sotanishy's code snippets for competitive programming
View the Project on GitHub sotanishy/cp-library-cpp
#include "data-structure/segtree/segment_tree_2d.hpp"
2D セグメント木は,モノイド $(T, \cdot, e)$ の重みを持つ2次元平面上の点集合に対する一点更新と矩形領域積取得を提供するデータ構造である.
この実装では,重みをもたせる点を先読みして初期化時に渡す必要がある.
空間計算量: $O(n)$
SegmentTree2D(vector<pair<X, Y>> pts)
pts
void update(X x, Y y, T val)
T fold(X sx, X tx, Y sy, Y ty)
#pragma once #include <algorithm> #include <bit> #include <cassert> #include <utility> #include <vector> #include "segment_tree.hpp" template <typename X, typename Y, typename M> class SegmentTree2D { using T = M::T; public: SegmentTree2D() = default; explicit SegmentTree2D(const std::vector<std::pair<X, Y>>& pts) { for (auto& [x, y] : pts) { xs.push_back(x); } std::ranges::sort(xs); xs.erase(std::ranges::unique(xs).begin(), xs.end()); const int n = xs.size(); size = std::bit_ceil((unsigned int)n); ys.resize(2 * size); seg.resize(2 * size); for (auto& [x, y] : pts) { ys[size + getx(x)].push_back(y); } for (int i = size + n - 1; i > 0; --i) { if (i >= size) { std::ranges::sort(ys[i]); } else { std::ranges::merge(ys[2 * i], ys[2 * i + 1], std::back_inserter(ys[i])); } ys[i].erase(std::ranges::unique(ys[i]).begin(), ys[i].end()); } for (int i = 1; i < size + n; ++i) { seg[i] = SegmentTree<M>(ys[i].size()); } } T get(X x, Y y) const { int kx = getx(x); assert(kx < (int)xs.size() && xs[kx] == x); kx += size; int ky = gety(kx, y); assert(ky < (int)ys[kx].size() && ys[kx][ky] == y); return seg[kx][ky]; } void update(X x, Y y, T val) { int kx = getx(x); assert(kx < (int)xs.size() && xs[kx] == x); kx += size; int ky = gety(kx, y); assert(ky < (int)ys[kx].size() && ys[kx][ky] == y); seg[kx].update(ky, val); while (kx >>= 1) { ky = gety(kx, y); int kl = gety(2 * kx, y), kr = gety(2 * kx + 1, y); T vl = (kl < (int)ys[2 * kx].size() && ys[2 * kx][kl] == y ? seg[2 * kx][kl] : M::id()); T vr = (kr < (int)ys[2 * kx + 1].size() && ys[2 * kx + 1][kr] == y ? seg[2 * kx + 1][kr] : M::id()); seg[kx].update(ky, M::op(vl, vr)); } } T fold(X sx, X tx, Y sy, Y ty) const { T ret = M::id(); for (int l = size + getx(sx), r = size + getx(tx); l < r; l >>= 1, r >>= 1) { if (l & 1) { ret = M::op(ret, seg[l].fold(gety(l, sy), gety(l, ty))); ++l; } if (r & 1) { --r; ret = M::op(ret, seg[r].fold(gety(r, sy), gety(r, ty))); } } return ret; } private: int size; std::vector<X> xs; std::vector<std::vector<Y>> ys; std::vector<SegmentTree<M>> seg; int getx(X x) const { return std::ranges::lower_bound(xs, x) - xs.begin(); } int gety(int k, Y y) const { return std::ranges::lower_bound(ys[k], y) - ys[k].begin(); } };
#line 2 "data-structure/segtree/segment_tree_2d.hpp" #include <algorithm> #include <bit> #include <cassert> #include <utility> #include <vector> #line 5 "data-structure/segtree/segment_tree.hpp" template <typename M> class SegmentTree { using T = M::T; public: SegmentTree() = default; explicit SegmentTree(int n) : SegmentTree(std::vector<T>(n, M::id())) {} explicit SegmentTree(const std::vector<T>& v) : size(std::bit_ceil(v.size())), node(2 * size, M::id()) { std::ranges::copy(v, node.begin() + size); for (int i = size - 1; i > 0; --i) { node[i] = M::op(node[2 * i], node[2 * i + 1]); } } T operator[](int k) const { return node[k + size]; } void update(int k, const T& x) { k += size; node[k] = x; while (k >>= 1) node[k] = M::op(node[2 * k], node[2 * k + 1]); } T fold(int l, int r) const { T vl = M::id(), vr = M::id(); for (l += size, r += size; l < r; l >>= 1, r >>= 1) { if (l & 1) vl = M::op(vl, node[l++]); if (r & 1) vr = M::op(node[--r], vr); } return M::op(vl, vr); } template <typename F> int find_first(int l, F cond) const { T v = M::id(); for (l += size; l > 0; l >>= 1) { if (l & 1) { T nv = M::op(v, node[l]); if (cond(nv)) { while (l < size) { nv = M::op(v, node[2 * l]); if (cond(nv)) { l = 2 * l; } else { v = nv, l = 2 * l + 1; } } return l + 1 - size; } v = nv; ++l; } } return -1; } template <typename F> int find_last(int r, F cond) const { T v = M::id(); for (r += size; r > 0; r >>= 1) { if (r & 1) { --r; T nv = M::op(node[r], v); if (cond(nv)) { while (r < size) { nv = M::op(node[2 * r + 1], v); if (cond(nv)) { r = 2 * r + 1; } else { v = nv, r = 2 * r; } } return r - size; } v = nv; } } return -1; } private: int size; std::vector<T> node; }; #line 9 "data-structure/segtree/segment_tree_2d.hpp" template <typename X, typename Y, typename M> class SegmentTree2D { using T = M::T; public: SegmentTree2D() = default; explicit SegmentTree2D(const std::vector<std::pair<X, Y>>& pts) { for (auto& [x, y] : pts) { xs.push_back(x); } std::ranges::sort(xs); xs.erase(std::ranges::unique(xs).begin(), xs.end()); const int n = xs.size(); size = std::bit_ceil((unsigned int)n); ys.resize(2 * size); seg.resize(2 * size); for (auto& [x, y] : pts) { ys[size + getx(x)].push_back(y); } for (int i = size + n - 1; i > 0; --i) { if (i >= size) { std::ranges::sort(ys[i]); } else { std::ranges::merge(ys[2 * i], ys[2 * i + 1], std::back_inserter(ys[i])); } ys[i].erase(std::ranges::unique(ys[i]).begin(), ys[i].end()); } for (int i = 1; i < size + n; ++i) { seg[i] = SegmentTree<M>(ys[i].size()); } } T get(X x, Y y) const { int kx = getx(x); assert(kx < (int)xs.size() && xs[kx] == x); kx += size; int ky = gety(kx, y); assert(ky < (int)ys[kx].size() && ys[kx][ky] == y); return seg[kx][ky]; } void update(X x, Y y, T val) { int kx = getx(x); assert(kx < (int)xs.size() && xs[kx] == x); kx += size; int ky = gety(kx, y); assert(ky < (int)ys[kx].size() && ys[kx][ky] == y); seg[kx].update(ky, val); while (kx >>= 1) { ky = gety(kx, y); int kl = gety(2 * kx, y), kr = gety(2 * kx + 1, y); T vl = (kl < (int)ys[2 * kx].size() && ys[2 * kx][kl] == y ? seg[2 * kx][kl] : M::id()); T vr = (kr < (int)ys[2 * kx + 1].size() && ys[2 * kx + 1][kr] == y ? seg[2 * kx + 1][kr] : M::id()); seg[kx].update(ky, M::op(vl, vr)); } } T fold(X sx, X tx, Y sy, Y ty) const { T ret = M::id(); for (int l = size + getx(sx), r = size + getx(tx); l < r; l >>= 1, r >>= 1) { if (l & 1) { ret = M::op(ret, seg[l].fold(gety(l, sy), gety(l, ty))); ++l; } if (r & 1) { --r; ret = M::op(ret, seg[r].fold(gety(r, sy), gety(r, ty))); } } return ret; } private: int size; std::vector<X> xs; std::vector<std::vector<Y>> ys; std::vector<SegmentTree<M>> seg; int getx(X x) const { return std::ranges::lower_bound(xs, x) - xs.begin(); } int gety(int k, Y y) const { return std::ranges::lower_bound(ys[k], y) - ys[k].begin(); } };