This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1720
#include "../../template/template.hpp"
#include "../../structure/others/permutation-tree.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"
using mint = modint998244353;
int main() {
int N, K;
cin >> N >> K;
vector< int > A(N);
cin >> A;
for(auto &a: A) --a;
using NP = PermutationTree::Node *;
auto dp = make_v< mint >(K + 1, N + 1);
dp[0][0] = 1;
MFP([&](auto rec, NP r) -> void {
if(r->is_cut() or r->is_leaf()) {
for(int k = 0; k < K; k++) {
dp[k + 1][r->r] += dp[k][r->l];
}
}
vector< mint > sum(K);
for(auto &c: r->ch) {
rec(c);
if(r->is_join()) {
for(int k = 0; k < K; k++) {
dp[k + 1][c->r] += sum[k];
sum[k] += dp[k][c->l];
}
}
}
})(PermutationTree::build(A));
for(int i = 1; i <= K; i++) {
cout << dp[i][N] << "\n";
}
}
#line 1 "test/verify/yukicoder-1720.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1720
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yukicoder-1720.test.cpp"
#line 1 "structure/segment-tree/lazy-segment-tree.hpp"
/**
* @brief Lazy-Segment-Tree(遅延伝搬セグメント木)
*
*/
template <typename T, typename E, typename F, typename G, typename H>
struct LazySegmentTree {
private:
int n{}, sz{}, height{};
vector<T> data;
vector<E> lazy;
const F f;
const G g;
const H h;
const T ti;
const E ei;
inline void update(int k) { data[k] = f(data[2 * k + 0], data[2 * k + 1]); }
inline void all_apply(int k, const E &x) {
data[k] = g(data[k], x);
if (k < sz) lazy[k] = h(lazy[k], x);
}
inline void propagate(int k) {
if (lazy[k] != ei) {
all_apply(2 * k + 0, lazy[k]);
all_apply(2 * k + 1, lazy[k]);
lazy[k] = ei;
}
}
public:
LazySegmentTree() = default;
explicit LazySegmentTree(int n, const F f, const G g, const H h, const T &ti,
const E &ei)
: n(n), f(f), g(g), h(h), ti(ti), ei(ei) {
sz = 1;
height = 0;
while (sz < n) sz <<= 1, height++;
data.assign(2 * sz, ti);
lazy.assign(2 * sz, ei);
}
explicit LazySegmentTree(const vector<T> &v, const F f, const G g, const H h,
const T &ti, const E &ei)
: LazySegmentTree(v.size(), f, g, h, ti, ei) {
build(v);
}
void build(const vector<T> &v) {
assert(n == (int)v.size());
for (int k = 0; k < n; k++) data[k + sz] = v[k];
for (int k = sz - 1; k > 0; k--) update(k);
}
void set(int k, const T &x) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
data[k] = x;
for (int i = 1; i <= height; i++) update(k >> i);
}
T get(int k) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
return data[k];
}
T operator[](int k) { return get(k); }
T prod(int l, int r) {
if (l >= r) return ti;
l += sz;
r += sz;
for (int i = height; i > 0; i--) {
if (((l >> i) << i) != l) propagate(l >> i);
if (((r >> i) << i) != r) propagate((r - 1) >> i);
}
T L = ti, R = ti;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) L = f(L, data[l++]);
if (r & 1) R = f(data[--r], R);
}
return f(L, R);
}
T all_prod() const { return data[1]; }
void apply(int k, const E &x) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
data[k] = g(data[k], x);
for (int i = 1; i <= height; i++) update(k >> i);
}
void apply(int l, int r, const E &x) {
if (l >= r) return;
l += sz;
r += sz;
for (int i = height; i > 0; i--) {
if (((l >> i) << i) != l) propagate(l >> i);
if (((r >> i) << i) != r) propagate((r - 1) >> i);
}
{
int l2 = l, r2 = r;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) all_apply(l++, x);
if (r & 1) all_apply(--r, x);
}
l = l2, r = r2;
}
for (int i = 1; i <= height; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <typename C>
int find_first(int l, const C &check) {
if (l >= n) return n;
l += sz;
for (int i = height; i > 0; i--) propagate(l >> i);
T sum = ti;
do {
while ((l & 1) == 0) l >>= 1;
if (check(f(sum, data[l]))) {
while (l < sz) {
propagate(l);
l <<= 1;
auto nxt = f(sum, data[l]);
if (not check(nxt)) {
sum = nxt;
l++;
}
}
return l + 1 - sz;
}
sum = f(sum, data[l++]);
} while ((l & -l) != l);
return n;
}
template <typename C>
int find_last(int r, const C &check) {
if (r <= 0) return -1;
r += sz;
for (int i = height; i > 0; i--) propagate((r - 1) >> i);
T sum = ti;
do {
r--;
while (r > 1 and (r & 1)) r >>= 1;
if (check(f(data[r], sum))) {
while (r < sz) {
propagate(r);
r = (r << 1) + 1;
auto nxt = f(data[r], sum);
if (not check(nxt)) {
sum = nxt;
r--;
}
}
return r - sz;
}
sum = f(data[r], sum);
} while ((r & -r) != r);
return -1;
}
};
template <typename T, typename E, typename F, typename G, typename H>
LazySegmentTree<T, E, F, G, H> get_lazy_segment_tree(int N, const F &f,
const G &g, const H &h,
const T &ti, const E &ei) {
return LazySegmentTree{N, f, g, h, ti, ei};
}
template <typename T, typename E, typename F, typename G, typename H>
LazySegmentTree<T, E, F, G, H> get_lazy_segment_tree(const vector<T> &v,
const F &f, const G &g,
const H &h, const T &ti,
const E &ei) {
return LazySegmentTree{v, f, g, h, ti, ei};
}
#line 2 "structure/others/permutation-tree.hpp"
/**
* @brief Permutation Tree(順列木)
*
* @see https://codeforces.com/blog/entry/78898
*/
struct PermutationTree {
public:
enum NodeType { JOIN_ASC, JOIN_DESC, LEAF, CUT };
struct Node {
NodeType type;
int l, r; // [l, r)
int min_v, max_v; // [min_v, max_v)
vector<Node *> ch;
size_t size() const { return r - l; }
bool is_join() const { return type == JOIN_ASC or type == JOIN_DESC; };
bool is_leaf() const { return type == LEAF; }
bool is_cut() const { return type == CUT; }
};
using NP = Node *;
PermutationTree() = default;
private:
static void add_child(NP t, NP c) {
t->ch.emplace_back(c);
t->l = min(t->l, c->l);
t->r = max(t->r, c->r);
t->min_v = min(t->min_v, c->min_v);
t->max_v = max(t->max_v, c->max_v);
}
public:
static NP build(vector<int> &A) {
int n = (int)A.size();
vector<int> desc{-1};
vector<int> asc{-1};
vector<NP> st;
auto f = [](int a, int b) { return min(a, b); };
auto g = [](int a, int b) { return a + b; };
constexpr int lim = (1 << 30) - 1;
auto seg = get_lazy_segment_tree(vector<int>(n), f, g, g, lim, 0);
for (int i = 0; i < n; i++) {
while (~desc.back() and A[i] > A[desc.back()]) {
seg.apply(desc[desc.size() - 2] + 1, desc.back() + 1,
A[i] - A[desc.back()]);
desc.pop_back();
}
while (~asc.back() and A[i] < A[asc.back()]) {
seg.apply(asc[asc.size() - 2] + 1, asc.back() + 1,
A[asc.back()] - A[i]);
asc.pop_back();
}
desc.emplace_back(i);
asc.emplace_back(i);
NP t = new Node{LEAF, i, i + 1, A[i], A[i] + 1, {}};
for (;;) {
NodeType type = CUT;
if (not st.empty()) {
if (st.back()->max_v == t->min_v) {
type = JOIN_ASC;
} else if (t->max_v == st.back()->min_v) {
type = JOIN_DESC;
}
}
if (type != CUT) {
NP r = st.back();
if (type != r->type) {
r = new Node{type, r->l, r->r, r->min_v, r->max_v, {r}};
}
add_child(r, t);
st.pop_back();
t = r;
} else if (seg.prod(0, i + 1 - (int)t->size()) == 0) {
t = new Node{CUT, t->l, t->r, t->min_v, t->max_v, {t}};
do {
add_child(t, st.back());
st.pop_back();
} while (t->max_v - t->min_v != t->size());
reverse(begin(t->ch), end(t->ch));
} else {
break;
}
}
st.emplace_back(t);
seg.apply(0, i + 1, -1);
}
return st[0];
}
};
#line 6 "test/verify/yukicoder-1720.test.cpp"
#line 2 "math/combinatorics/montgomery-mod-int.hpp"
template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
private:
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod_;
for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod_) % mod_;
static_assert(r * mod_ == 1, "invalid, r * mod != 1");
static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
public:
MontgomeryModInt() : x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
}
mint &operator+=(const mint &p) {
if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
return *this;
}
mint &operator-=(const mint &p) {
if (i32(x -= p.x) < 0) x += 2 * mod();
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inv();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const {
return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
}
bool operator!=(const mint &p) const {
return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
}
u32 val() const {
u32 ret = reduce(x);
return ret >= mod() ? ret - mod() : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inv() const { return pow(mod() - 2); }
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.val();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 mod() { return mod_; }
};
template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 8 "test/verify/yukicoder-1720.test.cpp"
using mint = modint998244353;
int main() {
int N, K;
cin >> N >> K;
vector< int > A(N);
cin >> A;
for(auto &a: A) --a;
using NP = PermutationTree::Node *;
auto dp = make_v< mint >(K + 1, N + 1);
dp[0][0] = 1;
MFP([&](auto rec, NP r) -> void {
if(r->is_cut() or r->is_leaf()) {
for(int k = 0; k < K; k++) {
dp[k + 1][r->r] += dp[k][r->l];
}
}
vector< mint > sum(K);
for(auto &c: r->ch) {
rec(c);
if(r->is_join()) {
for(int k = 0; k < K; k++) {
dp[k + 1][c->r] += sum[k];
sum[k] += dp[k][c->l];
}
}
}
})(PermutationTree::build(A));
for(int i = 1; i <= K; i++) {
cout << dp[i][N] << "\n";
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | 01_sample_01 | AC | 8 ms | 4 MB |
g++ | 01_sample_02 | AC | 7 ms | 4 MB |
g++ | 01_sample_03 | AC | 7 ms | 4 MB |
g++ | 02_random_01 | AC | 8 ms | 4 MB |
g++ | 02_random_02 | AC | 8 ms | 4 MB |
g++ | 02_random_03 | AC | 7 ms | 4 MB |
g++ | 02_random_04 | AC | 7 ms | 4 MB |
g++ | 02_random_05 | AC | 7 ms | 4 MB |
g++ | 02_random_06 | AC | 7 ms | 4 MB |
g++ | 02_random_07 | AC | 8 ms | 4 MB |
g++ | 02_random_08 | AC | 8 ms | 4 MB |
g++ | 02_random_09 | AC | 8 ms | 4 MB |
g++ | 02_random_10 | AC | 7 ms | 4 MB |
g++ | 02_random_11 | AC | 135 ms | 34 MB |
g++ | 02_random_12 | AC | 136 ms | 34 MB |
g++ | 02_random_14 | AC | 84 ms | 22 MB |
g++ | 02_random_15 | AC | 131 ms | 33 MB |
g++ | 02_random_16 | AC | 95 ms | 26 MB |
g++ | 03_handmade_01 | AC | 103 ms | 32 MB |
g++ | 03_handmade_02 | AC | 141 ms | 31 MB |
g++ | 03_handmade_03 | AC | 140 ms | 31 MB |
g++ | 03_handmade_04 | AC | 141 ms | 31 MB |
g++ | 03_handmade_05 | AC | 140 ms | 31 MB |
g++ | 03_handmade_06 | AC | 138 ms | 31 MB |
g++ | 03_handmade_07 | AC | 142 ms | 31 MB |
g++ | 03_handmade_08 | AC | 140 ms | 31 MB |
g++ | 03_handmade_09 | AC | 140 ms | 31 MB |
g++ | 03_handmade_10 | AC | 140 ms | 31 MB |
g++ | 03_handmade_11 | AC | 139 ms | 31 MB |
g++ | 03_handmade_12 | AC | 140 ms | 31 MB |
g++ | 03_handmade_13 | AC | 140 ms | 31 MB |
g++ | 03_handmade_14 | AC | 139 ms | 31 MB |
g++ | 03_handmade_15 | AC | 8 ms | 4 MB |
g++ | 04_manual_01 | AC | 7 ms | 4 MB |
g++ | 04_manual_02 | AC | 7 ms | 4 MB |
g++ | 04_manual_03 | AC | 8 ms | 4 MB |
g++ | 04_manual_04 | AC | 8 ms | 4 MB |
g++ | 04_manual_05 | AC | 8 ms | 4 MB |
g++ | 04_manual_06 | AC | 8 ms | 4 MB |
g++ | 04_manual_07 | AC | 8 ms | 4 MB |
g++ | 04_manual_08 | AC | 8 ms | 4 MB |
g++ | 04_manual_09 | AC | 7 ms | 4 MB |
g++ | 04_manual_10 | AC | 8 ms | 4 MB |
g++ | 04_manual_11 | AC | 115 ms | 29 MB |
g++ | 04_manual_12 | AC | 108 ms | 27 MB |
g++ | 04_manual_13 | AC | 99 ms | 25 MB |
g++ | 04_manual_14 | AC | 75 ms | 19 MB |
g++ | 04_manual_15 | AC | 100 ms | 25 MB |
g++ | 04_manual_16 | AC | 79 ms | 20 MB |
g++ | 04_manual_17 | AC | 117 ms | 29 MB |
g++ | 04_manual_18 | AC | 96 ms | 25 MB |
g++ | 04_manual_19 | AC | 79 ms | 20 MB |
g++ | 04_manual_20 | AC | 112 ms | 28 MB |
g++ | 04_manual_21 | AC | 132 ms | 32 MB |
g++ | 04_manual_22 | AC | 135 ms | 34 MB |
g++ | 04_manual_23 | AC | 134 ms | 31 MB |
g++ | 04_manual_24 | AC | 133 ms | 31 MB |
g++ | 04_manual_25 | AC | 135 ms | 34 MB |
g++ | 04_manual_26 | AC | 133 ms | 31 MB |
g++ | 04_manual_27 | AC | 134 ms | 31 MB |
g++ | 04_manual_28 | AC | 135 ms | 34 MB |
g++ | 04_manual_29 | AC | 133 ms | 32 MB |
g++ | 04_manual_30 | AC | 133 ms | 32 MB |
clang++ | 01_sample_01 | AC | 7 ms | 4 MB |
clang++ | 01_sample_02 | AC | 7 ms | 4 MB |
clang++ | 01_sample_03 | AC | 7 ms | 4 MB |
clang++ | 02_random_01 | AC | 7 ms | 4 MB |
clang++ | 02_random_02 | AC | 7 ms | 4 MB |
clang++ | 02_random_03 | AC | 7 ms | 4 MB |
clang++ | 02_random_04 | AC | 7 ms | 4 MB |
clang++ | 02_random_05 | AC | 8 ms | 4 MB |
clang++ | 02_random_06 | AC | 7 ms | 4 MB |
clang++ | 02_random_07 | AC | 7 ms | 4 MB |
clang++ | 02_random_08 | AC | 7 ms | 4 MB |
clang++ | 02_random_09 | AC | 7 ms | 4 MB |
clang++ | 02_random_10 | AC | 7 ms | 4 MB |
clang++ | 02_random_11 | AC | 131 ms | 34 MB |
clang++ | 02_random_12 | AC | 132 ms | 34 MB |
clang++ | 02_random_14 | AC | 81 ms | 22 MB |
clang++ | 02_random_15 | AC | 127 ms | 33 MB |
clang++ | 02_random_16 | AC | 92 ms | 26 MB |
clang++ | 03_handmade_01 | AC | 102 ms | 32 MB |
clang++ | 03_handmade_02 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_03 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_04 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_05 | AC | 134 ms | 31 MB |
clang++ | 03_handmade_06 | AC | 131 ms | 31 MB |
clang++ | 03_handmade_07 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_08 | AC | 137 ms | 31 MB |
clang++ | 03_handmade_09 | AC | 132 ms | 31 MB |
clang++ | 03_handmade_10 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_11 | AC | 131 ms | 31 MB |
clang++ | 03_handmade_12 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_13 | AC | 133 ms | 31 MB |
clang++ | 03_handmade_14 | AC | 132 ms | 31 MB |
clang++ | 03_handmade_15 | AC | 8 ms | 4 MB |
clang++ | 04_manual_01 | AC | 7 ms | 4 MB |
clang++ | 04_manual_02 | AC | 7 ms | 4 MB |
clang++ | 04_manual_03 | AC | 7 ms | 4 MB |
clang++ | 04_manual_04 | AC | 7 ms | 4 MB |
clang++ | 04_manual_05 | AC | 7 ms | 4 MB |
clang++ | 04_manual_06 | AC | 7 ms | 4 MB |
clang++ | 04_manual_07 | AC | 7 ms | 4 MB |
clang++ | 04_manual_08 | AC | 7 ms | 4 MB |
clang++ | 04_manual_09 | AC | 7 ms | 4 MB |
clang++ | 04_manual_10 | AC | 7 ms | 4 MB |
clang++ | 04_manual_11 | AC | 112 ms | 29 MB |
clang++ | 04_manual_12 | AC | 104 ms | 27 MB |
clang++ | 04_manual_13 | AC | 96 ms | 25 MB |
clang++ | 04_manual_14 | AC | 73 ms | 19 MB |
clang++ | 04_manual_15 | AC | 98 ms | 25 MB |
clang++ | 04_manual_16 | AC | 78 ms | 20 MB |
clang++ | 04_manual_17 | AC | 116 ms | 29 MB |
clang++ | 04_manual_18 | AC | 94 ms | 25 MB |
clang++ | 04_manual_19 | AC | 77 ms | 20 MB |
clang++ | 04_manual_20 | AC | 106 ms | 28 MB |
clang++ | 04_manual_21 | AC | 130 ms | 32 MB |
clang++ | 04_manual_22 | AC | 134 ms | 34 MB |
clang++ | 04_manual_23 | AC | 129 ms | 31 MB |
clang++ | 04_manual_24 | AC | 128 ms | 31 MB |
clang++ | 04_manual_25 | AC | 131 ms | 34 MB |
clang++ | 04_manual_26 | AC | 128 ms | 31 MB |
clang++ | 04_manual_27 | AC | 128 ms | 31 MB |
clang++ | 04_manual_28 | AC | 132 ms | 34 MB |
clang++ | 04_manual_29 | AC | 129 ms | 32 MB |
clang++ | 04_manual_30 | AC | 129 ms | 32 MB |