Plus-Minus-One-RMQ (structure/others/plus-minus-one-rmq.hpp)

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• Last update: 2024-05-01 23:44:47+09:00
• Include: #include "structure/others/plus-minus-one-rmq.hpp"

Depends on

• Sparse-Table(スパーステーブル) (structure/others/sparse-table.hpp)

Required by

• PMORMQ-Lowest-Common-Ancestor(最小共通祖先) (graph/tree/pmormq-lowest-common-ancestor.hpp)

Verified with

• test/verify/aoj-grl-5-c-4.test.cpp
• test/verify/yosupo-lca.test.cpp
• test/verify/yosupo-staticrmq-4.test.cpp

Code

#include "sparse-table.hpp"

/**
 * @brief Plus-Minus-One-RMQ
 **/
template <typename T>
struct PlusMinusOneRMQ {
  using F = function<int(int, int)>;

  int backet;
  vector<T> vs;
  vector<int> bidx, bbit;
  SparseTable<int, F> st;
  vector<vector<vector<int> > > lookup;

  explicit PlusMinusOneRMQ() = default;

  explicit PlusMinusOneRMQ(const vector<T> &vs) : vs(vs) {
    int n = (int)vs.size();
    backet = max(1, (31 - __builtin_clz(n)) / 2);
    int sz = (n + backet - 1) / backet;
    bidx.assign(sz, -1);
    bbit.assign(sz, 0);
    for (int i = 0; i < sz; i++) {
      int l = i * backet;
      int r = min(l + backet, n);
      bidx[i] = l;
      for (int j = l + 1; j < r; j++) {
        if (vs[j] < vs[bidx[i]]) bidx[i] = j;
        if (vs[j - 1] < vs[j]) bbit[i] |= 1 << (j - l - 1);
      }
    }
    F f = [&](int a, int b) { return vs[a] < vs[b] ? a : b; };
    st = get_sparse_table(bidx, f);
    lookup.assign(1 << (backet - 1),
                  vector<vector<int> >(backet, vector<int>(backet + 1)));
    for (int i = 0; i < (1 << (backet - 1)); i++) {
      for (int j = 0; j < backet; j++) {
        int sum = 0, ret = 0, pos = j;
        for (int k = j + 1; k <= backet; k++) {
          lookup[i][j][k] = pos;
          if (i & (1 << (k - 1)))
            ++sum;
          else
            --sum;
          if (sum < ret) {
            pos = k;
            ret = sum;
          }
        }
      }
    }
  }

  pair<T, int> fold(int l, int r) const {
    int lb = l / backet;
    int rb = r / backet;
    if (lb == rb) {
      int pos = lb * backet + lookup[bbit[lb]][l % backet][r % backet];
      return {vs[pos], pos};
    }
    int pos = lb * backet + lookup[bbit[lb]][l % backet][backet];
    if (r % backet > 0) {
      int sub = rb * backet + lookup[bbit[rb]][0][r % backet];
      if (vs[sub] < vs[pos]) pos = sub;
    }
    if (lb + 1 == rb) {
      return {vs[pos], pos};
    } else {
      int sub = st.fold(lb + 1, rb);
      if (vs[sub] < vs[pos]) pos = sub;
      return {vs[pos], pos};
    }
  }
};

#line 1 "structure/others/sparse-table.hpp"
/**
 * @brief Sparse-Table(スパーステーブル)
 *
 */
template <typename T, typename F>
struct SparseTable {
  F f;
  vector<vector<T> > st;
  vector<int> lookup;

  SparseTable() = default;

  explicit SparseTable(const vector<T> &v, const F &f) : f(f) {
    const int n = (int)v.size();
    const int b = 32 - __builtin_clz(n);
    st.assign(b, vector<T>(n));
    for (int i = 0; i < v.size(); i++) {
      st[0][i] = v[i];
    }
    for (int i = 1; i < b; i++) {
      for (int j = 0; j + (1 << i) <= n; j++) {
        st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
      }
    }
    lookup.resize(v.size() + 1);
    for (int i = 2; i < lookup.size(); i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  inline T fold(int l, int r) const {
    int b = lookup[r - l];
    return f(st[b][l], st[b][r - (1 << b)]);
  }
};

template <typename T, typename F>
SparseTable<T, F> get_sparse_table(const vector<T> &v, const F &f) {
  return SparseTable<T, F>(v, f);
}
#line 2 "structure/others/plus-minus-one-rmq.hpp"

/**
 * @brief Plus-Minus-One-RMQ
 **/
template <typename T>
struct PlusMinusOneRMQ {
  using F = function<int(int, int)>;

  int backet;
  vector<T> vs;
  vector<int> bidx, bbit;
  SparseTable<int, F> st;
  vector<vector<vector<int> > > lookup;

  explicit PlusMinusOneRMQ() = default;

  explicit PlusMinusOneRMQ(const vector<T> &vs) : vs(vs) {
    int n = (int)vs.size();
    backet = max(1, (31 - __builtin_clz(n)) / 2);
    int sz = (n + backet - 1) / backet;
    bidx.assign(sz, -1);
    bbit.assign(sz, 0);
    for (int i = 0; i < sz; i++) {
      int l = i * backet;
      int r = min(l + backet, n);
      bidx[i] = l;
      for (int j = l + 1; j < r; j++) {
        if (vs[j] < vs[bidx[i]]) bidx[i] = j;
        if (vs[j - 1] < vs[j]) bbit[i] |= 1 << (j - l - 1);
      }
    }
    F f = [&](int a, int b) { return vs[a] < vs[b] ? a : b; };
    st = get_sparse_table(bidx, f);
    lookup.assign(1 << (backet - 1),
                  vector<vector<int> >(backet, vector<int>(backet + 1)));
    for (int i = 0; i < (1 << (backet - 1)); i++) {
      for (int j = 0; j < backet; j++) {
        int sum = 0, ret = 0, pos = j;
        for (int k = j + 1; k <= backet; k++) {
          lookup[i][j][k] = pos;
          if (i & (1 << (k - 1)))
            ++sum;
          else
            --sum;
          if (sum < ret) {
            pos = k;
            ret = sum;
          }
        }
      }
    }
  }

  pair<T, int> fold(int l, int r) const {
    int lb = l / backet;
    int rb = r / backet;
    if (lb == rb) {
      int pos = lb * backet + lookup[bbit[lb]][l % backet][r % backet];
      return {vs[pos], pos};
    }
    int pos = lb * backet + lookup[bbit[lb]][l % backet][backet];
    if (r % backet > 0) {
      int sub = rb * backet + lookup[bbit[rb]][0][r % backet];
      if (vs[sub] < vs[pos]) pos = sub;
    }
    if (lb + 1 == rb) {
      return {vs[pos], pos};
    } else {
      int sub = st.fold(lb + 1, rb);
      if (vs[sub] < vs[pos]) pos = sub;
      return {vs[pos], pos};
    }
  }
};

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