize(const std::vector<Tp> &data_init) {
N = data_init.size(), head = 1;
while (head < N) head <<= 1;
range_min.assign(head * 2, defaultT);
range_add.assign(head * 2, 0);
std::copy(data_init.begin(), data_init.end(), range_min.begin() + head);
for (int pos = head; --pos;) _merge(pos);
}
RangeAddRangeMin() = default;
RangeAddRangeMin(const std::vector<Tp> &data_init) { initialize(data_init); }
void _add(int begin, int end, int pos, int l, int r, Tp vadd) noexcept {
if (r <= begin or end <= l) return;
if (begin <= l and r <= end) {
range_add[pos] += vadd;
return;
}
_add(begin, end, pos * 2, l, (l + r) / 2, vadd);
_add(begin, end, pos * 2 + 1, (l + r) / 2, r, vadd);
_merge(pos);
}
// Add `vadd` to (x_begin, ..., x_{end - 1})
void add(int begin, int end, Tp vadd) noexcept { return _add(begin, end, 1, 0, head, vadd); }
Tp _get(int begin, int end, int pos, int l, int r) const noexcept {
if (r <= begin or end <= l) return defaultT;
if (begin <= l and r <= end) return range_min[pos] + range_add[pos];
return f(_get(begin, end, pos * 2, l, (l + r) / 2), _get(begin, end, pos * 2 + 1, (l + r) / 2, r)) + range_add[pos];
}
// Return f(x_begin, ..., x_{end - 1})
Tp get(int pos) const noexcept { return prod(pos, pos + 1); }
Tp prod(int begin, int end) const noexcept { return _get(begin, end, 1, 0, head); }
};
struct permutation_tree {
enum NodeType {
JoinAsc,
JoinDesc,
Cut,
Leaf,
None,
};
struct node {
NodeType tp;
int L, R; // i in [L, R)
int mini, maxi; // A[i] in [mini, maxi]
std::vector<int> child;
int sz() const { return maxi - mini + 1; }
template <class OStream> friend OStream &operator<<(OStream &os, const node &n) {
os << "[[" << n.L << ',' << n.R << ")(ch:";
for (auto i : n.child) os << i << ',';
return os << ")(tp=" << n.tp << ")]";
}
};
int root;
std::vector<int> A;
std::vector<node> nodes;
bool is_adj(int lid, int rid) const { return nodes[lid].maxi + 1 == nodes[rid].mini; }
void add_child(int parid, int chid) {
nodes[parid].child.push_back(chid);
nodes[parid].L = std::min(nodes[parid].L, nodes[chid].L);
nodes[parid].R = std::max(nodes[parid].R, nodes[chid].R);
nodes[parid].mini = std::min(nodes[parid].mini, nodes[chid].mini);
nodes[parid].maxi = std::max(nodes[parid].maxi, nodes[chid].maxi);
}
NodeType findtype(int lid, int rid) const {
const auto &l = nodes[lid].tp, &r = nodes[rid].tp;
if (is_adj(lid, rid)) return NodeType::JoinAsc;
if (is_adj(rid, lid)) return NodeType::JoinDesc;
return NodeType::None;
}
permutation_tree(const std::vector<int> &A_) : root(-1), A(A_) { // A: 0-origin
RangeAddRangeMin<int> segtree((std::vector<int>(A.size())));
std::vector<std::pair<int, int>> hi{{A.size() + 1, -1}}, lo{{-1, -1}};
std::vector<int> st;
for (int i = 0; i < int(A.size()); ++i) {
while (A[i] > hi.back().first) {
segtree.add(hi[hi.size() - 2].second + 1, hi.back().second + 1, A[i] - hi.back().first);
hi.pop_back();
}
hi.emplace_back(A[i], i);
while (A[i] < lo.back().first) {
segtree.add(lo[lo.size() - 2].second + 1, lo.back().second + 1, lo.back().first - A[i]);
lo.pop_back();
}
lo.emplace_back(A[i], i);
int h = nodes.size();
nodes.push_back({NodeType::Leaf, i, i + 1, A[i], A[i], std::vector<int>{}});
while (true) {
NodeType join_tp;
if (st.size() and (join_tp = findtype(st.back(), h)) != NodeType::None) {
const node &vtp = nodes[st.back()];
// Insert v as the child of the top node in the stack
if (join_tp == vtp.tp) {
// Append child to existing Join node
add_child(st.back(), h);
h = st.back();
st.pop_back();
} else {
// Make new join node (with exactly two children)
// TODO: Refactor here
nodes.push_back({join_tp, std::min(vtp.L, nodes[h].L), std::max(vtp.R, nodes[h].R), std::min(vtp.mini, nodes[h].mini), std::max(vtp.maxi, nodes[h].maxi), {st.back(), h}});
h = nodes.size() - 1;
st.pop_back();
}
} else if (segtree.prod(0, i + 1 - nodes[h].sz()) == 0) {
// Make Cut node
// TODO: Refactor here
int sz = nodes[h].sz(), L = nodes[h].L, R = nodes[h].R, maxi = nodes[h].maxi, mini = nodes[h].mini;
int j;
std::vector<int> new_ch{h};
do {
int j = st.back();
st.pop_back();
new_ch.push_back(j);
node &n = nodes[j];
sz += n.sz(), L = n.L, maxi = std::max(maxi, n.maxi), mini = std::min(mini, n.mini);
} while (maxi - mini + 1 != sz);
std::reverse(new_ch.begin(), new_ch.end());
nodes.push_back({NodeType::Cut, L, R, mini, maxi, new_ch});
h = nodes.size() - 1;
} else {
break;
}
}
st.push_back(h);
segtree.add(0, i + 1, -1);
}
assert(st.size() == 1);
root = st[0];
}
void to_DOT(std::string filename = "") const {
if (filename.empty()) filename = "permutation_tree_" + std::to_string(A.size()) + ".DOT";
std::ofstream ss(filename);
ss << "digraph{\n";
int nleaf = 0;
for (int i = 0; i < int(nodes.size()); i++) {
ss << i << "[\n";
std::string lbl;
if (nodes[i].tp == NodeType::Leaf) {
lbl = "A[" + std::to_string(nleaf) + "] = " + std::to_string(A[nleaf]), nleaf++;
} else {
lbl += std::string(nodes[i].tp == NodeType::Cut ? "Cut" : "Join") + "\\n";
lbl += "[" + std::to_string(nodes[i].L) + ", " + std::to_string(nodes[i].R) + ")";
}
ss << "label = \"" << lbl << "\",\n";
ss << "]\n";
for (const auto &ch : nodes[i].child) {
ss << i << " -> " << ch << ";\n";
}
}
ss << "{rank = same;";
for (int i = 0; i < int(nodes.size()); i++) {
if (nodes[i].tp == NodeType::Leaf) ss << ' ' << i << ';';
}
ss << "}\n";
ss << "}\n";
ss.close();
return;
}
};
#include <atcoder/modint>
using mint = atcoder::modint998244353;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, K;
cin >> N >> K;
vector<int> P(N);
for (auto &x : P) cin >> x;
for (auto &x : P) x--;
permutation_tree tree(P);
vector dp(K + 1, vector<mint>(N + 1));
dp[0][0] = 1;
auto rec = [&](auto &&self, int now) -> void {
auto &v = tree.nodes[now];
if (v.tp == permutation_tree::Cut or v.tp == permutation_tree::Leaf) {
for (int k = 0; k < K; ++k) dp[k + 1][v.R] += dp[k][v.L];
}
vector<mint> sum(K);
for (auto ch : v.child) {
self(self, ch);
if (v.tp == permutation_tree::JoinAsc or v.tp == permutation_tree::JoinDesc) {
for (int k = 0; k < K; ++k) {
dp[k + 1][tree.nodes[ch].R] += sum[k];
sum[k] += dp[k][tree.nodes[ch].L];
}
}
}
};
rec(rec, tree.root);
for (int i = 1; i <= K; i++) cout << dp[i][N].val() << '\n';
}