結果

問題 No.1221 木 *= 3
ユーザー ningenMe
提出日時 2020-09-04 22:16:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 110 ms / 2,000 ms
コード長 13,947 bytes
コンパイル時間 2,979 ms
コンパイル使用メモリ 220,148 KB
最終ジャッジ日時 2025-01-14 05:54:22
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 18
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define ALL(obj) (obj).begin(),(obj).end()
template<class T> using priority_queue_reverse = priority_queue<T,vector<T>,greater<T>>;
constexpr long long MOD = 1'000'000'000LL + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433L;
template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x
    .second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj
    .begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr !
    = obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "")
    << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
vector<string> split(const string &str, const char delemiter) {vector<string> res;stringstream ss(str);string buffer; while( getline(ss, buffer,
    delemiter) ) res.push_back(buffer); return res;}
int msb(int x) {return x?31-__builtin_clz(x):-1;}
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}
/*
* @title Tree
* @docs md/graph/Tree.md
*/
template<class Operator> class Tree {
using TypeDist = typename Operator::TypeDist;
size_t num;
size_t ord;
enum METHODS{
MAKE_DEPTH,
MAKE_CHILD,
MAKE_PARENT,
MAKE_SIZE,
MAKE_SUBTREE,
MAKE_ANCESTOR,
MAKE_EOULERTOUR,
MAKE_HEAVY_LIGHT_DECOMPOSITION,
METHODS_SIZE,
};
array<int,METHODS_SIZE> executed_flag;
public:
vector<vector<pair<size_t,TypeDist>>> edge;
vector<size_t> depth;
vector<size_t> order;
vector<size_t> reorder;
vector<TypeDist> dist;
vector<pair<size_t,TypeDist>> parent;
vector<vector<pair<size_t,TypeDist>>> child;
vector<array<pair<size_t,TypeDist>,Operator::bit>> ancestor;
vector<size_t> size;
vector<vector<size_t>> subtree;
vector<size_t> head;
vector<size_t> hldorder;
vector<size_t> eulertour;
vector<pair<size_t,size_t>> eulertour_range;
Tree(const int num):num(num),edge(num),depth(num,-1),order(num),dist(num),executed_flag(){}
//O(1) anytime
void make_edge(const int& from, const int& to, const TypeDist w = 1) {
edge[from].push_back({to,w});
}
//O(N) anytime
void make_depth(const int root) {
executed_flag[MAKE_DEPTH]++;
depth[root] = 0;
dist[root] = Operator::unit_dist;
ord = 0;
dfs(root,-1);
order[ord++] = root;
reverse_copy(order.begin(),order.end(),back_inserter(reorder));
}
//O(N) anytime for forest
void make_depth(void) {
executed_flag[MAKE_DEPTH]++;
ord = 0;
for(size_t root = 0; root < num; ++root) {
if(depth[root] != -1) continue;
depth[root] = 0;
dist[root] = Operator::unit_dist;
dfs(root,-1);
order[ord++] = root;
}
reverse_copy(order.begin(),order.end(),back_inserter(reorder));
}
//for make_depth
void dfs(int curr, int prev){
for(auto& e:edge[curr]){
int next = e.first;
if(next==prev) continue;
depth[next] = depth[curr] + 1;
dist[next] = Operator::func_dist(dist[curr],e.second);
dfs(next,curr);
order[ord++] = next;
}
}
//for make_eulertour
void dfs(int from){
eulertour.push_back(from);
for(auto& e:child[from]){
int to = e.first;
dfs(to);
eulertour.push_back(from);
}
}
//O(N) after make_depth
void make_parent(const int root = 0) {
if(executed_flag[MAKE_PARENT]++) return;
if(!executed_flag[MAKE_DEPTH]) make_depth(root);
parent.resize(num,make_pair(num,Operator::unit_dist));
for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] > depth[e.first]) parent[i] = e;
}
//O(N) after make_depth
void make_child(const int root = 0) {
if(executed_flag[MAKE_CHILD]++) return;
if(!executed_flag[MAKE_DEPTH]) make_depth(root);
child.resize(num);
for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] < depth[e.first]) child[i].push_back(e);
}
//O(NlogN) after make_parent
void make_ancestor(const int root = 0) {
if(executed_flag[MAKE_ANCESTOR]++) return;
if(!executed_flag[MAKE_PARENT]) make_parent(root);
ancestor.resize(num);
for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Operator::unit_lca));
for (size_t j = 1; j < Operator::bit; ++j) {
for (size_t i = 0; i < num; ++i) {
size_t k = ancestor[i][j - 1].first;
ancestor[i][j] = Operator::func_lca(ancestor[k][j - 1],ancestor[i][j - 1]);
}
}
}
//O(logN) after make_ancestor
//return {lca,lca_dist} l and r must be connected
pair<size_t,TypeDist> lca(size_t l, size_t r) {
assert(executed_flag[MAKE_ANCESTOR]);
if (depth[l] < depth[r]) swap(l, r);
int diff = depth[l] - depth[r];
auto ancl = make_pair(l,Operator::unit_lca);
auto ancr = make_pair(r,Operator::unit_lca);
for (int j = 0; j < Operator::bit; ++j) {
if (diff & (1 << j)) {
ancl = Operator::func_lca(ancestor[ancl.first][j],ancl);
}
}
if(ancl.first==ancr.first) return ancl;
for (int j = Operator::bit - 1; 0 <= j; --j) {
if(ancestor[ancl.first][j].first!=ancestor[ancr.first][j].first) {
ancl = Operator::func_lca(ancestor[ancl.first][j],ancl);
ancr = Operator::func_lca(ancestor[ancr.first][j],ancr);
}
}
ancl = Operator::func_lca(ancestor[ancl.first][0],ancl);
ancr = Operator::func_lca(ancestor[ancr.first][0],ancr);
return Operator::func_lca(ancl,ancr);
}
//O(N) anytime
//pair<diameter,vertex_set>
pair<TypeDist,vector<int>> diameter(void){
make_depth(0);
int root = max_element(dist.begin(), dist.end()) - dist.begin();
make_depth(root);
int leaf = max_element(dist.begin(), dist.end()) - dist.begin();
make_parent();
TypeDist d = dist[leaf];
vector<int> v;
while (leaf != root) {
v.push_back(leaf);
leaf = parent[leaf].first;
}
v.push_back(root);
return make_pair(d,v);
}
//O(N^2) after make_depth
void make_subtree(const int root = 0) {
if(executed_flag[MAKE_SUBTREE]++) return;
if(!executed_flag[MAKE_DEPTH]) make_depth(root);
subtree.resize(num);
for (size_t i = 0; i < num; ++i) subtree[i].push_back(i);
for (size_t i = 0; i < num; ++i) for (auto& e : edge[order[i]]) if (depth[order[i]] < depth[e.first]) for(auto k: subtree[e.first])
            subtree[order[i]].push_back(k);
}
//O(N) after make_child
void make_size(const int root = 0) {
if(executed_flag[MAKE_SIZE]++) return;
if(!executed_flag[MAKE_CHILD]) make_child(root);
size.resize(num,1);
for (size_t i:order) for (auto e : child[i]) size[i] += size[e.first];
}
//(N) after make_depth and make_child
template<class TypeReroot> vector<TypeReroot> rerooting(vector<TypeReroot> rerootdp,vector<TypeReroot> rerootparent) {
assert(executed_flag[MAKE_CHILD]);
for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot(rerootdp[pa],rerootdp[e.first]);
for(size_t pa:reorder) {
if(depth[pa]) rerootdp[pa] = Operator::func_reroot(rerootdp[pa],rerootparent[pa]);
size_t m = child[pa].size();
for(int j = 0; j < m && depth[pa]; ++j){
size_t ch = child[pa][j].first;
rerootparent[ch] = Operator::func_reroot(rerootparent[ch],rerootparent[pa]);
}
if(m <= 1) continue;
vector<TypeReroot> l(m),r(m);
for(int j = 0; j < m; ++j) {
size_t ch = child[pa][j].first;
l[j] = rerootdp[ch];
r[j] = rerootdp[ch];
}
for(int j = 1; j+1 < m; ++j) l[j] = Operator::func_reroot_merge(l[j],l[j-1]);
for(int j = m-2; 0 <=j; --j) r[j] = Operator::func_reroot_merge(r[j],r[j+1]);
size_t chl = child[pa].front().first;
size_t chr = child[pa].back().first;
rerootparent[chl] = Operator::func_reroot(rerootparent[chl],r[1]);
rerootparent[chr] = Operator::func_reroot(rerootparent[chr],l[m-2]);
for(int j = 1; j+1 < m; ++j) {
size_t ch = child[pa][j].first;
rerootparent[ch] = Operator::func_reroot(rerootparent[ch],l[j-1]);
rerootparent[ch] = Operator::func_reroot(rerootparent[ch],r[j+1]);
}
}
return rerootdp;
}
//O(N) after make_depth,make_parent,make_child
void make_heavy_light_decomposition(const int root = 0){
if(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]++) return;
if(!executed_flag[MAKE_SIZE]) make_size(root);
if(!executed_flag[MAKE_PARENT]) make_parent(root);
head.resize(num);
hldorder.resize(num);
iota(head.begin(),head.end(),0);
for(size_t& pa:reorder) {
pair<size_t,size_t> maxi = {0,num};
for(auto& e:child[pa]) maxi = max(maxi,{size[e.first],e.first});
if(maxi.first) head[maxi.second] = head[pa];
}
stack<size_t> st_head,st_sub;
size_t cnt = 0;
for(size_t& root:reorder){
if(depth[root]) continue;
st_head.push(root);
while(st_head.size()){
size_t h = st_head.top();
st_head.pop();
st_sub.push(h);
while (st_sub.size()){
size_t pa = st_sub.top();
st_sub.pop();
hldorder[pa] = cnt++;
for(auto& e:child[pa]) {
if(head[e.first]==head[pa]) st_sub.push(e.first);
else st_head.push(e.first);
}
}
}
}
}
//after hld type 0: vertex, 1: edge
vector<pair<size_t,size_t>> path(size_t u,size_t v,int type = 0) {
assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]);
vector<pair<size_t,size_t>> path;
while(1){
if(hldorder[u]>hldorder[v]) swap(u,v);
if(head[u]!=head[v]) {
path.push_back({hldorder[head[v]],hldorder[v]});
v=parent[head[v]].first;
}
else {
path.push_back({hldorder[u],hldorder[v]});
break;
}
}
reverse(path.begin(),path.end());
if(type) path.front().first++;
return path;
}
size_t hld_lca(size_t u,size_t v){
assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]);
while(1){
if(hldorder[u]>hldorder[v]) swap(u,v);
if(head[u]==head[v]) return u;
v=parent[head[v]].first;
}
}
//O(N) after make_child and make_parent
void make_eulertour(const int root = 0){
if(executed_flag[MAKE_EOULERTOUR]++) return;
if(!executed_flag[MAKE_CHILD]) make_child(root);
if(!executed_flag[MAKE_PARENT]) make_parent(root);
dfs(reorder.front());
eulertour_range.resize(num);
for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i;
for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i;
}
};
//depth,dist
//https://atcoder.jp/contests/abc126/tasks/abc126_d
//child
//https://atcoder.jp/contests/abc133/tasks/abc133_e
//lca
//https://atcoder.jp/contests/abc014/tasks/abc014_4
//weighted lca
//https://atcoder.jp/contests/code-thanks-festival-2017-open/tasks/code_thanks_festival_2017_h
//https://atcoder.jp/contests/cf16-tournament-round1-open/tasks/asaporo_c
//diameter
//https://atcoder.jp/contests/agc033/tasks/agc033_c
//subtree
//https://atcoder.jp/contests/code-thanks-festival-2018/tasks/code_thanks_festival_2018_f
//rerooting
//https://yukicoder.me/problems/no/922
//size
//https://yukicoder.me/problems/no/872
//eulerTour
//https://yukicoder.me/problems/no/900
//hld
//https://yukicoder.me/problems/no/399
//https://yukicoder.me/problems/no/650
template<class T> struct TreeOperator{
using TypeDist = T;
inline static constexpr size_t bit = 20;
inline static constexpr TypeDist unit_dist = 0;
inline static constexpr TypeDist unit_lca = 0;
inline static constexpr TypeDist func_dist(const TypeDist& parent,const TypeDist& w){return parent+w;}
inline static constexpr pair<size_t,TypeDist> func_lca(const pair<size_t,TypeDist>& l,const pair<size_t,TypeDist>& r){return make_pair(l.first,l
        .second+r.second);}
template<class TypeReroot> inline static constexpr TypeReroot func_reroot(const TypeReroot& l,const TypeReroot& r) {
return {l.first+r.first+r.second,l.second+r.second};
}
template<class TypeReroot> inline static constexpr TypeReroot func_reroot_merge(const TypeReroot& l,const TypeReroot& r) {
return {l.first+r.first,l.second+r.second};
}
};
int main() {
cin.tie(0);ios::sync_with_stdio(false);
int N; cin >> N;
vector<ll> A(N),B(N);
for(int i = 0; i < N; ++i) cin >> A[i];
for(int i = 0; i < N; ++i) cin >> B[i];
corner(N==1,max(A[0],0LL));
Tree<TreeOperator<int>> tree(N);
for(int i = 0; i+1 < N; ++i) {
int u,v; cin >> u >> v;
u--,v--;
tree.make_edge(u,v);
tree.make_edge(v,u);
}
tree.make_child(0);
auto dp = multivector(N,2,-HIGHINF);
for(int pa:tree.order) {
ll sum0 = A[pa]; //
for(auto e: tree.child[pa]) {
int ch = e.first;
sum0 += max(dp[ch][0],dp[ch][1]);
}
chmax(dp[pa][0],sum0);
ll sum1 = 0;
for(auto e: tree.child[pa]) {
int ch = e.first;
sum1 += max(dp[ch][0],dp[ch][1]+B[pa]+B[ch]);
}
chmax(dp[pa][1],sum1);
}
cout << max(dp[0][0],dp[0][1]) << endl;
return 0;
}
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