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#define PROBLEM \ "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree" #include "../../data_structure/segtree.hpp" #include "../../graph/base.hpp" #include "../../template/template.hpp" #include "../../tree/contour_query_on_weighted_tree.hpp" namespace ebi { i64 op(i64 a, i64 b) { return a + b; } i64 e() { return 0; } void main_() { int n, q; std::cin >> n >> q; std::vector<i64> a(n); std::cin >> a; Graph<int> g(n); g.read_tree(0); contour_query_on_weighted_tree cq(g); std::vector<i64> data(cq.size(), 0); rep(v, 0, n) { for (auto i : cq.get_vertex(v)) { data[i] += a[v]; } } segtree<i64, op, e> seg(data); while (q--) { int type; std::cin >> type; if (type == 0) { int p; i64 x; std::cin >> p >> x; a[p] += x; for (auto i : cq.get_vertex(p)) { seg.set(i, seg.get(i) + x); } } else { int p, l, r; std::cin >> p >> l >> r; i64 ans = 0; if (l == 0) ans += a[p]; for (auto [il, ir] : cq.get_contour_from_vertex(p, l, r)) { ans += seg.prod(il, ir); } std::cout << ans << '\n'; } } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }
#line 1 "test/tree/Vertex_Add_Range_Contour_Sum_on_Tree_2.test.cpp" #define PROBLEM \ "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree" #line 2 "data_structure/segtree.hpp" #include <cassert> #include <vector> namespace ebi { template <class S, S (*op)(S, S), S (*e)()> struct segtree { private: int n; int sz; std::vector<S> data; void update(int i) { data[i] = op(data[2 * i], data[2 * i + 1]); } public: segtree(int n_) : segtree(std::vector<S>(n_, e())) {} segtree(const std::vector<S> &v) : n((int)v.size()), sz(1) { while (sz < n) sz *= 2; data = std::vector<S>(2 * sz, e()); for (int i = 0; i < n; i++) { data[sz + i] = v[i]; } for (int i = sz - 1; i >= 1; i--) update(i); } void set(int p, S x) { assert(0 <= p && p < n); p += sz; data[p] = x; while (p > 1) { p >>= 1; update(p); } } S get(int p) const { assert(0 <= p && p < n); return data[p + sz]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= n); S sml = e(), smr = e(); l += sz; r += sz; while (l < r) { if (l & 1) sml = op(sml, data[l++]); if (r & 1) smr = op(data[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return data[1]; } template <class F> int max_right(int l, F f) const { assert(0 <= l && l < n); assert(f(e())); if (l == n) return n; l += sz; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, data[l]))) { while (l < sz) { l = 2 * l; if (f(op(sm, data[l]))) { sm = op(sm, data[l]); l++; } } return l - sz; } sm = op(sm, data[l]); l++; } while ((l & -l) != l); return n; } template <class F> int min_left(int r, F f) const { assert(0 <= r && r <= n); assert(f(e())); if (r == 0) return 0; r += sz; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(data[r], sm))) { while (r < sz) { r = 2 * r + 1; if (f(op(data[r], sm))) { sm = op(data[r], sm); r--; } } return r + 1 - sz; } sm = op(data[r], sm); } while ((r & -r) != r); return 0; } S operator[](int p) const { return data[sz + p]; } }; } // namespace ebi #line 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 4 "data_structure/simple_csr.hpp" #include <utility> #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 1 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include <optional> #line 7 "template/io.hpp" namespace ebi { template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) { return os << pa.first << " " << pa.second; } template <typename T1, typename T2> std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) { return os >> pa.first >> pa.second; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template <typename T> std::istream &operator>>(std::istream &os, std::vector<T> &vec) { for (T &e : vec) std::cin >> e; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 8 "template/utility.hpp" namespace ebi { template <class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <class T> T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template <class T> T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits<i64>::max() / 4; constexpr int INF = std::numeric_limits<int>::max() / 2; const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 2 "tree/contour_query_on_weighted_tree.hpp" #line 7 "tree/contour_query_on_weighted_tree.hpp" #line 2 "tree/centroid_decomposition.hpp" #line 7 "tree/centroid_decomposition.hpp" namespace ebi { namespace internal { template <class F> void centroid_decomposition_dfs_naive(const std::vector<int> &par, const std::vector<int> &original_vs, F f) { const int n = (int)par.size(); assert(par.size() == original_vs.size()); int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> vs = {center}; color[center] = 0; int c = 1; for (const int v : std::views::iota(1, n)) { if (par[v] == center) { vs.emplace_back(v); color[v] = c++; } } if (center > 0) { for (int v = par[center]; v != -1; v = par[v]) { vs.emplace_back(v); color[v] = c; } c++; } for (const int v : std::views::iota(0, n)) { if (color[v] == -1) { vs.emplace_back(v); color[v] = color[par[v]]; } } std::vector<int> index_ptr(c + 1, 0); for (const int v : std::views::iota(0, n)) { index_ptr[color[v] + 1]++; } for (const int i : std::views::iota(0, c)) { index_ptr[i + 1] += index_ptr[i]; } auto counter = index_ptr; std::vector<int> ord(n); for (auto v : vs) { ord[counter[color[v]]++] = v; } std::vector<int> relabel(n); for (const int v : std::views::iota(0, n)) { relabel[ord[v]] = v; } std::vector<int> original_vs2(n); for (const int v : std::views::iota(0, n)) { original_vs2[relabel[v]] = original_vs[v]; } std::vector<int> relabel_par(n, -1); for (int v : std::views::iota(1, n)) { int a = relabel[v]; int b = relabel[par[v]]; if (a > b) std::swap(a, b); relabel_par[b] = a; } f(relabel_par, original_vs2, index_ptr); for (const int i : std::views::iota(1, c)) { int l = index_ptr[i], r = index_ptr[i + 1]; std::vector<int> par1(r - l, -1); std::vector<int> original_vs1(r - l, -1); for (int v : std::views::iota(l, r)) { par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l); original_vs1[v - l] = original_vs2[v]; } centroid_decomposition_dfs_naive(par1, original_vs1, f); } return; } template <class F> void one_third_centroid_decomposition(const std::vector<int> &par, const std::vector<int> &original_vs, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) return; int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } f(par2, original_vs2, n0, n1); one_third_centroid_decomposition(par0, original_vs0, f); one_third_centroid_decomposition(par1, original_vs1, f); return; } template <class F> void one_third_centroid_decomposition_virtual_real( const std::vector<int> &par, const std::vector<int> &original_vs, const std::vector<int> &is_real, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) { if (is_real[0] && is_real[1]) { f(par, original_vs, {0, 1}); } return; } int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; is_real2[v] = is_real[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; is_real0[v] = is_real[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; is_real1[idx] = is_real[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } if (is_real[center]) { color.assign(n, -1); color[0] = 0; for (const int v : std::views::iota(1, n)) { if (is_real2[v]) color[v] = 1; } f(par2, original_vs2, color); is_real0[0] = is_real1[0] = is_real2[0] = 0; } color.assign(n, -1); for (const int v : std::views::iota(1, n)) { if (is_real2[v]) { color[v] = int(v > n0); } } f(par2, original_vs2, color); one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0, f); one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1, f); return; } } // namespace internal template <int MODE, class T, class F> void centroid_decomposition(const Graph<T> &tree, F f) { int n = (int)tree.size(); if (n == 1) return; std::vector<int> bfs_order(n), par(n, -1); bfs_order[0] = 0; int l = 0, r = 1; while (l < r) { int v = bfs_order[l++]; for (auto e : tree[v]) { int nv = e.to; if (nv == par[v]) continue; bfs_order[r++] = nv; par[nv] = v; } } assert(l == n && r == n); { std::vector<int> relabel(n); for (int i : std::views::iota(0, n)) { relabel[bfs_order[i]] = i; } std::vector<int> relabel_par(n, -1); for (int i : std::views::iota(1, n)) { relabel_par[relabel[i]] = relabel[par[i]]; } std::swap(par, relabel_par); } static_assert(MODE == 0 || MODE == 1 || MODE == 2); if constexpr (MODE == 0) { internal::centroid_decomposition_dfs_naive(par, bfs_order, f); } else if constexpr (MODE == 1) { internal::one_third_centroid_decomposition(par, bfs_order, f); } else { internal::one_third_centroid_decomposition_virtual_real( par, bfs_order, std::vector<int>(n, 1), f); } } } // namespace ebi #line 10 "tree/contour_query_on_weighted_tree.hpp" namespace ebi { template <class T> struct contour_query_on_weighted_tree { contour_query_on_weighted_tree(const Graph<T> &tree) : n(int(tree.size())) { int t = 0; labels.resize(n); range = {0}; std::vector<int> rev(n, -1); auto f = [&](const std::vector<int> &par, const std::vector<int> &vs, const std::vector<int> &color) -> void { int sz = (int)par.size(); std::vector<T> depth(sz, -1); depth[0] = 0; for (int i : std::views::iota(0, sz)) { rev[vs[i]] = i; } for (int i : std::views::iota(0, sz)) { int v = vs[i]; for (auto e : tree[v]) { if (rev[e.to] == -1) continue; depth[rev[e.to]] = depth[rev[v]] + e.cost; } rev[v] = -1; } std::vector<int> red, blue; for (const int v : std::views::iota(0, sz)) { if (color[v] == 0) { red.emplace_back(v); } else if (color[v] == 1) { blue.emplace_back(v); } else { assert(color[v] == -1); } } if (red.empty() || blue.empty()) return; auto update = [&](std::vector<int> &s) -> void { std::sort(s.begin(), s.end(), [&](int i, int j) -> bool { return depth[i] < depth[j]; }); for (int i = 0; const int v : s) { dist.emplace_back(depth[v]); labels[vs[v]].emplace_back(t, i, depth[v]); i++; } range.emplace_back(dist.size()); t++; }; update(red); update(blue); }; centroid_decomposition<2>(tree, f); } std::size_t size() { return dist.size(); } // [0, k) std::vector<std::pair<std::size_t, std::size_t>> get_range_less_than_k_from_v(int v, T k) const { std::vector<std::pair<std::size_t, std::size_t>> res; for (auto [t, i, d] : labels[v]) { t ^= 1; std::size_t id_l = range[t]; std::size_t id_r = std::lower_bound(dist.begin() + range[t], dist.begin() + range[t + 1], k - d) - dist.begin(); res.emplace_back(id_l, id_r); } return res; } // [k, infty) std::vector<std::pair<std::size_t, std::size_t>> get_range_k_or_more_from_v( int v, T k) const { std::vector<std::pair<std::size_t, std::size_t>> res; for (auto [t, i, d] : labels[v]) { t ^= 1; std::size_t id_l = std::lower_bound(dist.begin() + range[t], dist.begin() + range[t + 1], k - d) - dist.begin(); std::size_t id_r = range[t + 1]; res.emplace_back(id_l, id_r); } return res; } // [l, r) std::vector<std::pair<std::size_t, std::size_t>> get_contour_from_vertex( int v, T l, T r) const { std::vector<std::pair<std::size_t, std::size_t>> res; for (auto [t, i, d] : labels[v]) { t ^= 1; std::size_t id_l = std::lower_bound(dist.begin() + range[t], dist.begin() + range[t + 1], l - d) - dist.begin(); std::size_t id_r = std::lower_bound(dist.begin() + range[t], dist.begin() + range[t + 1], r - d) - dist.begin(); res.emplace_back(id_l, id_r); } return res; } std::vector<std::size_t> get_vertex(int v) const { assert(0 <= v && v < n); std::vector<std::size_t> res; for (auto [t, i, _] : labels[v]) { res.emplace_back(range[t] + i); } return res; } std::pair<int, int> sub_range(int i) const { return {range[i], range[i + 1]}; } private: int n; std::vector<T> dist; std::vector<int> range; std::vector<std::vector<std::tuple<int, int, T>>> labels; }; } // namespace ebi #line 8 "test/tree/Vertex_Add_Range_Contour_Sum_on_Tree_2.test.cpp" namespace ebi { i64 op(i64 a, i64 b) { return a + b; } i64 e() { return 0; } void main_() { int n, q; std::cin >> n >> q; std::vector<i64> a(n); std::cin >> a; Graph<int> g(n); g.read_tree(0); contour_query_on_weighted_tree cq(g); std::vector<i64> data(cq.size(), 0); rep(v, 0, n) { for (auto i : cq.get_vertex(v)) { data[i] += a[v]; } } segtree<i64, op, e> seg(data); while (q--) { int type; std::cin >> type; if (type == 0) { int p; i64 x; std::cin >> p >> x; a[p] += x; for (auto i : cq.get_vertex(p)) { seg.set(i, seg.get(i) + x); } } else { int p, l, r; std::cin >> p >> l >> r; i64 ans = 0; if (l == 0) ans += a[p]; for (auto [il, ir] : cq.get_contour_from_vertex(p, l, r)) { ans += seg.prod(il, ir); } std::cout << ans << '\n'; } } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }