This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub ebi-fly13/Library
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/2450" #include "../../data_structure/lazy_segtree.hpp" #include "../../graph/base.hpp" #include "../../template/template.hpp" #include "../../tree/heavy_light_decomposition.hpp" using ebi::i64; using ebi::LNF; struct S { i64 sum; i64 lhs; i64 rhs; i64 ans; i64 sz; }; using F = i64; const F ID = LNF; S op(S a, S b) { if (a.sz == 0) return b; if (b.sz == 0) return a; return {a.sum + b.sum, std::max(a.lhs, a.sum + b.lhs), std::max(a.rhs + b.sum, b.rhs), std::max(std::max(a.ans, b.ans), a.rhs + b.lhs), a.sz + b.sz}; } S op_rev(S a, S b) { return op(b, a); } S e() { return {0, -LNF, -LNF, -LNF, 0}; } S mapping(F f, S x) { if (f != ID) { x.sum = f * x.sz; if (f < 0) { x.lhs = f; x.rhs = f; x.ans = f; } else { x.lhs = x.rhs = x.ans = x.sum; } } return x; } F composition(F f, F g) { return (f == ID) ? g : f; } F id() { return ID; } int main() { int n, q; std::cin >> n >> q; std::vector<i64> w(n); for (int i = 0; i < n; i++) std::cin >> w[i]; ebi::Graph<int> g(n); g.read_tree(); ebi::heavy_light_decomposition hld(g); std::vector<S> vec(n); for (int i = 0; i < n; i++) { vec[hld.idx(i)] = {w[i], w[i], w[i], w[i], 1}; } ebi::lazy_segtree<S, op, e, F, mapping, composition, id> seg1(vec); ebi::lazy_segtree<S, op_rev, e, F, mapping, composition, id> seg2(vec); F c = id(); S ans = e(); auto apply = [&](int u, int v) -> void { if (u > v) std::swap(u, v); seg1.apply(u, v, c); seg2.apply(u, v, c); }; auto prod = [&](int l, int r) -> void { if (l <= r) ans = op(ans, seg1.prod(l, r)); else ans = op(ans, seg2.prod(r, l)); }; while (q--) { int t, a, b; std::cin >> t >> a >> b >> c; a--; b--; if (t == 1) { hld.path_noncommutative_query(a, b, true, apply); } else { ans = e(); hld.path_noncommutative_query(a, b, true, prod); std::cout << ans.ans << '\n'; } } }
#line 1 "test/aoj/aoj_2450.test.cpp" #define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/2450" #line 2 "data_structure/lazy_segtree.hpp" /* reference: https://atcoder.github.io/ac-library/master/document_ja/lazysegtree.html */ #include <bit> #include <cassert> #include <cstdint> #include <ranges> #include <vector> namespace ebi { template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()> struct lazy_segtree { private: void update(int i) { data[i] = op(data[2 * i], data[2 * i + 1]); } void all_apply(int k, F f) { data[k] = mapping(f, data[k]); if (k < sz) lazy[k] = composition(f, lazy[k]); } void push(int i) { all_apply(2 * i, lazy[i]); all_apply(2 * i + 1, lazy[i]); lazy[i] = id(); } public: lazy_segtree(int n_) : lazy_segtree(std::vector<S>(n_, e())) {} lazy_segtree(const std::vector<S> &a) : n(a.size()), sz(std::bit_ceil(a.size())), lg2(std::countr_zero(std::uint32_t(sz))) { data = std::vector<S>(2 * sz, e()); lazy = std::vector<F>(sz, id()); for (int i : std::views::iota(0, n)) { data[sz + i] = a[i]; } for (int i : std::views::iota(1, sz) | std::views::reverse) { update(i); } } void set(int p, S x) { assert(0 <= p && p < n); p += sz; for (int i = lg2; i >= 1; i--) push(p >> i); data[p] = x; for (int i = 1; i <= lg2; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < n); p += sz; for (int i = lg2; i >= 1; i--) push(p >> i); return data[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= n); if (l == r) return e(); l += sz; r += sz; for (int i = lg2; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } S sml = e(), smr = e(); 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]; } void apply(int p, F f) { assert(0 <= p && p < n); p += sz; for (int i = lg2; i >= 1; i--) push(p >> i); data[p] = mapping(f, data[p]); for (int i = 1; i <= lg2; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= n); l += sz; r += sz; for (int i = lg2; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int memo_l = l, memo_r = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = memo_l; r = memo_r; } for (int i = 1; i <= lg2; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template <class G> int max_right(int l, G g) { assert(0 <= l && l <= n); assert(g(e())); if (l == n) return n; l += sz; for (int i = lg2; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, data[l]))) { while (l < sz) { push(l); l = l << 1; if (g(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 G> int min_left(int r, G g) { assert(0 <= r && r <= n); assert(g(e())); if (r == 0) return 0; r += sz; for (int i = lg2; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && r % 2) r >>= 1; if (!g(op(data[r], sm))) { while (r < sz) { push(r); r = (r << 1) + 1; if (g(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; } private: int n, sz, lg2; std::vector<S> data; std::vector<F> lazy; }; } // namespace ebi #line 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #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/heavy_light_decomposition.hpp" #line 6 "tree/heavy_light_decomposition.hpp" #line 8 "tree/heavy_light_decomposition.hpp" namespace ebi { template <class T> struct heavy_light_decomposition { private: void dfs_sz(int v, Graph<T> &g) { for (auto &e : g[v]) { if (e.to == par[v]) continue; par[e.to] = v; depth_[e.to] = depth_[v] + 1; dist[e.to] = dist[v] + e.cost; dfs_sz(e.to, g); sz[v] += sz[e.to]; if (sz[e.to] > sz[g[v][0].to] || g[v][0].to == par[v]) std::swap(e, g[v][0]); } } void dfs_hld(int v, const Graph<T> &g) { in[v] = num++; rev[in[v]] = v; for (auto e : g[v]) { if (e.to == par[v]) continue; nxt[e.to] = (e.to == g[v][0].to ? nxt[v] : e.to); dfs_hld(e.to, g); } out[v] = num; } // [u, v) パスの取得 (v は u の祖先) std::vector<std::pair<int, int>> ascend(int u, int v) const { std::vector<std::pair<int, int>> res; while (nxt[u] != nxt[v]) { res.emplace_back(in[u], in[nxt[u]]); u = par[nxt[u]]; } if (u != v) res.emplace_back(in[u], in[v] + 1); return res; } // (u, v] パスの取得 (u は v の祖先) std::vector<std::pair<int, int>> descend(int u, int v) const { if (u == v) return {}; if (nxt[u] == nxt[v]) return {{in[u] + 1, in[v]}}; auto res = descend(u, par[nxt[v]]); res.emplace_back(in[nxt[v]], in[v]); return res; } public: heavy_light_decomposition(Graph<T> gh, int root = 0) : n(gh.size()), sz(n, 1), in(n), out(n), nxt(n), par(n, -1), depth_(n, 0), rev(n), dist(n, 0) { nxt[root] = root; dfs_sz(root, gh); dfs_hld(root, gh); } int idx(int u) const { return in[u]; } int rev_idx(int i) const { return rev[i]; } int la(int v, int k) const { while (1) { int u = nxt[v]; if (in[u] <= in[v] - k) return rev[in[v] - k]; k -= in[v] - in[u] + 1; v = par[u]; } } int lca(int u, int v) const { while (nxt[u] != nxt[v]) { if (in[u] < in[v]) std::swap(u, v); u = par[nxt[u]]; } return depth_[u] < depth_[v] ? u : v; } int jump(int s, int t, int i) const { if (i == 0) return s; int l = lca(s, t); int d = depth_[s] + depth_[t] - depth_[l] * 2; if (d < i) return -1; if (depth_[s] - depth_[l] >= i) return la(s, i); i = d - i; return la(t, i); } std::vector<int> path(int s, int t) const { int l = lca(s, t); std::vector<int> a, b; for (; s != l; s = par[s]) a.emplace_back(s); for (; t != l; t = par[t]) b.emplace_back(t); a.emplace_back(l); std::reverse(b.begin(), b.end()); a.insert(a.end(), b.begin(), b.end()); return a; } int root_of_heavy_path(int u) const { return nxt[u]; } int parent(int u) const { return par[u]; } T distance(int u, int v) const { return dist[u] + dist[v] - 2 * dist[lca(u, v)]; } T distance_from_root(int v) const { return dist[v]; } T depth(int v) const { return depth_[v]; } bool at_path(int u, int v, int s) const { return distance(u, v) == distance(u, s) + distance(s, v); } template <class F> void path_noncommutative_query(int u, int v, bool vertex, const F &f) const { int l = lca(u, v); for (auto [a, b] : ascend(u, l)) f(a + 1, b); if (vertex) f(in[l], in[l] + 1); for (auto [a, b] : descend(l, v)) f(a, b + 1); } std::vector<std::pair<int, int>> path_sections(int u, int v, bool vertex) const { int l = lca(u, v); std::vector<std::pair<int, int>> sections; for (auto [a, b] : ascend(u, l)) sections.emplace_back(a + 1, b); if (vertex) sections.emplace_back(in[l], in[l] + 1); for (auto [a, b] : descend(l, v)) sections.emplace_back(a, b + 1); return sections; } template <class F> int max_path(int u, int v, bool vertex, F binary_search) const { int prev = -1; int l = lca(u, v); for (auto [a, b] : ascend(u, l)) { a++; int m = binary_search(a, b); if (m == b) { prev = rev[b]; } else { return (m == a ? prev : rev[m]); } } if (vertex) { int m = binary_search(in[l], in[l] + 1); if (m == in[l]) { return prev; } else { prev = l; } } for (auto [a, b] : descend(l, v)) { b++; int m = binary_search(a, b); if (m == b) { prev = rev[b - 1]; } else { return m == a ? prev : rev[m - 1]; } } return v; } template <class F> void subtree_query(int u, bool vertex, const F &f) { f(in[u] + int(!vertex), out[u]); } const std::vector<int> &dfs_order() const { return rev; } std::vector<std::pair<int, int>> lca_based_auxiliary_tree_dfs_order( std::vector<int> vs) const; std::pair<std::vector<int>, Graph<T>> lca_based_auxiliary_tree( std::vector<int> vs) const; private: int n; std::vector<int> sz, in, out, nxt, par, depth_, rev; std::vector<T> dist; int num = 0; }; } // namespace ebi #line 7 "test/aoj/aoj_2450.test.cpp" using ebi::i64; using ebi::LNF; struct S { i64 sum; i64 lhs; i64 rhs; i64 ans; i64 sz; }; using F = i64; const F ID = LNF; S op(S a, S b) { if (a.sz == 0) return b; if (b.sz == 0) return a; return {a.sum + b.sum, std::max(a.lhs, a.sum + b.lhs), std::max(a.rhs + b.sum, b.rhs), std::max(std::max(a.ans, b.ans), a.rhs + b.lhs), a.sz + b.sz}; } S op_rev(S a, S b) { return op(b, a); } S e() { return {0, -LNF, -LNF, -LNF, 0}; } S mapping(F f, S x) { if (f != ID) { x.sum = f * x.sz; if (f < 0) { x.lhs = f; x.rhs = f; x.ans = f; } else { x.lhs = x.rhs = x.ans = x.sum; } } return x; } F composition(F f, F g) { return (f == ID) ? g : f; } F id() { return ID; } int main() { int n, q; std::cin >> n >> q; std::vector<i64> w(n); for (int i = 0; i < n; i++) std::cin >> w[i]; ebi::Graph<int> g(n); g.read_tree(); ebi::heavy_light_decomposition hld(g); std::vector<S> vec(n); for (int i = 0; i < n; i++) { vec[hld.idx(i)] = {w[i], w[i], w[i], w[i], 1}; } ebi::lazy_segtree<S, op, e, F, mapping, composition, id> seg1(vec); ebi::lazy_segtree<S, op_rev, e, F, mapping, composition, id> seg2(vec); F c = id(); S ans = e(); auto apply = [&](int u, int v) -> void { if (u > v) std::swap(u, v); seg1.apply(u, v, c); seg2.apply(u, v, c); }; auto prod = [&](int l, int r) -> void { if (l <= r) ans = op(ans, seg1.prod(l, r)); else ans = op(ans, seg2.prod(r, l)); }; while (q--) { int t, a, b; std::cin >> t >> a >> b >> c; a--; b--; if (t == 1) { hld.path_noncommutative_query(a, b, true, apply); } else { ans = e(); hld.path_noncommutative_query(a, b, true, prod); std::cout << ans.ans << '\n'; } } }