結果
| 問題 |
No.1833 Subway Planning
|
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2022-02-16 20:33:09 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 289 ms / 4,000 ms |
| コード長 | 10,540 bytes |
| コンパイル時間 | 1,224 ms |
| コンパイル使用メモリ | 91,676 KB |
| 最終ジャッジ日時 | 2025-01-27 23:22:51 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 23 |
ソースコード
#include <vector>
#include <algorithm>
#include <utility>
namespace nachia{
struct AdjacencyList{
public:
struct AdjacencyListRange{
using iterator = typename std::vector<int>::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 int& operator[](int i) const { return begi[i]; }
};
private:
int mn;
std::vector<int> E;
std::vector<int> I;
public:
AdjacencyList(int n, std::vector<std::pair<int,int>> edges, bool rev){
mn = n;
std::vector<int> buf(n+1, 0);
for(auto [u,v] : edges){ ++buf[u]; if(rev) ++buf[v]; }
for(int i=1; i<=n; i++) buf[i] += buf[i-1];
E.resize(buf[n]);
for(int i=(int)edges.size()-1; i>=0; i--){
auto [u,v] = edges[i];
E[--buf[u]] = v;
if(rev) E[--buf[v]] = u;
}
I = std::move(buf);
}
AdjacencyList(const std::vector<std::vector<int>>& edges = {}){
int n = mn = edges.size();
std::vector<int> buf(n+1, 0);
for(int i=0; i<n; i++) buf[i+1] = buf[i] + edges[i].size();
E.resize(buf[n]);
for(int i=0; i<n; i++) for(int j=0; j<(int)edges[i].size(); j++) E[buf[i]+j] = edges[i][j];
I = std::move(buf);
}
static AdjacencyList from_raw(std::vector<int> targets, std::vector<int> bounds){
AdjacencyList res;
res.mn = bounds.size() - 1;
res.E = std::move(targets);
res.I = std::move(bounds);
return res;
}
AdjacencyListRange operator[](int u) const {
return AdjacencyListRange{ E.begin() + I[u], E.begin() + I[u+1] };
}
int num_vertices() const { return mn; }
int num_edges() const { return E.size(); }
AdjacencyList reversed_edges() const {
AdjacencyList res;
int n = res.mn = mn;
std::vector<int> buf(n+1, 0);
for(int v : E) ++buf[v];
for(int i=1; i<=n; i++) buf[i] += buf[i-1];
res.E.resize(buf[n]);
for(int u=0; u<n; u++) for(int v : operator[](u)) res.E[--buf[v]] = u;
res.I = std::move(buf);
return res;
}
};
struct AdjacencyListEdgeIndexed{
public:
struct Edge { int to; int edgeidx; };
struct AdjacencyListRange{
using iterator = typename std::vector<Edge>::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 Edge& operator[](int i) const { return begi[i]; }
};
private:
int mn;
std::vector<Edge> E;
std::vector<int> I;
public:
AdjacencyListEdgeIndexed(int n, const std::vector<std::pair<int,int>>& edges, bool rev){
mn = n;
std::vector<int> buf(n+1, 0);
for(auto [u,v] : edges){ ++buf[u]; if(rev) ++buf[v]; }
for(int i=1; i<=n; i++) buf[i] += buf[i-1];
E.resize(buf[n]);
for(int i=(int)edges.size()-1; i>=0; i--){
auto [u,v] = edges[i];
E[--buf[u]] = { v, i };
if(rev) E[--buf[v]] = { u, i };
}
I = std::move(buf);
}
AdjacencyListEdgeIndexed() : AdjacencyListEdgeIndexed(0, {}, false) {}
AdjacencyListRange operator[](int u) const {
return AdjacencyListRange{ E.begin() + I[u], E.begin() + I[u+1] };
}
int num_vertices() const { return mn; }
int num_edges() const { return E.size(); }
AdjacencyListEdgeIndexed reversed_edges() const {
AdjacencyListEdgeIndexed res;
int n = res.mn = mn;
std::vector<int> buf(n+1, 0);
for(auto [v,i] : E) ++buf[v];
for(int i=1; i<=n; i++) buf[i] += buf[i-1];
res.E.resize(buf[n]);
for(int u=0; u<n; u++) for(auto [v,i] : operator[](u)) res.E[--buf[v]] = {u,i};
res.I = std::move(buf);
return res;
}
};
} // 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 AdjacencyList& E = AdjacencyList(1, {}, false)){
N = E.num_vertices();
P.assign(N, -1);
I = {0};
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[0] = 0;
D.assign(N,0);
for(int p : I) if(p != 0){
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);
std::vector<int> dfs;
dfs.push_back(0);
while(dfs.size()){
int p = dfs.back();
rangeR[p] = rangeL[p] + Z[p];
int ir = rangeR[p];
dfs.pop_back();
for(int e : E[p]) if(P[p] != e) if(e != nx[p]){
rangeL[e] = (ir -= Z[e]);
dfs.push_back(e);
}
if(nx[p] != -1){
rangeL[nx[p]] = rangeL[p] + 1;
dfs.push_back(nx[p]);
}
}
I.resize(N);
for(int i=0; i<N; i++) I[rangeL[i]] = i;
}
int depth(int p) const { return D[p]; }
int to_seq(int vertex) const { return rangeL[vertex]; }
int to_vtx(int seqidx) const { return I[seqidx]; }
int parent_of(int v) const { return P[v]; }
int heavy_child_of(int v) const {
if(to_seq(v) == N-1) return -1;
int cand = to_vtx(to_seq(v) + 1);
if(PP[v] == PP[cand]) return cand;
return v;
}
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 move(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
#include <iostream>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
int N;
int D;
vector<pair<int,int>> edges;
vector<int> edgeC;
nachia::AdjacencyList adj;
nachia::HeavyLightDecomposition hld;
vector<int> C;
vector<int> lmaxC;
vector<int> rmaxC;
vector<int> smaxC;
vector<int> dp;
int main(){
cin >> N;
edges.resize(N-1);
edgeC.resize(N-1);
D = 0;
for(int i=0; i<N-1; i++){
int u,v,c; cin >> u >> v >> c; u--; v--;
edges[i] = {u,v};
edgeC[i] = c;
D = max(D, c);
}
adj = nachia::AdjacencyList(N, edges, true);
hld = nachia::HeavyLightDecomposition(adj);
C.resize(N);
for(int i=0; i<N-1; i++){
auto [u,v] = edges[i];
if(hld.parent_of(u) == v) C[u] = edgeC[i];
else C[v] = edgeC[i];
}
lmaxC.resize(N+1);
rmaxC.resize(N+1);
smaxC.resize(N+1);
for(int i=0; i<N; i++){
smaxC[i] = C[i];
lmaxC[hld.to_seq(i) + 1] = C[i];
rmaxC[hld.to_seq(i)] = C[i];
}
for(int i=0; i<N; i++) lmaxC[i+1] = max(lmaxC[i+1], lmaxC[i]);
for(int i=N; i>0; i--) rmaxC[i-1] = max(rmaxC[i-1], rmaxC[i]);
for(int i=N-1; i>0; i--){
int p = hld.to_vtx(i);
int pp = hld.parent_of(p);
smaxC[pp] = max(smaxC[pp], smaxC[p]);
}
dp.assign(N, 0);
int ans = D;
for(int i=N-1; i>=0; i--){
int p = hld.to_vtx(i);
int exmax0 = -1;
int exmax1 = -1;
int pans = 0;
for(int nx : adj[p]) if(hld.parent_of(p) != nx){
if(exmax1 == -1 || smaxC[exmax1] < smaxC[nx]){
if(exmax1 != -1) pans = max(pans, smaxC[exmax1]);
exmax1 = nx;
}
else{
pans = max(pans, smaxC[nx]);
continue;
}
if(exmax0 == -1 || smaxC[exmax0] < smaxC[exmax1]){
swap(exmax0, exmax1);
}
}
int dpupd = pans;
if(exmax1 != -1) dpupd = max(dpupd, smaxC[exmax1]);
if(exmax0 != -1) dpupd = max(dpupd, dp[exmax0]);
dpupd = max(dpupd, D - C[p]);
dp[p] = min(smaxC[p], dpupd);
if(exmax1 != -1) pans = max(pans, dp[exmax1]);
if(exmax0 != -1) pans = max(pans, dp[exmax0]);
auto subtree = hld.subtree(p);
pans = max(pans, lmaxC[subtree.first+1]);
pans = max(pans, rmaxC[subtree.second]);
ans = min(ans, pans);
}
cout << ans << '\n';
return 0;
}