結果
問題 | No.2342 Triple Tree Query (Hard) |
ユーザー |
👑 ![]() |
提出日時 | 2023-05-30 21:07:25 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 402 ms / 10,000 ms |
コード長 | 18,906 bytes |
コンパイル時間 | 1,995 ms |
コンパイル使用メモリ | 117,268 KB |
最終ジャッジ日時 | 2025-02-13 16:52:52 |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 36 |
ソースコード
#line 1 "..\\Main.cpp"#include <iostream>#include <string>#include <vector>#include <algorithm>#include <tuple>#include <atcoder/modint>#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\csr-array.hpp"#include <utility>#line 5 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\csr-array.hpp"namespace nachia{template<class Elem>class CsrArray{public:struct ListRange{using iterator = typename std::vector<Elem>::iterator;iterator begi, endi;iterator begin() const { return begi; }iterator end() const { return endi; }int size() const { return (int)std::distance(begi, endi); }Elem& operator[](int i) const { return begi[i]; }};struct ConstListRange{using iterator = typename std::vector<Elem>::const_iterator;iterator begi, endi;iterator begin() const { return begi; }iterator end() const { return endi; }int size() const { return (int)std::distance(begi, endi); }const Elem& operator[](int i) const { return begi[i]; }};private:int m_n;std::vector<Elem> m_list;std::vector<int> m_pos;public:CsrArray() : m_n(0), m_list(), m_pos() {}static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){CsrArray res;res.m_n = n;std::vector<int> buf(n+1, 0);for(auto& [u,v] : items){ ++buf[u]; }for(int i=1; i<=n; i++) buf[i] += buf[i-1];res.m_list.resize(buf[n]);for(int i=(int)items.size()-1; i>=0; i--){res.m_list[--buf[items[i].first]] = std::move(items[i].second);}res.m_pos = std::move(buf);return res;}static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){CsrArray res;res.m_n = pos.size() - 1;res.m_list = std::move(list);res.m_pos = std::move(pos);return res;}ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }int size() const { return m_n; }int fullSize() const { return (int)m_list.size(); }};} // namespace nachia#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\graph\\graph.hpp"#include <cassert>#line 6 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\graph\\graph.hpp"namespace nachia{struct Graph {public:struct Edge{int from, to;void reverse(){ std::swap(from, to); }};using Base = std::vector<std::pair<int, int>>;Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){m_e.resize(edges.size());for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };}template<class Cin>static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){Graph res(n, undirected, m);for(int i=0; i<m; i++){int u, v; cin >> u >> v;res[i].from = u - offset;res[i].to = v - offset;}return res;}int numVertices() const noexcept { return m_n; }int numEdges() const noexcept { return int(m_e.size()); }int addNode() noexcept { return m_n++; }int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }Edge& operator[](int ei) noexcept { return m_e[ei]; }const Edge& operator[](int ei) const noexcept { return m_e[ei]; }Edge& at(int ei) { return m_e.at(ei); }const Edge& at(int ei) const { return m_e.at(ei); }auto begin(){ return m_e.begin(); }auto end(){ return m_e.end(); }auto begin() const { return m_e.begin(); }auto end() const { return m_e.end(); }bool isUndirected() const noexcept { return m_isUndir; }void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }void contract(int newV, const std::vector<int>& mapping){assert(numVertices() == int(mapping.size()));for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }m_n = newV;}std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {int n = numVertices();assert(n == int(mapping.size()));for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);std::vector<int> indexV(n), newV(num);for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;std::vector<Graph> res; res.reserve(num);for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);return res;}CsrArray<int> getEdgeIndexArray(bool undirected) const {std::vector<std::pair<int, int>> src;src.reserve(numEdges() * (undirected ? 2 : 1));for(int i=0; i<numEdges(); i++){auto e = operator[](i);src.emplace_back(e.from, i);if(undirected) src.emplace_back(e.to, i);}return CsrArray<int>::Construct(numVertices(), src);}CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }CsrArray<int> getAdjacencyArray(bool undirected) const {std::vector<std::pair<int, int>> src;src.reserve(numEdges() * (undirected ? 2 : 1));for(auto e : m_e){src.emplace_back(e.from, e.to);if(undirected) src.emplace_back(e.to, e.from);}return CsrArray<int>::Construct(numVertices(), src);}CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }private:int m_n;std::vector<Edge> m_e;bool m_isUndir;};} // namespace nachia#line 6 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\tree\\heavy-light-decomposition.hpp"namespace nachia{struct HeavyLightDecomposition{private:int N;std::vector<int> P;std::vector<int> PP;std::vector<int> PD;std::vector<int> D;std::vector<int> I;std::vector<int> rangeL;std::vector<int> rangeR;public:HeavyLightDecomposition(const CsrArray<int>& E = CsrArray<int>::Construct(1, {}), int root = 0){N = E.size();P.assign(N, -1);I = {root};I.reserve(N);for(int i=0; i<(int)I.size(); i++){int p = I[i];for(int e : E[p]) if(P[p] != e){I.push_back(e);P[e] = p;}}std::vector<int> Z(N, 1);std::vector<int> nx(N, -1);PP.resize(N);for(int i=0; i<N; i++) PP[i] = i;for(int i=N-1; i>=1; i--){int p = I[i];Z[P[p]] += Z[p];if(nx[P[p]] == -1) nx[P[p]] = p;if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;}for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;PD.assign(N,N);PD[root] = 0;D.assign(N,0);for(int p : I) if(p != root){PP[p] = PP[PP[p]];PD[p] = std::min(PD[PP[p]], PD[P[p]]+1);D[p] = D[P[p]]+1;}rangeL.assign(N,0);rangeR.assign(N,0);for(int p : I){rangeR[p] = rangeL[p] + Z[p];int ir = rangeR[p];for(int e : E[p]) if(P[p] != e) if(e != nx[p]){rangeL[e] = (ir -= Z[e]);}if(nx[p] != -1){rangeL[nx[p]] = rangeL[p] + 1;}}I.resize(N);for(int i=0; i<N; i++) I[rangeL[i]] = i;}HeavyLightDecomposition(const Graph& tree, int root = 0): HeavyLightDecomposition(tree.getAdjacencyArray(true), root) {}int numVertices() const { return N; }int depth(int p) const { return D[p]; }int toSeq(int vertex) const { return rangeL[vertex]; }int toVtx(int seqidx) const { return I[seqidx]; }int toSeq2In(int vertex) const { return rangeL[vertex] * 2 - D[vertex]; }int toSeq2Out(int vertex) const { return rangeR[vertex] * 2 - D[vertex] - 1; }int parentOf(int v) const { return P[v]; }int heavyRootOf(int v) const { return PP[v]; }int heavyChildOf(int v) const {if(toSeq(v) == N-1) return -1;int cand = toVtx(toSeq(v) + 1);if(PP[v] == PP[cand]) return cand;return -1;}int lca(int u, int v) const {if(PD[u] < PD[v]) std::swap(u, v);while(PD[u] > PD[v]) u = P[PP[u]];while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }return (D[u] > D[v]) ? v : u;}int dist(int u, int v) const {return depth(u) + depth(v) - depth(lca(u,v)) * 2;}std::vector<std::pair<int,int>> path(int r, int c, bool include_root = true, bool reverse_path = false) const {if(PD[c] < PD[r]) return {};std::vector<std::pair<int,int>> res(PD[c]-PD[r]+1);for(int i=0; i<(int)res.size()-1; i++){res[i] = std::make_pair(rangeL[PP[c]], rangeL[c]+1);c = P[PP[c]];}if(PP[r] != PP[c] || D[r] > D[c]) return {};res.back() = std::make_pair(rangeL[r]+(include_root?0:1), rangeL[c]+1);if(res.back().first == res.back().second) res.pop_back();if(!reverse_path) std::reverse(res.begin(),res.end());else for(auto& a : res) a = std::make_pair(N - a.second, N - a.first);return res;}std::pair<int,int> subtree(int p){return std::make_pair(rangeL[p], rangeR[p]);}int median(int x, int y, int z) const {return lca(x,y) ^ lca(y,z) ^ lca(x,z);}int la(int from, int to, int d) const {if(d < 0) return -1;int g = lca(from,to);int dist0 = D[from] - D[g] * 2 + D[to];if(dist0 < d) return -1;int p = from;if(D[from] - D[g] < d){ p = to; d = dist0 - d; }while(D[p] - D[PP[p]] < d){d -= D[p] - D[PP[p]] + 1;p = P[PP[p]];}return I[rangeL[p] - d];}};} // namespace nachia#line 1 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\dual-segment-tree.hpp"#line 3 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\dual-segment-tree.hpp"namespace nachia{template<class F,F composition(F f, F x)>struct DualSegtree {struct Node { F f; bool propagated; };int N;int logN;std::vector<Node> A;void mapf(Node& a, F f) {a.propagated = false;a.f = composition(f, a.f);}void spread(int i) {if(A[i].propagated || !(i < N)) return;mapf(A[i*2], A[i].f);mapf(A[i*2+1], A[i].f);A[i] = A[0];}DualSegtree(int n, F id) {N=1; logN=0;while(N<n){ N *= 2; logN++; }A.assign(N*2, { id, true });}DualSegtree(const std::vector<F>& a) : DualSegtree(a.size()) {for(int i=0; i<a.size(); i++){ A[i+N].f = a[i]; A[i+N].propagated = false; }}void clear(int p) {p += N;for(int d=logN; d; d--) spread(p >> d);A[p] = A[0];}F get(int p){p += N;for(int d=logN; d; d--) spread(p >> d);return A[p].f;}void apply(int l, int r, F f){if(!(l < r)) return;if(l == 0 && r == N){ mapf(A[1], f); return; }l += N; r += N;for(int d=logN; d; d--){if((l >> d) << d != l) spread(l >> d);if((r >> d) << d != r) spread(r >> d);}while(l < r){if(l&1){ mapf(A[l++], f); } l /= 2;if(r&1){ mapf(A[--r], f); } r /= 2;}}void apply(int p, F f){p += N;for(int d=logN; d; d--) spread(p >> d);mapf(A[p], f);}};} // namespace nachia;#line 10 "..\\Main.cpp"using namespace std;using i32 = int;using u32 = unsigned int;using i64 = long long;using u64 = unsigned long long;#define rep(i,n) for(int i=0; i<(int)(n); i++)const i64 INF = 1001001001001001001;using Modint = atcoder::static_modint<998244353>;struct Affine {Modint c, d;static Affine Construct(int c, int d){ return Affine{ Modint::raw(c), Modint::raw(d) }; }Modint eval(Modint x) const { return c*x+d; }};Affine f1(Affine a, Affine b){Affine res;res.c = a.c * b.c;res.d = a.c * b.d + a.d;return res;}int naive(){int N, Q; cin >> N >> Q;auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);auto hld = nachia::HeavyLightDecomposition(tree);vector<Modint> X(N); rep(i,N){ int x; cin >> x; X[i] = x; }rep(i,Q){int t; cin >> t;if(t == 1){int v; cin >> v; v--;cout << X[v].val() << endl;}if(t == 2){int v,k,c,d; cin >> v >> k >> c >> d; v--;auto f = Affine::Construct(c,d);rep(j,N) if(hld.dist(v,j) <= k) X[j] = f.eval(X[j]);}if(t == 3){int v,c,d; cin >> v >> c >> d; v--;auto f = Affine::Construct(c,d);auto [l,r] = hld.subtree(v);for(int j=l; j<r; j++){int w = hld.toVtx(j);X[w] = f.eval(X[w]);}}if(t == 4){int v,w,c,d; cin >> v >> w >> c >> d; v--; w--;auto f = Affine::Construct(c,d);int di = hld.dist(v, w);rep(x,N) if(hld.dist(v,x) + hld.dist(w,x) == di) X[x] = f.eval(X[x]);}}return 0;}int main(){//return naive();int maxK = 10;int N, Q; cin >> N >> Q;auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);auto hld = nachia::HeavyLightDecomposition(tree);tree = nachia::Graph(N, false);rep(i,N) if(hld.parentOf(i) >= 0) tree.addEdge(hld.parentOf(i), i);auto adj = tree.getAdjacencyArray();vector<int> h11(N); rep(i,N) h11[i] = (hld.depth(i) <= maxK) ? -1 : hld.toSeq(hld.la(i, 0, maxK+1));vector<int> ord(N); rep(i,N) ord[i] = i;sort(ord.begin(), ord.end(), [&](int a, int b){return make_tuple(h11[a], hld.depth(a), hld.toSeq(a)) < make_tuple(h11[b], hld.depth(b), hld.toSeq(b));});vector<int> pos(N); rep(i,N) pos[ord[i]] = i;vector<int> hdepth(N);rep(i,N) hdepth[i] = hld.depth(i) - hld.depth(hld.heavyRootOf(i));auto isOnHeavy = [&](int v){ return hdepth[v] > maxK; };/*cout << "##" << endl;rep(i,N) cout << isOnHeavy(i);cout << endl;*/vector<vector<pair<int, int>>> seq(N, vector<pair<int,int>>(maxK+1, {N,0}));rep(v,N){int w = v;int p = pos[v];for(int k=0; k<=maxK; k++){seq[w][k].first = min(seq[w][k].first, p);seq[w][k].second = max(seq[w][k].second, p+1);w = hld.parentOf(w);if(w < 0) break;}}rep(i,N) for(auto& a : seq[i]) if(a.first >= a.second) a = {0,0};/*cout << "###" << endl;cout << "h10 = ";rep(i,N) cout << h10[i] << " ";cout << endl;cout << "seq : " << endl;rep(k,maxK+1){cout << " k = " << (k/10) << (k%10) << " : ";rep(i,N) cout << seq[i][k].first << "-" << seq[i][k].second << " ";cout << endl;} cout << endl;*/vector<int> h11pos(N+1, 0);rep(i,N) h11pos[h11[ord[i]]+1] = i+1;rep(i,N) h11pos[i+1] = max(h11pos[i+1], h11pos[i]);vector<pair<int, int>> subtree(N, {0,0});rep(i,N) subtree[i] = { h11pos[hld.subtree(i).first], h11pos[hld.subtree(i).second] };vector<Modint> X(N);rep(i,N){ int x; cin >> x; X[i] = Modint::raw(x); }nachia::DualSegtree<Affine, f1> rq(N, Affine::Construct(1,0));nachia::DualSegtree<Affine, f1> rqh(N, Affine::Construct(1,0));auto applyVtx = [&](int v, Affine f){if(isOnHeavy(v)){rqh.apply(hld.toSeq(v), f);}else{rq.apply(pos[v], f);}};auto heavyDec = [&](int v, int k) -> int {int s = hld.toSeq(v);s += k;if(s >= N) return -1;int w = hld.toVtx(s);//if(hld.heavyRootOf(w) != hld.heavyRootOf(v) || !isOnHeavy(w)) return -1;if(!isOnHeavy(w)) return -1;return w;};auto applyDec = [&](int v, int k, Affine f, bool doHeavy = true){if(k == 0){if(isOnHeavy(v)){if(doHeavy) rqh.apply(hld.toSeq(v), f);}else{rq.apply(pos[v], f);}return;}if(doHeavy){int hd = heavyDec(v, k);if(hd >= 0) applyVtx(hd, f);}auto [l,r] = seq[v][k];if(l <= r) rq.apply(l, r, f);};auto applyPath = [&](int r, int c, Affine f){for(auto [a, b] : hld.path(r, c)){while(a < b && !isOnHeavy(hld.toVtx(a))){int av = hld.toVtx(a);applyVtx(av, f);a++;}rqh.apply(a, b, f);}};rep(i,Q){int t; cin >> t;if(t == 1){int v; cin >> v; v--;Affine f = (isOnHeavy(v) ? rqh.get(hld.toSeq(v)) : rq.get(pos[v]));cout << f.eval(X[v]).val() << '\n';}if(t == 2){int v, k, c, d; cin >> v >> k >> c >> d; v--;Affine af = Affine::Construct(c, d);while(k >= 0){applyDec(v, k, af);k--; if(k < 0) break;applyDec(v, k, af);if(hld.parentOf(v) < 0){while(k > 0){k--;applyDec(v, k, af);}break;}v = hld.parentOf(v);}}if(t == 3){int v, c, d; cin >> v >> c >> d; v--;Affine af = Affine::Construct(c, d);auto st = hld.subtree(v);rqh.apply(st.first, st.second, af);for(int k=0; k<=maxK; k++) applyDec(v, k, af, false);rq.apply(subtree[v].first, subtree[v].second, af);}if(t == 4){int u, v, c, d; cin >> u >> v >> c >> d; u--; v--;Affine af = Affine::Construct(c, d);int h = hld.lca(u, v);applyPath(h, u, af);if(h != v) applyPath(hld.la(h, v, 1), v, af);}}return 0;}struct ios_do_not_sync{ios_do_not_sync(){ios::sync_with_stdio(false);cin.tie(nullptr);}} ios_do_not_sync_instance;