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/* * @title SegmentTree2D - 非再帰抽象化セグメント木2D * @docs md/segment-tree/SegmentTree2D.md */ template<class Monoid> class SegmentTree2D { using TypeNode = typename Monoid::TypeNode; class SegmentTree { size_t length; vector<TypeNode> node; public: //unitで初期化 SegmentTree(const size_t num) { for (length = 1; length <= num; length *= 2); node.resize(2 * length, Monoid::unit_node); for (int i = length - 1; i >= 0; --i) node[i] = Monoid::func_fold(node[(i<<1)+0],node[(i<<1)+1]); } //[idx,idx+1) void operate(size_t idx, const TypeNode var) { if(idx < 0 || length <= idx) return; idx += length; node[idx] = Monoid::func_operate(node[idx],var); while(idx >>= 1) node[idx] = Monoid::func_fold(node[(idx<<1)+0],node[(idx<<1)+1]); } //[l,r) TypeNode fold(int l, int r) { if (l < 0 || length <= l || r < 0 || length < r) return Monoid::unit_node; TypeNode vl = Monoid::unit_node, vr = Monoid::unit_node; for(l += length, r += length; l < r; l >>=1, r >>=1) { if(l&1) vl = Monoid::func_fold(vl,node[l++]); if(r&1) vr = Monoid::func_fold(node[--r],vr); } return Monoid::func_fold(vl,vr); } void print() { cout << "{"; for(int i=0; i < length; ++i) cout << fold(i,i+1) << " }"[i+1==length]; cout << endl; } }; size_t height,width; vector<SegmentTree> node; public: SegmentTree2D(const size_t h, const size_t w):width(w) { for (height = 1; height <= h; height *= 2); SegmentTree seg(width); node.resize(2 * height, seg); for (int i = height - 1; i >= 0; --i) { for(int j=0; j < width; ++j) { node[i].operate(j, Monoid::func_fold(node[(i<<1)+0].fold(j,j+1),node[(i<<1)+1].fold(j,j+1))); } } } //[u,u+1)*[l,l+1) に operate void operate(size_t u, size_t l, const TypeNode var) { if(u < 0 || height <= u || l < 0 || width <= l) return; u += height; node[u].operate(l, var); while(u >>= 1) node[u].operate(l, Monoid::func_fold(node[(u<<1)+0].fold(l,l+1),node[(u<<1)+1].fold(l,l+1))); } //[u,d),[l,r) TypeNode fold(int u, int d, int l, int r) { if(u < 0 || height <= u || d < 0 || height < d || l < 0 || width <= l || r < 0 || width < r) return Monoid::unit_node; TypeNode vu = Monoid::unit_node, vd = Monoid::unit_node; for(u += height, d += height; u < d; u >>=1, d >>=1) { if(u&1) vu = Monoid::func_fold(vu,node[u++].fold(l,r)); if(d&1) vd = Monoid::func_fold(node[--d].fold(l,r),vd); } return Monoid::func_fold(vu,vd); } void print() { for(int i=height; i < 2*height; ++i) { node[i].print(); } } };
#line 1 "lib/10-segment-tree/SegmentTree2D.cpp" /* * @title SegmentTree2D - 非再帰抽象化セグメント木2D * @docs md/segment-tree/SegmentTree2D.md */ template<class Monoid> class SegmentTree2D { using TypeNode = typename Monoid::TypeNode; class SegmentTree { size_t length; vector<TypeNode> node; public: //unitで初期化 SegmentTree(const size_t num) { for (length = 1; length <= num; length *= 2); node.resize(2 * length, Monoid::unit_node); for (int i = length - 1; i >= 0; --i) node[i] = Monoid::func_fold(node[(i<<1)+0],node[(i<<1)+1]); } //[idx,idx+1) void operate(size_t idx, const TypeNode var) { if(idx < 0 || length <= idx) return; idx += length; node[idx] = Monoid::func_operate(node[idx],var); while(idx >>= 1) node[idx] = Monoid::func_fold(node[(idx<<1)+0],node[(idx<<1)+1]); } //[l,r) TypeNode fold(int l, int r) { if (l < 0 || length <= l || r < 0 || length < r) return Monoid::unit_node; TypeNode vl = Monoid::unit_node, vr = Monoid::unit_node; for(l += length, r += length; l < r; l >>=1, r >>=1) { if(l&1) vl = Monoid::func_fold(vl,node[l++]); if(r&1) vr = Monoid::func_fold(node[--r],vr); } return Monoid::func_fold(vl,vr); } void print() { cout << "{"; for(int i=0; i < length; ++i) cout << fold(i,i+1) << " }"[i+1==length]; cout << endl; } }; size_t height,width; vector<SegmentTree> node; public: SegmentTree2D(const size_t h, const size_t w):width(w) { for (height = 1; height <= h; height *= 2); SegmentTree seg(width); node.resize(2 * height, seg); for (int i = height - 1; i >= 0; --i) { for(int j=0; j < width; ++j) { node[i].operate(j, Monoid::func_fold(node[(i<<1)+0].fold(j,j+1),node[(i<<1)+1].fold(j,j+1))); } } } //[u,u+1)*[l,l+1) に operate void operate(size_t u, size_t l, const TypeNode var) { if(u < 0 || height <= u || l < 0 || width <= l) return; u += height; node[u].operate(l, var); while(u >>= 1) node[u].operate(l, Monoid::func_fold(node[(u<<1)+0].fold(l,l+1),node[(u<<1)+1].fold(l,l+1))); } //[u,d),[l,r) TypeNode fold(int u, int d, int l, int r) { if(u < 0 || height <= u || d < 0 || height < d || l < 0 || width <= l || r < 0 || width < r) return Monoid::unit_node; TypeNode vu = Monoid::unit_node, vd = Monoid::unit_node; for(u += height, d += height; u < d; u >>=1, d >>=1) { if(u&1) vu = Monoid::func_fold(vu,node[u++].fold(l,r)); if(d&1) vd = Monoid::func_fold(node[--d].fold(l,r),vd); } return Monoid::func_fold(vu,vd); } void print() { for(int i=height; i < 2*height; ++i) { node[i].print(); } } };