data_structure/fenwick_tree.hpp

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• Last update: 2022-08-25 19:28:35+09:00
• Include: #include "data_structure/fenwick_tree.hpp"

Depends on

• data_structure/operations.hpp

Required by

• data_structure/range_add_range_sum.hpp

Verified with

• data_structure/test/dsl_2_g.test.cpp
• data_structure/test/point_add_range_sum.test.cpp
• data_structure/test/point_add_rectangle_sum.test.cpp
• graph/test/vertex_add_path_sum.test.cpp
• graph/test/vertex_add_subtree_sum.test.cpp

Code

#pragma once

#include <cassert>
#include <vector>

#include "operations.hpp"

template <typename CommutativeGroup>
class FenwickTree {
public:
    using Value = typename CommutativeGroup::Value;

private:
    std::vector<Value> data;

public:
    FenwickTree(int n) : data(n, CommutativeGroup::id()) {}

    void add(int idx, const Value &x) {
        assert(idx >= 0 && idx < (int) data.size());
        for (; idx < (int) data.size(); idx |= idx + 1) {
            data[idx] = CommutativeGroup::op(data[idx], x);
        }
    }

    Value sum(int r) const {
        assert(r >= 0 && r <= (int) data.size());
        Value ret = CommutativeGroup::id();
        for (; r > 0; r &= r - 1) {
            ret = CommutativeGroup::op(ret, data[r - 1]);
        }
        return ret;
    }

    Value sum(int l, int r) const {
        assert(l >= 0 && l <= r && r <= (int) data.size());
        return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l)));
    }
};

template <typename T>
using FenwickTreeAdd = FenwickTree<Add<T>>;

#line 2 "data_structure/fenwick_tree.hpp"

#include <cassert>
#include <vector>

#line 2 "data_structure/operations.hpp"

#include <limits>
#include <utility>

template <typename T>
struct Add {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs + rhs;
    }
    static Value inv(const Value &x) {
        return -x;
    }
};

template <typename T>
struct Mul {
    using Value = T;
    static Value id() {
        return Value(1);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs * rhs;
    }
    static Value inv(const Value &x) {
        return Value(1) / x;
    }
};

template <typename T>
struct Min {
    using Value = T;
    static Value id() {
        return std::numeric_limits<T>::max();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::min(lhs, rhs);
    }
};

template <typename T>
struct Max {
    using Value = T;
    static Value id() {
        return std::numeric_limits<Value>::min();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::max(lhs, rhs);
    }
};

template <typename T>
struct Xor {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs ^ rhs;
    }
    static Value inv(const Value &x) {
        return x;
    }
};

template <typename Monoid>
struct Reversible {
    using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
    static Value id() {
        return Value(Monoid::id(), Monoid::id());
    }
    static Value op(const Value &v1, const Value &v2) {
        return Value(
            Monoid::op(v1.first, v2.first),
            Monoid::op(v2.second, v1.second));
    }
};

#line 7 "data_structure/fenwick_tree.hpp"

template <typename CommutativeGroup>
class FenwickTree {
public:
    using Value = typename CommutativeGroup::Value;

private:
    std::vector<Value> data;

public:
    FenwickTree(int n) : data(n, CommutativeGroup::id()) {}

    void add(int idx, const Value &x) {
        assert(idx >= 0 && idx < (int) data.size());
        for (; idx < (int) data.size(); idx |= idx + 1) {
            data[idx] = CommutativeGroup::op(data[idx], x);
        }
    }

    Value sum(int r) const {
        assert(r >= 0 && r <= (int) data.size());
        Value ret = CommutativeGroup::id();
        for (; r > 0; r &= r - 1) {
            ret = CommutativeGroup::op(ret, data[r - 1]);
        }
        return ret;
    }

    Value sum(int l, int r) const {
        assert(l >= 0 && l <= r && r <= (int) data.size());
        return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l)));
    }
};

template <typename T>
using FenwickTreeAdd = FenwickTree<Add<T>>;

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