結果
| 問題 | No.2523 Trick Flower |
| ユーザー |
👑  hitonanode
|
| 提出日時 | 2023-10-27 22:52:11 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 28,152 bytes |
| コンパイル時間 | 3,106 ms |
| コンパイル使用メモリ | 236,128 KB |
| 実行使用メモリ | 24,416 KB |
| 最終ジャッジ日時 | 2023-10-27 22:52:19 |
| 合計ジャッジ時間 | 7,668 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge13 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
4,348 KB |
| testcase_01 | AC | 2 ms
4,348 KB |
| testcase_02 | AC | 2 ms
4,348 KB |
| testcase_03 | AC | 1 ms
4,348 KB |
| testcase_04 | AC | 2 ms
4,348 KB |
| testcase_05 | AC | 1 ms
4,348 KB |
| testcase_06 | AC | 1 ms
4,348 KB |
| testcase_07 | RE | - |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | AC | 155 ms
23,584 KB |
| testcase_16 | AC | 139 ms
23,652 KB |
| testcase_17 | AC | 71 ms
24,416 KB |
| testcase_18 | AC | 64 ms
21,020 KB |
| testcase_19 | AC | 137 ms
23,420 KB |
| testcase_20 | AC | 118 ms
23,392 KB |
| testcase_21 | RE | - |
| testcase_22 | AC | 119 ms
23,408 KB |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | AC | 97 ms
21,164 KB |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | RE | - |
| testcase_30 | WA | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | AC | 120 ms
23,172 KB |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <algorithm>
#include <cassert>
#include <deque>
#include <fstream>
#include <functional>
#include <limits>
#include <queue>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1>
struct shortest_path {
int V, E;
bool single_positive_weight;
T wmin, wmax;
std::vector<std::pair<int, T>> tos;
std::vector<int> head;
std::vector<std::tuple<int, int, T>> edges;
void build_() {
if (int(tos.size()) == E and int(head.size()) == V + 1) return;
tos.resize(E);
head.assign(V + 1, 0);
for (const auto &e : edges) ++head[std::get<0>(e) + 1];
for (int i = 0; i < V; ++i) head[i + 1] += head[i];
auto cur = head;
for (const auto &e : edges) {
tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e));
}
}
shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {}
void add_edge(int s, int t, T w) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
edges.emplace_back(s, t, w);
++E;
if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
wmin = std::min(wmin, w);
wmax = std::max(wmax, w);
}
void add_bi_edge(int u, int v, T w) {
add_edge(u, v, w);
add_edge(v, u, w);
}
std::vector<T> dist;
std::vector<int> prev;
// Dijkstra algorithm
// - Requirement: wmin >= 0
// - Complexity: O(E log E)
using Pque = std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>,
std::greater<std::pair<T, int>>>;
template <class Heap = Pque> void dijkstra(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
Heap pq;
pq.emplace(0, s);
while (!pq.empty()) {
T d;
int v;
std::tie(d, v) = pq.top();
pq.pop();
if (t == v) return;
if (dist[v] < d) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = d + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
pq.emplace(dnx, nx.first);
}
}
}
}
// Dijkstra algorithm
// - Requirement: wmin >= 0
// - Complexity: O(V^2 + E)
void dijkstra_vquad(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::vector<char> fixed(V, false);
while (true) {
int r = INVALID;
T dr = INF;
for (int i = 0; i < V; i++) {
if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i];
}
if (r == INVALID or r == t) break;
fixed[r] = true;
int nxt;
T dx;
for (int e = head[r]; e < head[r + 1]; ++e) {
std::tie(nxt, dx) = tos[e];
if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r;
}
}
}
// Bellman-Ford algorithm
// - Requirement: no negative loop
// - Complexity: O(VE)
bool bellman_ford(int s, int nb_loop) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
for (int l = 0; l < nb_loop; l++) {
bool upd = false;
for (int v = 0; v < V; v++) {
if (dist[v] == INF) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true;
}
}
if (!upd) return true;
}
return false;
}
// Bellman-ford algorithm using deque
// - Requirement: no negative loop
// - Complexity: O(VE)
void spfa(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::deque<int> q;
std::vector<char> in_queue(V);
q.push_back(s), in_queue[s] = 1;
while (!q.empty()) {
int now = q.front();
q.pop_front(), in_queue[now] = 0;
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[now] + nx.second;
int nxt = nx.first;
if (dist[nxt] > dnx) {
dist[nxt] = dnx;
if (!in_queue[nxt]) {
if (q.size() and dnx < dist[q.front()]) { // Small label first optimization
q.push_front(nxt);
} else {
q.push_back(nxt);
}
prev[nxt] = now, in_queue[nxt] = 1;
}
}
}
}
}
// 01-BFS
// - Requirement: all weights must be 0 or w (positive constant).
// - Complexity: O(V + E)
void zero_one_bfs(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> q(V * 4);
int ql = V * 2, qr = V * 2;
q[qr++] = s;
while (ql < qr) {
int v = q[ql++];
if (v == t) return;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
if (nx.second) {
q[qr++] = nx.first;
} else {
q[--ql] = nx.first;
}
}
}
}
}
// Dial's algorithm
// - Requirement: wmin >= 0
// - Complexity: O(wmax * V + E)
void dial(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<std::vector<std::pair<int, T>>> q(wmax + 1);
q[0].emplace_back(s, dist[s]);
int ninq = 1;
int cur = 0;
T dcur = 0;
for (; ninq; ++cur, ++dcur) {
if (cur == wmax + 1) cur = 0;
while (!q[cur].empty()) {
int v = q[cur].back().first;
T dnow = q[cur].back().second;
q[cur].pop_back(), --ninq;
if (v == t) return;
if (dist[v] < dnow) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
int nxtcur = cur + int(nx.second);
if (nxtcur >= int(q.size())) nxtcur -= q.size();
q[nxtcur].emplace_back(nx.first, dnx), ++ninq;
}
}
}
}
}
// Solver for DAG
// - Requirement: graph is DAG
// - Complexity: O(V + E)
bool dag_solver(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> indeg(V, 0);
std::vector<int> q(V * 2);
int ql = 0, qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
++indeg[nx.first];
if (indeg[nx.first] == 1) q[qr++] = nx.first;
}
}
ql = qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
--indeg[nx.first];
if (dist[nx.first] > dist[now] + nx.second)
dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now;
if (indeg[nx.first] == 0) q[qr++] = nx.first;
}
}
return *max_element(indeg.begin(), indeg.end()) == 0;
}
// Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal]
// If not reachable to goal, return {}
std::vector<int> retrieve_path(int goal) const {
assert(int(prev.size()) == V);
assert(0 <= goal and goal < V);
if (dist[goal] == INF) return {};
std::vector<int> ret{goal};
while (prev[goal] != INVALID) {
goal = prev[goal];
ret.push_back(goal);
}
std::reverse(ret.begin(), ret.end());
return ret;
}
void solve(int s, int t = INVALID) {
if (wmin >= 0) {
if (single_positive_weight) {
zero_one_bfs(s, t);
} else if (wmax <= 10) {
dial(s, t);
} else {
if ((long long)V * V < (E << 4)) {
dijkstra_vquad(s, t);
} else {
dijkstra(s, t);
}
}
} else {
bellman_ford(s, V);
}
}
// Warshall-Floyd algorithm
// - Requirement: no negative loop
// - Complexity: O(E + V^3)
std::vector<std::vector<T>> floyd_warshall() {
build_();
std::vector<std::vector<T>> dist2d(V, std::vector<T>(V, INF));
for (int i = 0; i < V; i++) {
dist2d[i][i] = 0;
for (const auto &e : edges) {
int s = std::get<0>(e), t = std::get<1>(e);
dist2d[s][t] = std::min(dist2d[s][t], std::get<2>(e));
}
}
for (int k = 0; k < V; k++) {
for (int i = 0; i < V; i++) {
if (dist2d[i][k] == INF) continue;
for (int j = 0; j < V; j++) {
if (dist2d[k][j] == INF) continue;
dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
}
}
}
return dist2d;
}
void to_dot(std::string filename = "shortest_path") const {
std::ofstream ss(filename + ".DOT");
ss << "digraph{\n";
build_();
for (int i = 0; i < V; i++) {
for (int e = head[i]; e < head[i + 1]; ++e) {
ss << i << "->" << tos[e].first << "[label=" << tos[e].second << "];\n";
}
}
ss << "}\n";
ss.close();
return;
}
};
#include <algorithm>
#include <cassert>
#include <functional>
#include <queue>
#include <stack>
#include <utility>
#include <vector>
// Heavy-Light Decomposition of trees
// Based on http://beet-aizu.hatenablog.com/entry/2017/12/12/235950
struct HeavyLightDecomposition {
int V;
int k;
int nb_heavy_path;
std::vector<std::vector<int>> e;
std::vector<int> par; // par[i] = parent of vertex i (Default: -1)
std::vector<int> depth; // depth[i] = distance between root and vertex i
std::vector<int> subtree_sz; // subtree_sz[i] = size of subtree whose root is i
std::vector<int> heavy_child; // heavy_child[i] = child of vertex i on heavy path (Default: -1)
std::vector<int> tree_id; // tree_id[i] = id of tree vertex i belongs to
std::vector<int> aligned_id,
aligned_id_inv; // aligned_id[i] = aligned id for vertex i (consecutive on heavy edges)
std::vector<int> head; // head[i] = id of vertex on heavy path of vertex i, nearest to root
std::vector<int> head_ids; // consist of head vertex id's
std::vector<int> heavy_path_id; // heavy_path_id[i] = heavy_path_id for vertex [i]
HeavyLightDecomposition(int sz = 0)
: V(sz), k(0), nb_heavy_path(0), e(sz), par(sz), depth(sz), subtree_sz(sz), heavy_child(sz),
tree_id(sz, -1), aligned_id(sz), aligned_id_inv(sz), head(sz), heavy_path_id(sz, -1) {}
void add_edge(int u, int v) {
e[u].emplace_back(v);
e[v].emplace_back(u);
}
void _build_dfs(int root) {
std::stack<std::pair<int, int>> st;
par[root] = -1;
depth[root] = 0;
st.emplace(root, 0);
while (!st.empty()) {
int now = st.top().first;
int &i = st.top().second;
if (i < (int)e[now].size()) {
int nxt = e[now][i++];
if (nxt == par[now]) continue;
par[nxt] = now;
depth[nxt] = depth[now] + 1;
st.emplace(nxt, 0);
} else {
st.pop();
int max_sub_sz = 0;
subtree_sz[now] = 1;
heavy_child[now] = -1;
for (auto nxt : e[now]) {
if (nxt == par[now]) continue;
subtree_sz[now] += subtree_sz[nxt];
if (max_sub_sz < subtree_sz[nxt])
max_sub_sz = subtree_sz[nxt], heavy_child[now] = nxt;
}
}
}
}
void _build_bfs(int root, int tree_id_now) {
std::queue<int> q({root});
while (!q.empty()) {
int h = q.front();
q.pop();
head_ids.emplace_back(h);
for (int now = h; now != -1; now = heavy_child[now]) {
tree_id[now] = tree_id_now;
aligned_id[now] = k++;
aligned_id_inv[aligned_id[now]] = now;
heavy_path_id[now] = nb_heavy_path;
head[now] = h;
for (int nxt : e[now])
if (nxt != par[now] and nxt != heavy_child[now]) q.push(nxt);
}
nb_heavy_path++;
}
}
void build(std::vector<int> roots = {0}) {
int tree_id_now = 0;
for (auto r : roots) _build_dfs(r), _build_bfs(r, tree_id_now++);
}
template <class T> std::vector<T> segtree_rearrange(const std::vector<T> &data) const {
assert(int(data.size()) == V);
std::vector<T> ret;
ret.reserve(V);
for (int i = 0; i < V; i++) ret.emplace_back(data[aligned_id_inv[i]]);
return ret;
}
// query for vertices on path [u, v] (INCLUSIVE)
void
for_each_vertex(int u, int v, const std::function<void(int ancestor, int descendant)> &f) const {
while (true) {
if (aligned_id[u] > aligned_id[v]) std::swap(u, v);
f(std::max(aligned_id[head[v]], aligned_id[u]), aligned_id[v]);
if (head[u] == head[v]) break;
v = par[head[v]];
}
}
void for_each_vertex_noncommutative(
int from, int to, const std::function<void(int ancestor, int descendant)> &fup,
const std::function<void(int ancestor, int descendant)> &fdown) const {
int u = from, v = to;
const int lca = lowest_common_ancestor(u, v), dlca = depth[lca];
while (u >= 0 and depth[u] > dlca) {
const int p = (depth[head[u]] > dlca ? head[u] : lca);
fup(aligned_id[p] + (p == lca), aligned_id[u]), u = par[p];
}
static std::vector<std::pair<int, int>> lrs;
int sz = 0;
while (v >= 0 and depth[v] >= dlca) {
const int p = (depth[head[v]] >= dlca ? head[v] : lca);
if (int(lrs.size()) == sz) lrs.emplace_back(0, 0);
lrs.at(sz++) = {p, v}, v = par.at(p);
}
while (sz--) fdown(aligned_id[lrs.at(sz).first], aligned_id[lrs.at(sz).second]);
}
// query for edges on path [u, v]
void for_each_edge(int u, int v, const std::function<void(int, int)> &f) const {
while (true) {
if (aligned_id[u] > aligned_id[v]) std::swap(u, v);
if (head[u] != head[v]) {
f(aligned_id[head[v]], aligned_id[v]);
v = par[head[v]];
} else {
if (u != v) f(aligned_id[u] + 1, aligned_id[v]);
break;
}
}
}
// lowest_common_ancestor: O(log V)
int lowest_common_ancestor(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
while (true) {
if (aligned_id[u] > aligned_id[v]) std::swap(u, v);
if (head[u] == head[v]) return u;
v = par[head[v]];
}
}
int distance(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
return depth[u] + depth[v] - 2 * depth[lowest_common_ancestor(u, v)];
}
// Level ancestor, O(log V)
// if k-th parent is out of range, return -1
int kth_parent(int v, int k) const {
if (k < 0) return -1;
while (v >= 0) {
int h = head.at(v), len = depth.at(v) - depth.at(h);
if (k <= len) return aligned_id_inv.at(aligned_id.at(v) - k);
k -= len + 1, v = par.at(h);
}
return -1;
}
// Jump on tree, O(log V)
int s_to_t_by_k_steps(int s, int t, int k) const {
if (k < 0) return -1;
if (k == 0) return s;
int lca = lowest_common_ancestor(s, t);
if (k <= depth.at(s) - depth.at(lca)) return kth_parent(s, k);
return kth_parent(t, depth.at(s) + depth.at(t) - depth.at(lca) * 2 - k);
}
};
// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
std::vector<int> par, cou;
UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (cou[x] < cou[y]) std::swap(x, y);
par[y] = x, cou[x] += cou[y];
return true;
}
int count(int x) { return cou[find(x)]; }
bool same(int x, int y) { return find(x) == find(y); }
std::vector<std::vector<int>> groups() {
std::vector<std::vector<int>> ret(par.size());
for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i);
ret.erase(std::remove_if(ret.begin(), ret.end(),
[&](const std::vector<int> &v) { return v.empty(); }),
ret.end());
return ret;
}
};
int main() {
vector<lint> Anew, Bnew;
int R;
vector<int> pars;
vector<int> vsord;
{
int N;
cin >> N;
vector<lint> A(N), B(N), C(N);
cin >> A >> B >> C;
// dbg(make_tuple(N, A, B, C));
REP(i, N) C.at(i)--;
UnionFind ufinit(N);
HeavyLightDecomposition hld(N);
vector<pint> loop_es;
REP(i, N) {
const int j = C.at(i);
if (ufinit.unite(i, j)) {
hld.add_edge(i, j);
} else {
loop_es.emplace_back(i, j);
}
}
hld.build();
UnionFind uf(N);
for (auto [a, b] : loop_es) {
uf.unite(a, b);
while (a != b) {
if (a < 0) break;
if (b < 0) break;
if (hld.depth.at(a) > hld.depth.at(b)) {
int j = hld.par.at(a);
uf.unite(a, j);
a = j;
} else {
int j = hld.par.at(b);
uf.unite(b, j);
b = j;
}
}
}
vector<int> rs;
REP(i, N) if (uf.find(i) == i) rs.push_back(i);
R = rs.size();
Anew.assign(R, 0), Bnew.assign(R, 0);
REP(i, N) {
Anew.at(arglb(rs, uf.find(i))) += A.at(i);
Bnew.at(arglb(rs, uf.find(i))) += B.at(i);
}
pars.assign(R, -1);
shortest_path<int> sp(R + 1);
REP(i, N) {
int p = arglb(rs, uf.find(C.at(i)));
int c = arglb(rs, uf.find(i));
dbg(make_tuple(p, c));
if (p != c) {
sp.add_edge(p, c, 1);
pars.at(c) = p;
} else {
sp.add_edge(R, c, 0);
}
}
sp.solve(R);
// dbg(sp.dist);
vsord.resize(R);
REP(r, R) vsord.at(r) = r;
sort(ALL(vsord), [&](int i, int j) { return sp.dist.at(i) > sp.dist.at(j); });
dbg(vsord);
}
lint ok = 0, ng = accumulate(ALL(Anew), 0LL) / max(1LL, accumulate(ALL(Bnew), 0LL)) + 1;
// dbg(ng);
while (ng > ok + 1) {
const auto c = (ok + ng) / 2;
vector<lint> req(R);
REP(r, R) req.at(r) = Bnew.at(r) * c;
// dbg(make_tuple(c, req, Bnew));
bool failure = false;
for (int v : vsord) {
req.at(v) -= Anew.at(v);
if (req.at(v) > 0) {
int p = pars.at(v);
if (p < 0) {
failure = true;
break;
} else {
req.at(p) += req.at(v);
}
}
}
(failure ? ng : ok) = c;
}
cout << ok << '\n';
}