test/verify/yukicoder-1720.test.cpp

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• Last update: 2022-09-11 00:53:50+09:00
• Problem: https://yukicoder.me/problems/no/1720

Depends on

• Montgomery ModInt (math/combinatorics/montgomery-mod-int.hpp)
• Permutation Tree(順列木) (structure/others/permutation-tree.hpp)
• Lazy-Segment-Tree(遅延伝搬セグメント木) (structure/segment-tree/lazy-segment-tree.hpp)
• template/template.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1720"

#include "../../template/template.hpp"

#include "../../structure/others/permutation-tree.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"

const int MOD = 998244353;
using mint = MontgomeryModInt< MOD >;

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"
#define PROBLEM "https://yukicoder.me/problems/no/1720"

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

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)
 * @docs docs/lazy-segment-tree.md
 */
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)
 * @docs docs/permutation-tree.md
 * @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 1 "math/combinatorics/montgomery-mod-int.hpp"
/**
 * @brief Montgomery ModInt
 */
template< uint32_t mod, bool fast = false >
struct MontgomeryModInt {
  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;

  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.inverse();
    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 get() 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 inverse() const {
    return pow(mod - 2);
  }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.get();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static u32 get_mod() { return mod; }
};

using modint = MontgomeryModInt< mod >;
#line 8 "test/verify/yukicoder-1720.test.cpp"

const int MOD = 998244353;
using mint = MontgomeryModInt< MOD >;

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";
  }
}

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