cplib-cpp
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other_algorithms/test/permutation_tree.yuki1720.test.cpp
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- Last update: 2025-08-25 00:44:48+09:00
- Problem: https://yukicoder.me/problems/no/1720
Depends on
- modint.hpp
- Permutation tree （順列木）
(other_algorithms/permutation_tree.hpp)
- Range Add Range Min (known as the Starry sky tree)
(segmenttree/range-add-range-min.hpp)
Code
#define PROBLEM "https://yukicoder.me/problems/no/1720"
#include "../permutation_tree.hpp"
#include "../../modint.hpp"
#include <iostream>
using mint = ModInt<998244353>;
using namespace std;
int N, K;
permutation_tree tree;
vector<vector<mint>> dp;
void rec(int now) {
const 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) {
rec(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];
}
}
}
};
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
cin >> N >> K;
vector<int> P(N);
for (auto &x : P) cin >> x;
for (auto &x : P) x--;
tree = permutation_tree(P);
dp.assign(K + 1, vector<mint>(N + 1));
dp[0][0] = 1;
rec(tree.root);
for (int i = 1; i <= K; i++) cout << dp[i][N] << '\n';
}#line 1 "other_algorithms/test/permutation_tree.yuki1720.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1720"
#line 2 "segmenttree/range-add-range-min.hpp"
#include <algorithm>
#include <limits>
#include <vector>
// CUT begin
// StarrySkyTree: segment tree for Range Minimum Query & Range Add Query
// Complexity: $O(N)$ (construction), $O(\log N)$ (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); }
};
#line 4 "other_algorithms/permutation_tree.hpp"
#include <cassert>
#include <fstream>
#include <string>
#line 8 "other_algorithms/permutation_tree.hpp"
// Permutation tree
// Complexity: O(N log N)
// https://codeforces.com/blog/entry/78898 https://yukicoder.me/problems/no/1720
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 R - L; }
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;
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);
}
permutation_tree() : root(-1) {}
permutation_tree(const std::vector<int> &A_) : root(-1), A(A_) { // A: nonempty perm., 0-origin
assert(!A.empty());
RangeAddRangeMin<int> seg((std::vector<int>(A.size())));
std::vector<int> hi{-1}, lo{-1};
std::vector<int> st;
for (int i = 0; i < int(A.size()); ++i) {
while (hi.back() >= 0 and A[i] > A[hi.back()]) {
seg.add(hi[hi.size() - 2] + 1, hi.back() + 1, A[i] - A[hi.back()]);
hi.pop_back();
}
hi.push_back(i);
while (lo.back() >= 0 and A[i] < A[lo.back()]) {
seg.add(lo[lo.size() - 2] + 1, lo.back() + 1, A[lo.back()] - A[i]);
lo.pop_back();
}
lo.push_back(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 = NodeType::None;
if (!st.empty() and nodes[st.back()].maxi + 1 == nodes[h].mini) join_tp = JoinAsc;
if (!st.empty() and nodes[h].maxi + 1 == nodes[st.back()].mini) join_tp = JoinDesc;
if (!st.empty() and join_tp != 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)
int j = st.back();
nodes.push_back(
{join_tp, nodes[j].L, nodes[j].R, nodes[j].mini, nodes[j].maxi, {j}});
st.pop_back();
_add_child(nodes.size() - 1, h);
h = nodes.size() - 1;
}
} else if (seg.prod(0, i + 1 - nodes[h].sz()) == 0) {
// Make Cut node
int L = nodes[h].L, R = nodes[h].R, maxi = nodes[h].maxi, mini = nodes[h].mini;
nodes.push_back({NodeType::Cut, L, R, mini, maxi, {h}});
h = nodes.size() - 1;
do {
_add_child(h, st.back());
st.pop_back();
} while (nodes[h].maxi - nodes[h].mini + 1 != nodes[h].sz());
std::reverse(nodes[h].child.begin(), nodes[h].child.end());
} else {
break;
}
}
st.push_back(h);
seg.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_v=" + 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();
}
};
#line 3 "modint.hpp"
#include <iostream>
#include <set>
#line 6 "modint.hpp"
template <int md> struct ModInt {
static_assert(md > 1);
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr static ModInt fac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[n];
}
constexpr static ModInt facinv(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[n];
}
constexpr static ModInt doublefac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
long long k = (n + 1) / 2;
return (n & 1) ? ModInt::fac(k * 2) / (ModInt(2).pow(k) * ModInt::fac(k))
: ModInt::fac(k) * ModInt(2).pow(k);
}
constexpr static ModInt nCr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(r) * ModInt::facinv(n - r);
}
constexpr static ModInt nPr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(n - r);
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt::nCr(n, r);
r = std::min(r, n - r);
ModInt ret = ModInt::facinv(r);
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt::facinv(k), sum += k;
}
return ret * ModInt::fac(sum);
}
template <class... Args> static ModInt multinomial(Args... args) {
int sum = (0 + ... + args);
ModInt result = (1 * ... * ModInt::facinv(args));
return ModInt::fac(sum) * result;
}
// Catalan number, C_n = binom(2n, n) / (n + 1) = # of Dyck words of length 2n
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt::fac(n * 2) * ModInt::facinv(n + 1) * ModInt::facinv(n);
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#line 5 "other_algorithms/test/permutation_tree.yuki1720.test.cpp"
using mint = ModInt<998244353>;
using namespace std;
int N, K;
permutation_tree tree;
vector<vector<mint>> dp;
void rec(int now) {
const 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) {
rec(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];
}
}
}
};
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
cin >> N >> K;
vector<int> P(N);
for (auto &x : P) cin >> x;
for (auto &x : P) x--;
tree = permutation_tree(P);
dp.assign(K + 1, vector<mint>(N + 1));
dp[0][0] = 1;
rec(tree.root);
for (int i = 1; i <= K; i++) cout << dp[i][N] << '\n';
}