seq/cartesian_tree.hpp

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• Last update: 2023-04-14 22:08:47+09:00
• Include: #include "seq/cartesian_tree.hpp"
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Required by

• string/suffix_tree.hpp

Verified with

• test/2_library_checker/tree/cartesian_tree.test.cpp
• test/3_yukicoder/2361.test.cpp
• test/3_yukicoder/2574.test.cpp
• test/4_aoj/DPL_3_B.test.cpp
• test/4_aoj/DPL_3_C.test.cpp
• test/5_atcoder/abc234g.test.cpp

Code

/*
辞書順で高さを unique して、木にしている。
極大長方形アルゴリズムで線形時間構築。
*/
template <typename T, bool IS_MIN>
struct CartesianTree {
  int n;
  vc<T>& A;
  vc<pair<int, int>> range;
  vc<int> lch, rch, par;
  int root;

  CartesianTree(vc<T>& A) : n(len(A)), A(A) {
    range.assign(n, {-1, -1});
    lch.assign(n, -1);
    rch.assign(n, -1);
    par.assign(n, -1);
    if (n == 1) {
      range[0] = {0, 1};
      root = 0;
      return;
    }
    auto is_sm = [&](int i, int j) -> bool {
      if (IS_MIN) return (A[i] < A[j]) || (A[i] == A[j] && i < j);
      return (A[i] > A[j]) || (A[i] == A[j] && i < j);
    };
    vc<int> st;
    FOR(i, n) {
      while (!st.empty() && is_sm(i, st.back())) {
        lch[i] = st.back();
        st.pop_back();
      }
      range[i].fi = (st.empty() ? 0 : st.back() + 1);
      st.eb(i);
    }
    st.clear();
    FOR_R(i, n) {
      while (!st.empty() && is_sm(i, st.back())) {
        rch[i] = st.back();
        st.pop_back();
      }
      range[i].se = (st.empty() ? n : st.back());
      st.eb(i);
    }
    FOR(i, n) if (lch[i] != -1) par[lch[i]] = i;
    FOR(i, n) if (rch[i] != -1) par[rch[i]] = i;
    FOR(i, n) if (par[i] == -1) root = i;
  }

  // (l, r, h)

  tuple<int, int, T> maximum_rectangle(int i) {
    auto [l, r] = range[i];
    return {l, r, A[i]};
  }

  // (l, r, h)

  T max_rectangle_area() {
    assert(IS_MIN);
    T res = 0;
    FOR(i, n) {
      auto [l, r, h] = maximum_rectangle(i);
      chmax(res, (r - l) * h);
    }
    return res;
  }

  ll count_subrectangle(bool baseline) {
    assert(IS_MIN);
    ll res = 0;
    FOR(i, n) {
      auto [l, r, h] = maximum_rectangle(i);
      ll x = (baseline ? h : h * (h + 1) / 2);
      res += x * (i - l + 1) * (r - i);
    }
    return res;
  }
};

#line 1 "seq/cartesian_tree.hpp"
/*
辞書順で高さを unique して、木にしている。
極大長方形アルゴリズムで線形時間構築。
*/
template <typename T, bool IS_MIN>
struct CartesianTree {
  int n;
  vc<T>& A;
  vc<pair<int, int>> range;
  vc<int> lch, rch, par;
  int root;

  CartesianTree(vc<T>& A) : n(len(A)), A(A) {
    range.assign(n, {-1, -1});
    lch.assign(n, -1);
    rch.assign(n, -1);
    par.assign(n, -1);
    if (n == 1) {
      range[0] = {0, 1};
      root = 0;
      return;
    }
    auto is_sm = [&](int i, int j) -> bool {
      if (IS_MIN) return (A[i] < A[j]) || (A[i] == A[j] && i < j);
      return (A[i] > A[j]) || (A[i] == A[j] && i < j);
    };
    vc<int> st;
    FOR(i, n) {
      while (!st.empty() && is_sm(i, st.back())) {
        lch[i] = st.back();
        st.pop_back();
      }
      range[i].fi = (st.empty() ? 0 : st.back() + 1);
      st.eb(i);
    }
    st.clear();
    FOR_R(i, n) {
      while (!st.empty() && is_sm(i, st.back())) {
        rch[i] = st.back();
        st.pop_back();
      }
      range[i].se = (st.empty() ? n : st.back());
      st.eb(i);
    }
    FOR(i, n) if (lch[i] != -1) par[lch[i]] = i;
    FOR(i, n) if (rch[i] != -1) par[rch[i]] = i;
    FOR(i, n) if (par[i] == -1) root = i;
  }

  // (l, r, h)

  tuple<int, int, T> maximum_rectangle(int i) {
    auto [l, r] = range[i];
    return {l, r, A[i]};
  }

  // (l, r, h)

  T max_rectangle_area() {
    assert(IS_MIN);
    T res = 0;
    FOR(i, n) {
      auto [l, r, h] = maximum_rectangle(i);
      chmax(res, (r - l) * h);
    }
    return res;
  }

  ll count_subrectangle(bool baseline) {
    assert(IS_MIN);
    ll res = 0;
    FOR(i, n) {
      auto [l, r, h] = maximum_rectangle(i);
      ll x = (baseline ? h : h * (h + 1) / 2);
      res += x * (i - l + 1) * (r - i);
    }
    return res;
  }
};

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