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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#835825 | #9924. Reconstruction | ucup-team5243# | WA | 364ms | 65736kb | C++17 | 14.4kb | 2024-12-28 14:51:17 | 2024-12-28 14:51:18 |
Judging History
answer
#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
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;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <utility>
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
#include <cassert>
namespace nachia{
struct Graph {
public:
struct Edge{
int from, to;
void reverse(){ std::swap(from, to); }
int xorval() const { return from ^ to; }
};
Graph() : m_n(0), m_e(0), m_isUndir(false) {}
explicit Graph(int n, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
explicit Graph(int n, const std::vector<std::pair<int, int>>& edges, int 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, int 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
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.assign(N, 0); I[0] = root;
int iI = 1;
for(int i=0; i<iI; i++){
int p = I[i];
for(int e : E[p]) if(P[p] != e){
I[iI++] = 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;
}
}
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 vtx) const { return rangeL[vtx]; }
int toVtx(int seqidx) const { return I[seqidx]; }
int toSeq2In(int vtx) const { return rangeL[vtx] * 2 - D[vtx]; }
int toSeq2Out(int vtx) const { return rangeR[vtx] * 2 - D[vtx] - 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;
/*
if(rangeL[u] > rangeL[v]) std::swap(u, v);
int h = rangeL[u];
while(h < rangeL[PP[v]]){ v = P[PP[v]]; }
return rangeL[v] <= h ? v : u;
*/
}
int dist(int u, int v) const {
return depth(u) + depth(v) - depth(lca(u,v)) * 2;
}
struct Range{
int l; int r;
int size() const { return r-l; }
bool includes(int x) const { return l <= x && x < r; }
};
std::vector<Range> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
if(PD[c] < PD[r]) return {};
std::vector<Range> res(PD[c]-PD[r]+1);
for(int i=0; i<(int)res.size()-1; i++){
res[i] = { rangeL[PP[c]], rangeL[c]+1 };
c = P[PP[c]];
}
if(PP[r] != PP[c] || D[r] > D[c]) return {};
res.back() = { rangeL[r]+(include_root?0:1), rangeL[c]+1 };
if(res.back().l == res.back().r) res.pop_back();
if(!reverse_path) std::reverse(res.begin(),res.end());
else for(auto& a : res) a = { N - a.r, N - a.l };
return res;
}
Range subtree(int p) const { return { 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];
}
struct ChildrenIterRange {
struct Iter {
const HeavyLightDecomposition& hld; int s;
int operator*() const { return hld.toVtx(s); }
Iter& operator++(){
s += hld.subtree(hld.I[s]).size();
return *this;
}
Iter operator++(int) const { auto a = *this; return ++a; }
bool operator==(Iter& r) const { return s == r.s; }
bool operator!=(Iter& r) const { return s != r.s; }
};
const HeavyLightDecomposition& hld; int v;
Iter begin() const { return { hld, hld.rangeL[v] + 1 }; }
Iter end() const { return { hld, hld.rangeR[v] }; }
};
ChildrenIterRange children(int v) const {
return ChildrenIterRange{ *this, v };
}
};
} // namespace nachia
void testcase(){
int N; cin >> N;
vector<vector<int>> T(N);
rep(i,N-1){
int u,v; cin >> u >> v; u--; v--;
T[u].push_back(v);
T[v].push_back(u);
}
auto X = nachia::Graph::Input(cin, N, true, N-1, 1);
auto adjX = X.getAdjacencyArray();
auto hld = nachia::HeavyLightDecomposition(X, 0);
vector<int> imos(N+1);
auto addSubtree = [&](int u, int v){
//cout << " subtree " << u << " -> " << v << endl;
auto [l,r] = hld.subtree(v);
if(l <= hld.toSeq(u) && hld.toSeq(u) < r){
imos[0] += 1;
imos[l] -= 1;
imos[r] += 1;
imos[N] -= 1;
} else {
imos[l+1] += 1;
imos[r] -= 1;
}
};
auto addVtx = [&](int v){
//cout << " vtx " << v << endl;
int p = hld.toSeq(v);
imos[p] += 1;
imos[p+1] -= 1;
};
//cout << "##" << endl;
auto bad = [&](){ cout << string(N, '0') << "\n"; };
rep(v,N){
//cout << "v = " << v << endl;
if(T[v].size() + 1 < adjX[v].size()){ bad(); return; }
vector<int> F(T[v].size());
rep(i,T[v].size()) F[i] = hld.la(v, T[v][i], 1);
vector<int> G = F;
sort(G.begin(), G.end());
vector<int> cnt;
for(int w : adjX[v]) cnt.push_back(
upper_bound(G.begin(), G.end(), w) - lower_bound(G.begin(), G.end(), w));
int cntcnt1 = 0;
for(auto a : cnt) if(a == 1) cntcnt1++;
if(T[v].size() + 1 == adjX[v].size()){
if(cntcnt1 != int(T[v].size())){ bad(); return; }
rep(i,adjX[v].size()) if(cnt[i] != 1){
addSubtree(v, adjX[v][i]);
addVtx(adjX[v][i]);
}
} else if(T[v].size() == adjX[v].size()){
addVtx(v);
if(cntcnt1 != int(T[v].size())){ bad(); return; }
for(int w : T[v]){ addSubtree(v, w); addVtx(w); }
} else {
if(cntcnt1 != int(adjX[v].size()-1)){ bad(); return; }
int maxdist = v;
int way = -1;
rep(i,adjX[v].size()) if(cnt[i] != 1) way = adjX[v][i];
rep(i,G.size())
rep(i,T[v].size()){
int w = T[v][i];
if(way == F[i]){
int med = hld.median(v, maxdist, w);
if(med == w) continue;
if(med != maxdist){ bad(); return; }
maxdist = w;
}
}
addSubtree(v, maxdist);
addVtx(maxdist);
}
}
rep(i,N) imos[i+1] += imos[i];
//rep(i,N){ cout << imos[hld.toSeq(i)] << " "; } cout << endl;
rep(v,N){
int p = hld.toSeq(v);
if(imos[p] == N){
cout << "1";
} else{
cout << "0";
}
} cout << "\n";
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
//int T; cin >> T;
//rep(t,T) testcase();
testcase();
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3496kb
input:
3 1 2 2 3 2 1 1 3
output:
001
result:
ok single line: '001'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3560kb
input:
6 1 3 3 4 3 6 4 5 5 2 1 3 1 4 4 5 5 2 3 6
output:
010110
result:
ok single line: '010110'
Test #3:
score: 0
Accepted
time: 0ms
memory: 3840kb
input:
1
output:
1
result:
ok single line: '1'
Test #4:
score: 0
Accepted
time: 0ms
memory: 3548kb
input:
2 1 2 1 2
output:
11
result:
ok single line: '11'
Test #5:
score: -100
Wrong Answer
time: 364ms
memory: 65736kb
input:
500000 321614 78209 64619 204431 81539 336200 128603 201377 132521 391792 41587 137224 174146 381680 341915 451206 493371 256005 259794 168656 161914 462290 105839 333679 377214 267008 283062 457340 219692 196741 123276 321510 473789 410796 498171 203543 178249 456921 255509 449152 294196 457566 277...
output:
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...
result:
wrong answer 1st lines differ - expected: '000000000000000000000000000000...0000000000000000000000000000000', found: '000000000000000000000000000000...0000000000000000000000000000000'