This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub maspypy/library
#include "ds/segtree/segtree_2d.hpp"
// 点の重複があっても別の点として set などがされる template <typename Monoid, typename XY, bool SMALL_X = false> struct SegTree_2D { using MX = Monoid; using S = typename MX::value_type; static_assert(MX::commute); int N; // X to idx vc<XY> keyX; int minX; // top node の点列 vc<XY> all_Y; vc<int> pos; // segtree data int NX, log, size; vc<int> indptr; vc<S> dat; // fractional cascading vc<int> to_left; SegTree_2D(vc<XY>& X, vc<XY>& Y) : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> { return {X[i], Y[i], MX::unit()}; }) {} SegTree_2D(vc<XY>& X, vc<XY>& Y, vc<S>& vals) : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> { return {X[i], Y[i], vals[i]}; }) {} // f(i) = (x,y,val) template <typename F> SegTree_2D(int N, F f) { vc<XY> X(N), Y(N); vc<S> wt(N); FOR(i, N) { auto [a, b, c] = f(i); X[i] = a, Y[i] = b, wt[i] = c; } if (!SMALL_X) { keyX = X; UNIQUE(keyX); NX = len(keyX); } else { minX = (X.empty() ? 0 : MIN(X)); NX = (X.empty() ? 1 : MAX(X) - minX + 1); } log = 0; while ((1 << log) < NX) ++log; size = (1 << log); vc<int> IX(N); FOR(i, N) IX[i] = xtoi(X[i]); indptr.assign(2 * size, 0); for (auto i: IX) { i += size; while (i) indptr[i]++, i /= 2; } indptr = cumsum<int>(indptr); dat.assign(2 * indptr.back(), MX::unit()); to_left.assign(indptr[size], 0); vc<int> ptr = indptr; vc<int> I = argsort(Y); pos.resize(N); FOR(i, N) pos[I[i]] = i; for (auto raw_idx: I) { int i = IX[raw_idx] + size; int j = -1; while (i) { int p = ptr[i]; ptr[i]++; dat[indptr[i + 1] + p] = wt[raw_idx]; if (j != -1) { to_left[p] = (j % 2 == 0); } j = i, i /= 2; } } to_left = cumsum<int>(to_left); FOR(i, 2 * size) { int off = 2 * indptr[i], n = indptr[i + 1] - indptr[i]; FOR_R(j, 1, n) { dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]); } } all_Y = Y; sort(all(all_Y)); } // 最初に与えた点群の index void multiply(int raw_idx, S val) { int i = 1, p = pos[raw_idx]; while (1) { multiply_i(i, p - indptr[i], val); if (i >= size) break; int lc = to_left[p] - to_left[indptr[i]]; int rc = (p - indptr[i]) - lc; if (to_left[p + 1] - to_left[p]) { p = indptr[2 * i + 0] + lc; i = 2 * i + 0; } else { p = indptr[2 * i + 1] + rc; i = 2 * i + 1; } } } // 最初に与えた点群の index void set(int raw_idx, S val) { int i = 1, p = pos[raw_idx]; while (1) { set_i(i, p - indptr[i], val); if (i >= size) break; int lc = to_left[p] - to_left[indptr[i]]; int rc = (p - indptr[i]) - lc; if (to_left[p + 1] - to_left[p]) { p = indptr[2 * i + 0] + lc; i = 2 * i + 0; } else { p = indptr[2 * i + 1] + rc; i = 2 * i + 1; } } } S prod(XY lx, XY rx, XY ly, XY ry) { assert(lx <= rx && ly <= ry); int L = xtoi(lx), R = xtoi(rx); S res = MX::unit(); auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void { if (a == b || R <= l || r <= L) return; if (L <= l && r <= R) { res = MX::op(res, prod_i(i, a, b)); return; } int la = to_left[indptr[i] + a] - to_left[indptr[i]]; int ra = a - la; int lb = to_left[indptr[i] + b] - to_left[indptr[i]]; int rb = b - lb; int m = (l + r) / 2; dfs(dfs, 2 * i + 0, l, m, la, lb); dfs(dfs, 2 * i + 1, m, r, ra, rb); }; dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry)); return res; } // 矩形内の全点を数える, NlogN int count(XY lx, XY rx, XY ly, XY ry) { assert(lx <= rx && ly <= ry); int L = xtoi(lx), R = xtoi(rx); int res = 0; auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void { if (a == b || R <= l || r <= L) return; if (L <= l && r <= R) { res += b - a; return; } int la = to_left[indptr[i] + a] - to_left[indptr[i]]; int ra = a - la; int lb = to_left[indptr[i] + b] - to_left[indptr[i]]; int rb = b - lb; int m = (l + r) / 2; dfs(dfs, 2 * i + 0, l, m, la, lb); dfs(dfs, 2 * i + 1, m, r, ra, rb); }; dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry)); return res; } private: inline int xtoi(XY x) { if constexpr (SMALL_X) return clamp<XY>(x - minX, 0, NX); return LB(keyX, x); } S prod_i(int i, int a, int b) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; int L = n + a, R = n + b; S val = MX::unit(); while (L < R) { if (L & 1) val = MX::op(val, dat[off + (L++)]); if (R & 1) val = MX::op(dat[off + (--R)], val); L >>= 1, R >>= 1; } return val; } void multiply_i(int i, int j, S val) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; j += n; while (j) { dat[off + j] = MX::op(dat[off + j], val); j >>= 1; } } void set_i(int i, int j, S val) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; j += n; dat[off + j] = val; while (j > 1) { j /= 2; dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]); } } };
#line 1 "ds/segtree/segtree_2d.hpp" // 点の重複があっても別の点として set などがされる template <typename Monoid, typename XY, bool SMALL_X = false> struct SegTree_2D { using MX = Monoid; using S = typename MX::value_type; static_assert(MX::commute); int N; // X to idx vc<XY> keyX; int minX; // top node の点列 vc<XY> all_Y; vc<int> pos; // segtree data int NX, log, size; vc<int> indptr; vc<S> dat; // fractional cascading vc<int> to_left; SegTree_2D(vc<XY>& X, vc<XY>& Y) : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> { return {X[i], Y[i], MX::unit()}; }) {} SegTree_2D(vc<XY>& X, vc<XY>& Y, vc<S>& vals) : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> { return {X[i], Y[i], vals[i]}; }) {} // f(i) = (x,y,val) template <typename F> SegTree_2D(int N, F f) { vc<XY> X(N), Y(N); vc<S> wt(N); FOR(i, N) { auto [a, b, c] = f(i); X[i] = a, Y[i] = b, wt[i] = c; } if (!SMALL_X) { keyX = X; UNIQUE(keyX); NX = len(keyX); } else { minX = (X.empty() ? 0 : MIN(X)); NX = (X.empty() ? 1 : MAX(X) - minX + 1); } log = 0; while ((1 << log) < NX) ++log; size = (1 << log); vc<int> IX(N); FOR(i, N) IX[i] = xtoi(X[i]); indptr.assign(2 * size, 0); for (auto i: IX) { i += size; while (i) indptr[i]++, i /= 2; } indptr = cumsum<int>(indptr); dat.assign(2 * indptr.back(), MX::unit()); to_left.assign(indptr[size], 0); vc<int> ptr = indptr; vc<int> I = argsort(Y); pos.resize(N); FOR(i, N) pos[I[i]] = i; for (auto raw_idx: I) { int i = IX[raw_idx] + size; int j = -1; while (i) { int p = ptr[i]; ptr[i]++; dat[indptr[i + 1] + p] = wt[raw_idx]; if (j != -1) { to_left[p] = (j % 2 == 0); } j = i, i /= 2; } } to_left = cumsum<int>(to_left); FOR(i, 2 * size) { int off = 2 * indptr[i], n = indptr[i + 1] - indptr[i]; FOR_R(j, 1, n) { dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]); } } all_Y = Y; sort(all(all_Y)); } // 最初に与えた点群の index void multiply(int raw_idx, S val) { int i = 1, p = pos[raw_idx]; while (1) { multiply_i(i, p - indptr[i], val); if (i >= size) break; int lc = to_left[p] - to_left[indptr[i]]; int rc = (p - indptr[i]) - lc; if (to_left[p + 1] - to_left[p]) { p = indptr[2 * i + 0] + lc; i = 2 * i + 0; } else { p = indptr[2 * i + 1] + rc; i = 2 * i + 1; } } } // 最初に与えた点群の index void set(int raw_idx, S val) { int i = 1, p = pos[raw_idx]; while (1) { set_i(i, p - indptr[i], val); if (i >= size) break; int lc = to_left[p] - to_left[indptr[i]]; int rc = (p - indptr[i]) - lc; if (to_left[p + 1] - to_left[p]) { p = indptr[2 * i + 0] + lc; i = 2 * i + 0; } else { p = indptr[2 * i + 1] + rc; i = 2 * i + 1; } } } S prod(XY lx, XY rx, XY ly, XY ry) { assert(lx <= rx && ly <= ry); int L = xtoi(lx), R = xtoi(rx); S res = MX::unit(); auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void { if (a == b || R <= l || r <= L) return; if (L <= l && r <= R) { res = MX::op(res, prod_i(i, a, b)); return; } int la = to_left[indptr[i] + a] - to_left[indptr[i]]; int ra = a - la; int lb = to_left[indptr[i] + b] - to_left[indptr[i]]; int rb = b - lb; int m = (l + r) / 2; dfs(dfs, 2 * i + 0, l, m, la, lb); dfs(dfs, 2 * i + 1, m, r, ra, rb); }; dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry)); return res; } // 矩形内の全点を数える, NlogN int count(XY lx, XY rx, XY ly, XY ry) { assert(lx <= rx && ly <= ry); int L = xtoi(lx), R = xtoi(rx); int res = 0; auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void { if (a == b || R <= l || r <= L) return; if (L <= l && r <= R) { res += b - a; return; } int la = to_left[indptr[i] + a] - to_left[indptr[i]]; int ra = a - la; int lb = to_left[indptr[i] + b] - to_left[indptr[i]]; int rb = b - lb; int m = (l + r) / 2; dfs(dfs, 2 * i + 0, l, m, la, lb); dfs(dfs, 2 * i + 1, m, r, ra, rb); }; dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry)); return res; } private: inline int xtoi(XY x) { if constexpr (SMALL_X) return clamp<XY>(x - minX, 0, NX); return LB(keyX, x); } S prod_i(int i, int a, int b) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; int L = n + a, R = n + b; S val = MX::unit(); while (L < R) { if (L & 1) val = MX::op(val, dat[off + (L++)]); if (R & 1) val = MX::op(dat[off + (--R)], val); L >>= 1, R >>= 1; } return val; } void multiply_i(int i, int j, S val) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; j += n; while (j) { dat[off + j] = MX::op(dat[off + j], val); j >>= 1; } } void set_i(int i, int j, S val) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; int off = 2 * LID; j += n; dat[off + j] = val; while (j > 1) { j /= 2; dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]); } } };