Sliding Window Aggregation
(data-structure/sliding_window_aggregation.hpp)

• View this file on GitHub
• Last update: 2024-01-08 02:22:28+09:00
• Include: #include "data-structure/sliding_window_aggregation.hpp"

Description

Sliding window aggregation は，半群 $(T, \cdot)$ を扱い，要素の総和の計算が可能なキューである．スタックを2つ用いてキューをシミュレートする．

Operations

• void push(T x)
  • $x$ をキューの末尾に追加する
  • 時間計算量: $O(1)$
• void pop()
  • キューの先頭要素を削除する
  • 時間計算量: $\mathrm{amortized}\ O(1)$
• bool empty()
  • キューが空かどうか判定する
  • 時間計算量: $O(1)$
• T fold()
  • キューの要素全体の演算結果を返す
  • 時間計算量: $O(1)$

Reference

• Sliding Window Aggregation
• Constant-Time Sliding Window Aggregation

Verified with

• test/yosupo/queue_operate_all_composite.test.cpp

Code

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

template <typename S>
class SlidingWindowAggregation {
    using T = typename S::T;

   public:
    void push(const T& x) {
        if (back.empty())
            back.emplace(x, x);
        else
            back.emplace(x, S::op(back.top().second, x));
    }

    void pop() {
        assert(!empty());
        if (front.empty()) {
            T x = back.top().first;
            back.pop();
            front.emplace(x, x);
            while (!back.empty()) {
                x = back.top().first;
                back.pop();
                front.emplace(x, S::op(x, front.top().second));
            }
        }
        front.pop();
    }

    bool empty() const { return front.empty() && back.empty(); }

    T fold() const {
        assert(!empty());
        if (front.empty()) return back.top().second;
        if (back.empty()) return front.top().second;
        return S::op(front.top().second, back.top().second);
    }

   private:
    std::stack<std::pair<T, T>> front, back;
};

#line 2 "data-structure/sliding_window_aggregation.hpp"
#include <cassert>
#include <stack>
#include <utility>

template <typename S>
class SlidingWindowAggregation {
    using T = typename S::T;

   public:
    void push(const T& x) {
        if (back.empty())
            back.emplace(x, x);
        else
            back.emplace(x, S::op(back.top().second, x));
    }

    void pop() {
        assert(!empty());
        if (front.empty()) {
            T x = back.top().first;
            back.pop();
            front.emplace(x, x);
            while (!back.empty()) {
                x = back.top().first;
                back.pop();
                front.emplace(x, S::op(x, front.top().second));
            }
        }
        front.pop();
    }

    bool empty() const { return front.empty() && back.empty(); }

    T fold() const {
        assert(!empty());
        if (front.empty()) return back.top().second;
        if (back.empty()) return front.top().second;
        return S::op(front.top().second, back.top().second);
    }

   private:
    std::stack<std::pair<T, T>> front, back;
};

Back to top page