結果
| 問題 |
No.2491 Pochi and A Warp Machine
|
| ユーザー |
 Nachia
|
| 提出日時 | 2023-09-29 22:35:05 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,009 ms / 3,000 ms |
| コード長 | 23,030 bytes |
| コンパイル時間 | 2,387 ms |
| コンパイル使用メモリ | 151,124 KB |
| 最終ジャッジ日時 | 2025-02-17 03:25:57 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 40 |
ソースコード
#line 1 "..\\Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
#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 6 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\tree\\centroid-decomposition-binary-tree copy.hpp"
#include <cassert>
#include <queue>
namespace nachia {
struct CentroidDecompositionBinaryTree{
private:
struct VectorIntView{
using Iter = typename std::vector<int>::iterator;
Iter li, ri;
VectorIntView(std::vector<int>& src, int l, int r) :
li(src.begin() + l) ,
ri(src.begin() + r)
{}
Iter begin() const { return li; }
Iter end() const { return ri; }
int size() const { return ri - li; }
int& operator[](int i) const { return li[i]; }
};
struct CDBTNode{
int array_idx;
int cd_depth;
int sib;
int parent;
int array_left;
int size;
int exclude_cent;
int component_root = 0;
};
struct UpdatePoint { int i; int p; };
struct QueryRange { int i, l, r; };
std::vector<std::vector<int>> cd_dist;
std::vector<CDBTNode> bt_nodes;
std::vector<std::vector<int>> bt_arrays;
std::vector<std::vector<int>> bt_arrays_sep;
std::vector<std::vector<UpdatePoint>> update_points;
QueryRange get_one_node_range(const CDBTNode& node, int l, int r){
QueryRange res;
res.i = node.array_idx;
res.l = bt_arrays_sep[res.i][node.array_left + std::max(0, std::min(l - node.exclude_cent, node.size))];
res.r = bt_arrays_sep[res.i][node.array_left + std::max(0, std::min(r - node.exclude_cent, node.size))];
return res;
}
VectorIntView array_for_node(std::vector<std::vector<int>>& src, const CDBTNode& node){
return VectorIntView(src[node.array_idx], node.array_left, node.array_left + node.size);
}
VectorIntView sep_for_node(std::vector<std::vector<int>>& src, const CDBTNode& node){
return VectorIntView(src[node.array_idx], node.array_left, node.array_left + (node.size + 1));
}
static int find_centroid(
const CsrArray<int>& adj,
std::vector<int>& Z,
int root
){
while(true){
int nx = -1;
for(int c : adj[root]) if(Z[c] * 2 > Z[root]){ nx = c; break; }
if(nx < 0) break;
Z[root] -= Z[nx]; Z[nx] += Z[root];
root = nx;
}
return root;
}
public:
CentroidDecompositionBinaryTree() {}
CentroidDecompositionBinaryTree(const CsrArray<int>& adj){
int n = adj.size();
assert(1 <= n);
if(n == 1){
cd_dist = {{0}};
bt_nodes = {{0,0,-1,-1,0,1,0}};
bt_arrays = {{0}};
bt_arrays_sep = {{0,1}};
update_points = {{{0,0}}};
return;
}
std::vector<int> Z;
{
std::vector<int> bfs = {0};
std::vector<int> P(n,-1);
for(int i=0; i<n; i++){
int p = bfs[i];
for(int e : adj[p]) if(P[p] != e){
P[e] = p;
bfs.push_back(e);
}
}
Z.assign(n, 1);
for(int i=n-1; i>=1; i--) Z[P[bfs[i]]] += Z[bfs[i]];
}
std::vector<std::pair<int,int>> cd_bfs;
std::vector<int> cd_bfs_adji = { 1 };
std::vector<int> cd_dep(n, -1);
std::vector<int> cd_component_size(n);
cd_bfs.push_back(std::make_pair(-1, find_centroid(adj, Z, 0)));
cd_dep[cd_bfs.front().second] = 0;
for(int i=0; i<(int)cd_bfs.size(); i++){
int g = cd_bfs[i].second;
cd_component_size[g] = Z[g];
Z[g] = 0;
for(int nx : adj[g]) if(cd_dep[nx] == -1){
int nxg = find_centroid(adj, Z, nx);
cd_bfs.push_back(std::make_pair(nx, nxg));
cd_dep[nxg] = cd_dep[g] + 1;
}
cd_bfs_adji.push_back(cd_bfs.size());
}
int cd_height = *std::max_element(cd_dep.begin(), cd_dep.end());
cd_dist.assign(cd_height+1, std::vector<int>(n, -1));
for(int dep=0; dep<=cd_height; dep++){
std::vector<int> bfs;
for(int s=0; s<n; s++) if(cd_dep[s] == dep) bfs.push_back(s);
for(auto s : bfs) cd_dist[dep][s] = 0;
for(int i=0; i<(int)bfs.size(); i++){
int p = bfs[i];
for(int e : adj[p]) if(cd_dep[e] > dep) if(cd_dist[dep][e] == -1){
bfs.push_back(e);
cd_dist[dep][e] = cd_dist[dep][p] + 1;
}
}
}
bt_nodes.resize(n*2-1);
for(auto& v : bt_nodes) v.sib = v.array_idx = v.parent = -1;
{
std::vector<int> cdbt_root_id(n);
for(int i=0; i<n; i++) cdbt_root_id[i] = i;
int cdbt_node_count = n;
std::vector<std::pair<int,int>> bt_children(n*2-1);
for(int i=0; i<n; i++){
bt_nodes[i].cd_depth = cd_dep[i];
bt_nodes[i].array_idx = i;
bt_nodes[i].size = 1;
bt_nodes[i].component_root = i;
}
std::priority_queue<std::pair<int,int>> Que; // ( -size, root )
for(int ii=n-1; ii>=0; ii--){
auto [nx,g] = cd_bfs[ii];
Que.push(std::make_pair(-1, g));
for(int ei=cd_bfs_adji[ii]; ei<cd_bfs_adji[ii+1]; ei++){
auto [enx,eg] = cd_bfs[ei];
Que.push(std::make_pair(-bt_nodes[cdbt_root_id[eg]].size, cdbt_root_id[eg]));
}
while(Que.size() >= 2){
auto a = Que.top().second; Que.pop();
auto b = Que.top().second; Que.pop();
int idx = cdbt_node_count;
bt_nodes[a].sib = b;
bt_nodes[b].sib = a;
bt_nodes[a].parent = idx;
bt_nodes[b].parent = idx;
bt_nodes[idx].cd_depth = cd_dep[g];
bt_nodes[idx].size = bt_nodes[a].size + bt_nodes[b].size;
bt_nodes[idx].exclude_cent = bt_nodes[a].exclude_cent & bt_nodes[b].exclude_cent;
bt_nodes[a].component_root = g;
bt_nodes[b].component_root = g;
bt_children[idx] = std::make_pair(a,b);
Que.push(std::make_pair(-bt_nodes[idx].size, idx));
cdbt_node_count++;
}
auto r = Que.top().second; Que.pop();
bt_nodes[r].cd_depth--;
cdbt_root_id[g] = r;
bt_nodes[r].exclude_cent = 1;
}
bt_nodes.back().array_idx = -1;
std::vector<int> arraysz(n*2-1);
for(int idx=n*2-2; idx>=n; idx--){
auto [a,b] = bt_children[idx];
bt_nodes[a].array_idx = a;
bt_nodes[a].array_left = arraysz[a];
arraysz[a] += bt_nodes[a].size;
bt_nodes[b].array_idx = b;
bt_nodes[b].array_left = arraysz[b];
arraysz[b] += bt_nodes[b].size;
}
bt_arrays.resize(arraysz.size());
for(int i=0; i<(int)arraysz.size(); i++) bt_arrays[i].resize(arraysz[i]);
bt_arrays_sep.resize(arraysz.size());
for(int i=0; i<(int)arraysz.size(); i++) bt_arrays_sep[i].resize(arraysz[i] + 1);
for(int idx=0; idx<n; idx++){
auto& node = bt_nodes[idx];
auto array_view = array_for_node(bt_arrays, node);
auto sep_view = sep_for_node(bt_arrays_sep, node);
array_view[0] = idx;
sep_view[0] = node.array_left;
sep_view[1] = node.array_left + 1;
}
std::vector<int> sep_buf(n+1, 0);
for(int idx=n; idx<2*n-1; idx++) if(bt_nodes[idx].parent >= 0){
auto& node = bt_nodes[idx];
auto [a,b] = bt_children[idx];
int dep = node.cd_depth;
auto array_view = array_for_node(bt_arrays, node);
auto sep_view = sep_for_node(bt_arrays_sep, node);
int ex = node.exclude_cent;
for(int i=0; i<=node.size; i++) sep_buf[i] = 0;
for(int p : array_for_node(bt_arrays, bt_nodes[a])) sep_buf[cd_dist[dep][p] - ex]++;
for(int p : array_for_node(bt_arrays, bt_nodes[b])) sep_buf[cd_dist[dep][p] - ex]++;
for(int i=0; i<node.size; i++) sep_buf[i+1] += sep_buf[i];
for(int p : array_for_node(bt_arrays, bt_nodes[a])) array_view[--sep_buf[cd_dist[dep][p] - ex]] = p;
for(int p : array_for_node(bt_arrays, bt_nodes[b])) array_view[--sep_buf[cd_dist[dep][p] - ex]] = p;
for(int i=0; i<=node.size; i++) sep_view[i] = sep_buf[i] + node.array_left;
}
}
update_points.resize(n);
for(int i=0; i<(int)bt_arrays.size(); i++){
for(int j=0; j<(int)bt_arrays[i].size(); j++){
update_points[bt_arrays[i][j]].push_back({ i, j });
}
}
}
int get_root_of(int p) const { return bt_nodes[p].component_root; }
int get_array_count() const { return bt_arrays.size(); }
const std::vector<int>& get_array(int id) const { return bt_arrays[id]; }
const std::vector<UpdatePoint>& get_update_points(int vtx) const { return update_points[vtx]; }
std::vector<QueryRange> get_query_range(int from, int distl, int distr){
int p = from;
std::vector<QueryRange> res;
if(distl <= 0 && 0 < distr){
res.push_back({
bt_nodes[p].array_idx,
bt_nodes[p].array_left,
bt_nodes[p].array_left + 1
});
}
while(bt_nodes[p].parent != -1){
auto& sibnode = bt_nodes[bt_nodes[p].sib];
int d = cd_dist[sibnode.cd_depth][from];
auto tmp = get_one_node_range(sibnode, distl-d, distr-d);
if(tmp.l < tmp.r) res.push_back(tmp);
p = bt_nodes[p].parent;
}
return res;
}
};
} // namespace nachia
#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 9 "..\\Main.cpp"
#include <atcoder/segtree>
#include <atcoder/fenwicktree>
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;
i64 stadd(i64 a, i64 b){ return a+b; }
i64 ste(){ return 0; }
void testcase(){
int N; cin >> N;
auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);
auto cd = nachia::CentroidDecompositionBinaryTree(tree.getAdjacencyArray());
auto hld = nachia::HeavyLightDecomposition(tree);
using RQ = atcoder::fenwick_tree<i64>;
auto C = vector(cd.get_array_count(), pair<RQ, RQ>());
rep(i,C.size()){
C[i].first = RQ(cd.get_array(i).size() + 1);
C[i].second = RQ(cd.get_array(i).size() + 1);
}
vector<i64> dist(N);
rep(i,N-1) dist[i] = hld.dist(i,i+1);
vector<i64> distsum(N); rep(i,N-1) distsum[i+1] = distsum[i] + dist[i];
dist[N-1] = 0;
vector<i64> ans(N);
// cout << "dist : "; rep(i,N){ cout << dist[i] << " "; } cout << endl;
// cout << cd.get_array_count() << endl;
for(int x=N-1; x>=0; x--){
// cout << "f ";
// rep(k,N){
// i64 f = distsum[N-1];
// for(auto [i,p] : cd.get_update_points(k)){
// int g = cd.get_root_of(i);
// int d = hld.dist(g, k);
// f += C[i].first.sum(0, p+1);
// f += C[i].second.sum(0, p+1) * d;
// }
// cout << f << " ";
// } cout << endl;
// cout << "x = " << x << endl;
ans[x] += distsum[N-1];
for(auto [i,p] : cd.get_update_points(x)){
// cout << " i = " << i << " , p = " << p << endl;
int g = cd.get_root_of(i);
int d = hld.dist(g, x);
ans[x] += C[i].first.sum(0, p+1);
ans[x] += C[i].second.sum(0, p+1) * d;
}
if(x != N-1){
for(auto [i,l,r] : cd.get_query_range(x+1, 0, dist[x] - 1)){
int g = cd.get_root_of(i);
int d = hld.dist(g, x+1) + 1;
//cout << " i = " << i << " , g = " << g << " , d = " << d << " , l = " << l << " , r = " << r << endl;
C[i].first.add(l, d - dist[x]);
C[i].first.add(r, dist[x] - d);
C[i].second.add(l, 1);
C[i].second.add(r, -1);
}
}
}
rep(i,N) cout << ans[i] << '\n';
//cout << "##" << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
testcase();
return 0;
}