Segment tree (Add $ai + b$)
(Mylib/DataStructure/SegmentTree/segment_tree_linear_add.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

• update(l, r, a, b)
  • [l, r)にa * i + b(aを公差、bを初項とする等差数列)を加算する。

Requirements

Notes

Problems

• HUPC2020Day1 B Triangle Addition

References

Verified with

• test/aoj/3165/main.test.cpp

Code

#pragma once
#include <cassert>
#include <utility>
#include <vector>

namespace haar_lib {
  template <typename T>
  class segment_tree_linear_add {
  public:
    using value_type = T;

  private:
    using P = std::pair<T, T>;

    int depth_, size_, hsize_;
    std::vector<P> data_;
    std::vector<int> from_;

    P add(P a, P b) {
      return {a.first + b.first, a.second + b.second};
    }

    void propagate(int i) {
      if (i < hsize_) {
        data_[i << 1 | 0] = add(data_[i << 1 | 0], data_[i]);

        const int len = hsize_ >> (31 - __builtin_clz(i) + 1);
        data_[i].first += data_[i].second * len;
        data_[i << 1 | 1] = add(data_[i << 1 | 1], data_[i]);

        data_[i] = P();
      }
    }

    void propagate_top_down(int i) {
      std::vector<int> temp;
      while (i > 1) {
        i >>= 1;
        temp.push_back(i);
      }

      for (auto it = temp.rbegin(); it != temp.rend(); ++it) propagate(*it);
    }

  public:
    segment_tree_linear_add() {}
    segment_tree_linear_add(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
                                     size_(1 << depth_),
                                     hsize_(size_ / 2),
                                     data_(size_, P()),
                                     from_(size_) {
      int s = 0;
      for (int i = 1; i < size_; ++i) {
        from_[i] = s;
        int l    = hsize_ >> (31 - __builtin_clz(i));
        s += l;
        if (s == hsize_) s = 0;
      }
    }

    void update(int l, int r, T a, T b) {
      assert(0 <= l and l <= r and r <= hsize_);
      int L = l + hsize_;
      int R = r + hsize_;

      while (L < R) {
        if (R & 1) {
          --R;
          data_[R] = add(std::make_pair(b + a * (from_[R] - l), a), data_[R]);
        }
        if (L & 1) {
          data_[L] = add(std::make_pair(b + a * (from_[L] - l), a), data_[L]);
          ++L;
        }
        L >>= 1;
        R >>= 1;
      }
    }

    T operator[](int i) {
      assert(0 <= i and i < hsize_);
      propagate_top_down(i + hsize_);
      return data_[i + hsize_].first;
    }

    std::vector<T> get_all(int n) {
      std::vector<T> ret(n);
      for (int i = 1; i < hsize_; ++i) propagate(i);
      for (int i = hsize_; i < hsize_ + n; ++i) ret[i - hsize_] = data_[i].first;
      return ret;
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/DataStructure/SegmentTree/segment_tree_linear_add.cpp"
#include <cassert>
#include <utility>
#include <vector>

namespace haar_lib {
  template <typename T>
  class segment_tree_linear_add {
  public:
    using value_type = T;

  private:
    using P = std::pair<T, T>;

    int depth_, size_, hsize_;
    std::vector<P> data_;
    std::vector<int> from_;

    P add(P a, P b) {
      return {a.first + b.first, a.second + b.second};
    }

    void propagate(int i) {
      if (i < hsize_) {
        data_[i << 1 | 0] = add(data_[i << 1 | 0], data_[i]);

        const int len = hsize_ >> (31 - __builtin_clz(i) + 1);
        data_[i].first += data_[i].second * len;
        data_[i << 1 | 1] = add(data_[i << 1 | 1], data_[i]);

        data_[i] = P();
      }
    }

    void propagate_top_down(int i) {
      std::vector<int> temp;
      while (i > 1) {
        i >>= 1;
        temp.push_back(i);
      }

      for (auto it = temp.rbegin(); it != temp.rend(); ++it) propagate(*it);
    }

  public:
    segment_tree_linear_add() {}
    segment_tree_linear_add(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
                                     size_(1 << depth_),
                                     hsize_(size_ / 2),
                                     data_(size_, P()),
                                     from_(size_) {
      int s = 0;
      for (int i = 1; i < size_; ++i) {
        from_[i] = s;
        int l    = hsize_ >> (31 - __builtin_clz(i));
        s += l;
        if (s == hsize_) s = 0;
      }
    }

    void update(int l, int r, T a, T b) {
      assert(0 <= l and l <= r and r <= hsize_);
      int L = l + hsize_;
      int R = r + hsize_;

      while (L < R) {
        if (R & 1) {
          --R;
          data_[R] = add(std::make_pair(b + a * (from_[R] - l), a), data_[R]);
        }
        if (L & 1) {
          data_[L] = add(std::make_pair(b + a * (from_[L] - l), a), data_[L]);
          ++L;
        }
        L >>= 1;
        R >>= 1;
      }
    }

    T operator[](int i) {
      assert(0 <= i and i < hsize_);
      propagate_top_down(i + hsize_);
      return data_[i + hsize_].first;
    }

    std::vector<T> get_all(int n) {
      std::vector<T> ret(n);
      for (int i = 1; i < hsize_; ++i) propagate(i);
      for (int i = hsize_; i < hsize_ + n; ++i) ret[i - hsize_] = data_[i].first;
      return ret;
    }
  };
}  // namespace haar_lib

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