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#include "src/data-structure/fenwick-tree.hpp"
長さ $n$ の列 $(a_0, a_1, \cdots, a_{n-1})$ に対し
を $O(\log n)$ で求めることが可能なデータ構造
(1) FenwickTree<T>(usize n) (2) FenwickTree<T>(const std::vector<T> &as)
T()
as[i]
void add(usize k, const T &v)
$a_{k} \leftarrow a_{k} + v$ で更新を行う。
T sum(usize l, usize r) const
$a_{l} + a_{l+1} + \cdots + a_{r-1}$ を返す。
#pragma once #include "src/cpp-template/header/rep.hpp" #include "src/cpp-template/header/size-alias.hpp" #include <cassert> #include <vector> namespace luz { template < typename T > class FenwickTree { usize n; std::vector< T > vals; T sum(usize k) const { T result(0); while (k > 0) { result += vals[k]; k -= k & -k; } return result; } public: FenwickTree() = default; explicit FenwickTree(usize n): n(n), vals(n + 1, T()) {} explicit FenwickTree(const std::vector< T > &as) : n(as.size()), vals(as.size() + 1, T()) { for (usize i: rep(1, as.size() + 1)) { vals[i] = as[i - 1]; } for (usize i: rep(1, as.size() + 1)) { usize j = i + (i & -i); if (j <= as.size()) { vals[j] += vals[i]; } } } void add(usize k, const T &v) { assert(k < n); k++; while (k <= n) { vals[k] += v; k += k & -k; } } T sum(usize l, usize r) const { assert(l <= r and r <= n); return sum(r) - sum(l); } }; } // namespace luz
#line 2 "src/data-structure/fenwick-tree.hpp" #line 2 "src/cpp-template/header/rep.hpp" #line 2 "src/cpp-template/header/size-alias.hpp" #include <cstddef> namespace luz { using isize = std::ptrdiff_t; using usize = std::size_t; } // namespace luz #line 4 "src/cpp-template/header/rep.hpp" #include <algorithm> namespace luz { struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct rrep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; } // namespace luz #line 5 "src/data-structure/fenwick-tree.hpp" #include <cassert> #include <vector> namespace luz { template < typename T > class FenwickTree { usize n; std::vector< T > vals; T sum(usize k) const { T result(0); while (k > 0) { result += vals[k]; k -= k & -k; } return result; } public: FenwickTree() = default; explicit FenwickTree(usize n): n(n), vals(n + 1, T()) {} explicit FenwickTree(const std::vector< T > &as) : n(as.size()), vals(as.size() + 1, T()) { for (usize i: rep(1, as.size() + 1)) { vals[i] = as[i - 1]; } for (usize i: rep(1, as.size() + 1)) { usize j = i + (i & -i); if (j <= as.size()) { vals[j] += vals[i]; } } } void add(usize k, const T &v) { assert(k < n); k++; while (k <= n) { vals[k] += v; k += k & -k; } } T sum(usize l, usize r) const { assert(l <= r and r <= n); return sum(r) - sum(l); } }; } // namespace luz