結果
| 問題 |
No.19 ステージの選択
|
| ユーザー |
 kjnh10
|
| 提出日時 | 2020-05-28 12:48:32 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 4 ms / 5,000 ms |
| コード長 | 20,375 bytes |
| コンパイル時間 | 4,226 ms |
| コンパイル使用メモリ | 228,332 KB |
| 最終ジャッジ日時 | 2025-01-10 16:03:41 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 24 |
ソースコード
#line 2 "header.hpp"
//%snippet.set('header')%
//%snippet.fold()%
#ifndef HEADER_H
#define HEADER_H
// template version 2.0
using namespace std;
#include <bits/stdc++.h>
// varibable settings
const long long INF = 1e18;
template <class T> constexpr T inf = numeric_limits<T>::max() / 2.1;
#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _rrep(i, n) rrepi(i, 0, n)
#define rrepi(i, a, b) for (ll i = (ll)((b)-1); i >= (ll)(a); --i)
#define r_rep(...) _overload3(__VA_ARGS__, rrepi, _rrep, )(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
#define ub upper_bound
#define lb lower_bound
#define lpos(A, x) (lower_bound(all(A), x) - A.begin())
#define upos(A, x) (upper_bound(all(A), x) - A.begin())
template <class T> inline void chmax(T &a, const T &b) { if ((a) < (b)) (a) = (b); }
template <class T> inline void chmin(T &a, const T &b) { if ((a) > (b)) (a) = (b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector<decltype(cont)>(x, cont); }
#define divceil(a, b) ((a) + (b)-1) / (b)
#define is_in(x, a, b) ((a) <= (x) && (x) < (b))
#define uni(x) sort(all(x)); x.erase(unique(all(x)), x.end())
#define slice(l, r) substr(l, r - l)
typedef long long ll;
typedef long double ld;
using vl = vector<ll>;
using vvl = vector<vl>;
using pll = pair<ll, ll>;
template <typename T>
using PQ = priority_queue<T, vector<T>, greater<T>>;
void check_input() { assert(cin.eof() == 0); int tmp; cin >> tmp; assert(cin.eof() == 1); }
#if defined(PCM) || defined(LOCAL)
#else
#define dump(...) ;
#define dump_1d(...) ;
#define dump_2d(...) ;
#define cerrendl ;
#endif
#endif /* HEADER_H */
//%snippet.end()%
#line 2 "solve.cpp"
template<class T=ll> using vec = vector<T>;
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;
// snippet:segment_tree {{{
template <typename T> struct SegmentTree { // {{{
private:
using F = function<T(T, T)>;
int n; // 元の配列のサイズ
int N; // n以上の最小の2冪
vector<T> node;
F merge;
T identity;
public:
SegmentTree() {}
SegmentTree(vector<T> a, F f, T id) : merge(f), identity(id) {
n = a.size();
N = 1;
while (N < n) N *= 2;
node.resize(2 * N - 1, identity);
for (int i = 0; i < n; i++) node[i + N - 1] = a[i];
for (int i = N - 2; i >= 0; i--)
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
SegmentTree(int n, F f, T id) : SegmentTree(vector<T>(n, id), f, id) {}
T& operator[](int i) { return node[i + N - 1]; }
void update(int i, T val) {
i += (N - 1);
node[i] = val;
while (i > 0) {
i = (i - 1) / 2;
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
}
void add(int i, T val) {
i += (N - 1);
node[i] += val;
while (i > 0) {
i = (i - 1) / 2;
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
}
// query for [l, r)
T query(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (r <= a || b <= l) return identity;
if (a <= l && r <= b) return node[k];
T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
return merge(vl, vr);
}
#if defined(PCM) || defined(LOCAL)
friend ostream& operator<<(ostream& os, SegmentTree<T>& sg) { //
os << "[";
for (int i = 0; i < sg.n; i++) {
os << sg[i] << (i == sg.n - 1 ? "]\n" : ", ");
}
return os;
}
#endif
};/*}}}*/
// sample of initialize SegmentTree:
// -----------------------------------------------
// auto mymin=[](auto a, auto b){return min(a,b);};
// SegmentTree<ll> seg(a, mymin, 1e18);
// auto mymax=[](auto a, auto b){return max(a,b);};
// SegmentTree<ll> seg(a, mymax, -1e18);
// auto add=[](auto a, auto b){return a+b;};
// SegmentTree<ll> seg(a, add, 0);
// -----------------------------------------------
// snippet:segment_tree }}}
// snippet:edge {{{
template<class Cost=ll>
struct Edge {
int from, to;
Cost cost;
int idx;
Edge(){};
Edge(int from, int to, Cost cost, int idx)
: from(from), to(to), cost(cost), idx(idx) {}
friend ostream& operator<<(ostream& os, const Edge& e) {
// os << "(f:" << e.from << ", t:" << e.to << ", c:" << e.cost << ", i" << e.idx << ")"; // detailed
os << "(" << e.from << "," << e.to << ")";
return os;
}
};
// snippet:edge }}}
// snippet:UnionFind {{{
struct UnionFind {
vector<int> par; // par[x]: parent of x. if root, -size.
int gcount; // count of groups
UnionFind() {}
UnionFind(int _n) : par(_n, -1), gcount(_n) {}
bool merge(int x, int y) {
x = root(x);
y = root(y);
if (x != y) {
if (par[y] < par[x]) swap(x, y);
par[x] += par[y];
par[y] = x;
gcount--;
}
return x != y;
}
int root(int x) {
if (is_root(x)){
return x;
}
else{
return par[x] = root(par[x]); // 経路圧縮
// return root(par[x]); // 経路圧縮なし
}
}
bool is_root(int x) { return par[x] < 0; }
bool same(int x, int y) { return root(x) == root(y); }
int size(int x) { return -par[root(x)]; }
#if defined(PCM) || defined(LOCAL) // {{{
friend ostream& operator<<(ostream& os, UnionFind& uf) {
map<int, vector<int>> group;
rep(i, sz(uf.par)) { group[uf.root(i)].pb(i); }
os << endl;
each(g, group) { os << g << endl; }
return os;
}
#endif // }}}
};
// snippet:UnionFind }}}
// snippet:tree {{{
template<class Cost=ll>
struct tree {
int n;
vector<int> par; // par[i]: dfs木における親
vector<Cost> cost; // par[i]: dfs木における親への辺のコスト
vector<int> dfstrv; // dfstrv[i]: dfs木でi番目に訪れるノード。dpはこれを逆順に回す
vector<int> ord; // ord[u]: uのdfs木における訪問順
vector<int> end; // end[u]: uのdfs終了時のカウンター
vector<int> psize; // psize[u]: uのpartial tree size
// uの部分木は[ord[u], end[u])
// ordとdfstrvは逆変換
vector<int> depth; // depth[i]: dfs木でのiの深さ
vector<Cost> ldepth; // ldepth[i]: dfs木でのrootからの距離
vector<vector<Edge<Cost>>> adj_list; // 辺(隣接リスト)
auto operator[](int pos) const { return adj_list[pos]; }
vector<vector<int>> children;
vector<int> euler_tour;
vector<int> et_fpos; // euler_tour first occurence position
SegmentTree<int> _seg; // seg(map(ord, euler_tour), mymin, 1e18)
vector<int> head_of_comp;
int _counter = 0;
tree(){};/*{{{*/
tree(int n)
: n(n),
par(n),
cost(n),
ord(n),
end(n),
psize(n),
depth(n),
ldepth(n),
adj_list(n),
children(n),
et_fpos(n),
head_of_comp(n){};/*}}}*/
void add_edge(int u, int v, Cost cost, int idx=-1) { /*{{{*/
adj_list[u].emplace_back(u, v, cost, idx);
adj_list[v].emplace_back(v, u, cost, idx);
} /*}}}*/
void add_edge(int u, int v) { /*{{{*/
adj_list[u].emplace_back(u, v, 1, -1);
adj_list[v].emplace_back(v, u, 1, -1);
} /*}}}*/
void build(int root) { /*{{{*/
_counter = 0;
// par[root] = -1;
// cost[root] = -1;
_dfs_psize(root, -1);
_dfs_tree(root, -1, root);
_dfs_et(root);
vector<int> ini(2 * n - 1);
rep(i, 2 * n - 1) ini[i] = ord[euler_tour[i]];
_seg = SegmentTree<int>(
ini, [](auto a, auto b) { return min(a, b); }, numeric_limits<int>().max());
} /*}}}*/
int _dfs_psize(int u, int pre) { /*{{{*/
psize[u] = 1;
each(edge, adj_list[u]) {
if (edge.to == pre) continue;
psize[u] += _dfs_psize(edge.to, u);
}
return psize[u];
} /*}}}*/
void _dfs_tree(int u, int pre, int head_node) { /*{{{*/
dfstrv.pb(u);
ord[u] = _counter;
if (pre != -1) {
depth[u] = depth[pre] + 1;
ldepth[u] = ldepth[pre] + cost[u];
}
_counter++;
{
// set most heavy child to top
int max_psize = 0;
int most_heavy_i = -1;
rep(i, sz(adj_list[u])) {
if (adj_list[u][i].to == pre) continue;
if (psize[adj_list[u][i].to] > max_psize) {
most_heavy_i = i;
max_psize = psize[adj_list[u][i].to];
}
}
if (most_heavy_i != -1) swap(adj_list[u][most_heavy_i], adj_list[u][0]);
}
head_of_comp[u] = head_node;
rep(i, sz(adj_list[u])) {
int v = adj_list[u][i].to;
if (v == pre) continue;
children[u].pb(v);
par[v] = u;
cost[v] = adj_list[u][i].cost;
if (i == 0)
_dfs_tree(v, u, head_node); // continue components
else
_dfs_tree(v, u, v); // new
}
end[u] = _counter;
} /*}}}*/
void _dfs_et(int u) { /*{{{*/
et_fpos[u] = euler_tour.size();
euler_tour.pb(u);
each(v, children[u]) {
_dfs_et(v);
euler_tour.pb(u);
}
} /*}}}*/
int lca(int u, int v) { /*{{{*/
if (u == v) return u;
if (et_fpos[u] > et_fpos[v]) swap(u, v);
return dfstrv[_seg.query(et_fpos[u], et_fpos[v])];
} /*}}}*/
int dist(int u, int v) { /*{{{*/
int p = lca(u, v);
return depth[u] + depth[v] - 2 * depth[p];
} /*}}}*/
Cost ldist(int u, int v) { // length dist{{{
int p = lca(u, v);
return ldepth[u] + ldepth[v] - 2 * ldepth[p];
} /*}}}*/
pair<int, int> diameter() { /*{{{*/
int u, v;
Cost max_len = *max_element(all(ldepth));
rep(i, n) {
if (ldepth[i] == max_len) {
u = i;
break;
}
}
Cost md = -1;
rep(i, n) {
Cost d = ldist(u, i);
if (d > md) {
v = i;
md = d;
}
}
return mp(u, v);
} /*}}}*/
vector<pair<int, int>> hld_path(int u, int v, bool for_edge=true) { //{{{
// 閉区間をvectorで返す。for_edge=trueでlcaは除いて返すことに注意。
vector<pair<int, int>> res;
while (head_of_comp[u] != head_of_comp[v]) {
if (depth[head_of_comp[u]] < depth[head_of_comp[v]]) {
res.push_back({ord[head_of_comp[v]], ord[v]});
v = par[head_of_comp[v]];
} else {
res.push_back({ord[head_of_comp[u]], ord[u]});
u = par[head_of_comp[u]];
}
}
res.push_back({min(ord[u], ord[v]) + (for_edge?1:0), max(ord[u], ord[v])});
return res;
} //}}}
#if defined(PCM) || defined(LOCAL) /*{{{*/
friend ostream& operator<<(ostream& os, const tree& tr) {
os << endl;
os << "par: " << tr.par << endl;
os << "cost: " << tr.cost << endl;
os << "dfstrv: " << tr.dfstrv << endl;
os << "ord: " << tr.ord << endl;
os << "end: " << tr.end << endl;
os << "depth: " << tr.depth << endl;
os << "children: " << tr.children << endl;
os << "euler_tour: " << tr.euler_tour << endl;
os << "et_fpos: " << tr.et_fpos << endl;
os << "head_of_comp:" << tr.head_of_comp << endl;
return os;
}
#endif /*}}}*/
};
// snippet:tree }}}
// snippet:Graph {{{
template<class Cost=ll>
struct Graph {
using Pos = int; // int以外には対応しない。
int n; // 頂点数
vector<vector<Edge<Cost>>> adj_list;
auto operator[](Pos pos) const { return adj_list[pos]; }
vector<Edge<Cost>> edges;
tree<Cost> tr;
Pos root;
vector<int> _used_in_dfs;
vector<int> lowlink;
Cost zerocost;
Cost infcost;
Graph() {}
Graph(int _n) : n(_n), adj_list(_n), tr(n), _used_in_dfs(n), zerocost(0LL), infcost(INF) { }
Graph(int _n, Cost zc, Cost ic) : n(_n), adj_list(_n), tr(n), _used_in_dfs(n), zerocost(zc), infcost(ic) { }
void add_edge(Pos from, Pos to, Cost cost, int idx=-1) {/*{{{*/
adj_list[from].emplace_back(from, to, cost, idx);
edges.emplace_back(from, to, cost, idx);
}
void add_edge(Pos from, Pos to) { // for ll
adj_list[from].emplace_back(from, to, 1, -1);
edges.emplace_back(from, to, 1, -1);
}/*}}}*/
void build_tree(Pos _root) {/*{{{*/
root = _root;
_dfs_tree(root);
tr.build(root);
_make_lowlink();
}/*}}}*/
vector<int> make_bipartite() {/*{{{*/
UnionFind buf(2 * n);
rep(u, n) {
each(e, adj_list[u]) {
buf.merge(u, e.to + n);
buf.merge(e.to, u + n);
}
}
vector<int> res(n, -1);
rep(u, n) {
if (buf.same(u, u + n)) return res;
}
rep(u, n) {
if (buf.same(0, u)) res[u] = 0;
else res[u] = 1;
}
return res;
}/*}}}*/
void _dfs_tree(Pos u) {/*{{{*/
_used_in_dfs[u] = 1;
each(e, adj_list[u]) {
if (_used_in_dfs[e.to]) continue;
tr.add_edge(u, e.to, e.cost);
_dfs_tree(e.to);
}
}/*}}}*/
void _make_lowlink() {/*{{{*/
lowlink = vector<Pos>(n, numeric_limits<Pos>().max());
r_rep(i, n) {
Pos u = tr.dfstrv[i];
chmin(lowlink[u], tr.ord[u]);
each(e, adj_list[u]) {
if (e.to == tr.par[u])
continue;
else if (tr.ord[e.to] < tr.ord[u]) {
chmin(lowlink[u], tr.ord[e.to]);
} else {
chmin(lowlink[u], lowlink[e.to]);
}
}
}
}/*}}}*/
vector<Pos> get_articulation_points() {/*{{{*/
if (sz(lowlink) == 0) throw("make_lowlik() beforehand");
vector<Pos> res;
if (sz(tr.children[root]) > 1) {
res.push_back(root);
}
rep(u, 0, n) {
if (u == root) continue;
bool is_kan = false;
each(v, tr.children[u]) {
if (tr.ord[u] <= lowlink[v]) {
is_kan = true;
}
}
if (is_kan) res.push_back(u);
}
return res;
}/*}}}*/
vector<Edge<Cost>> get_bridges() {/*{{{*/
if (sz(lowlink) == 0) throw("make_lowlik() beforehand");
vector<Edge<Cost>> res;
each(edge, edges){
if (tr.ord[edge.from] < lowlink[edge.to]) res.push_back(edge);
}
return res;
}/*}}}*/
vector<Edge<Cost>> kruskal_tree() {/*{{{*/
// 使用される辺のvectorを返す
vector<Edge<Cost>> res(n - 1);
sort(all(edges), [&](auto l, auto r) { return l.cost < r.cost; });
UnionFind uf(n);
Cost total_cost = zerocost;
int idx = 0;
each(e, edges) {
if (uf.same(e.from, e.to)) continue;
uf.merge(e.from, e.to);
total_cost = total_cost + e.cost;
res[idx] = e;
idx++;
}
assert(idx == n - 1);
return res;
}/*}}}*/
vector<Cost> dijkstra(vector<Pos> starts) { // 多点スタート{{{
vector<Cost> dist(n, infcost); // 最短距離
PQ<pair<Cost, Pos>> pq;
each(start, starts) {
dist[start] = zerocost;
pq.push(make_pair(zerocost, start));
}
while (!pq.empty()) {
auto cp = pq.top();
pq.pop();
auto [cost, u] = cp;
for (const auto& edge : adj_list[u]) {
Cost new_cost = cost + edge.cost; // TODO: 問題によってはここが変更の必要あり
if (new_cost < dist[edge.to]) {
dist[edge.to] = new_cost;
pq.push(make_pair(new_cost, edge.to));
}
}
}
return dist;
};/*}}}*/
vector<Cost> dijkstra(Pos start) { // 1点スタート{{{
vector<Pos> starts = {start};
return dijkstra(starts);
};/*}}}*/
};
// snippet:Graph }}}
// snippet:StronglyConnectedComponents {{{
struct StronglyConnectedComponents {
const Graph<> &g; //{{{
vector<int> comp; // comp[i]: iが属する強連結成分が何番目の成分か
Graph<> dag; // 縮約されたDAG graph. sizeをとれば強連結成分の個数が分かる。
Graph<> _rg; // reversed graph
vector<int> _order; // order[i]: 帰りがけ順
vector<int> _used;
StronglyConnectedComponents(Graph<> &_g)
: g(_g), comp(_g.n, -1), _rg(_g.n), _used(_g.n) {
for (int i = 0; i < g.n; i++) {
for (auto e : g[i]) {
_rg.add_edge(e.to, e.from, e.cost, e.idx);
}
}
}
int operator[](int k) { return comp[k]; }
void build() {
for (int i = 0; i < g.n; i++) _dfs(i);
reverse(begin(_order), end(_order));
int cnt = 0;
for (int u : _order)
if (comp[u] == -1) _rdfs(u, cnt), cnt++;
dag = Graph(cnt);
for (int u = 0; u < g.n; u++) {
for (auto &e : g[u]) {
if (comp[u] == comp[e.to]) continue;
dag.add_edge(comp[u], comp[e.to]);
}
}
}
void _dfs(int idx) {
if (_used[idx]) return;
_used[idx] = true;
for (auto &e : g[idx]) _dfs(e.to);
_order.push_back(idx);
}
void _rdfs(int idx, int cnt) {
if (comp[idx] != -1) return;
comp[idx] = cnt;
for (auto e : _rg[idx]) _rdfs(e.to, cnt);
} //}}}
};
// how to use
// StronglyConnectedComponents scc(g); // g: Graph
// scc.build();
// dump(scc.comp, scc.dag);
// snippet:StronglyConnectedComponents }}}
int solve() {
ll n;cin>>n;
Graph<ll> g(n);
vec<double> L(n);
rep(i, n){
cin>>L[i];
int p;cin>>p;
p--;
if(i==p) continue;
g.add_edge(p, i, 1);
}
StronglyConnectedComponents scc(g);
scc.build();
dump(scc.comp);
dump(scc.dag.adj_list);
map<ll, vec<int>> group;
rep(i, n){
group[scc.comp[i]].pb(i);
}
double ans = 0;
// duの入次数
vec<ll> cnt(sz(scc.dag.adj_list));
each(el, scc.dag.adj_list){
each(edge, el){
dump(edge.to);
cnt[edge.to]++;
}
}
each(el, group){
auto [du, v] = el;
sort(all(v), [&](auto &l, auto &r){return L[l] < L[r];});
if (sz(v)==1){
ans += L[v[0]] / (cnt[du]==0 ? 1: 2);
}
else{
rep(i, sz(v)){
if (i!=0) ans += L[v[i]] / 2;
if (i==0) ans += L[v[i]];
}
}
}
printf("%.1f\n", ans);
return 0;
}
int main(){/*{{{*/
solve();
check_input();
return 0;
}/*}}}*/