結果
| 問題 | No.2160 みたりのDominator |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-01-02 11:49:31 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 31,396 bytes |
| コンパイル時間 | 3,108 ms |
| コンパイル使用メモリ | 218,880 KB |
| 実行使用メモリ | 57,500 KB |
| 最終ジャッジ日時 | 2024-11-27 00:41:06 |
| 合計ジャッジ時間 | 14,791 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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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
5,248 KB |
| testcase_01 | AC | 61 ms
33,628 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 1 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 1 ms
5,248 KB |
| testcase_10 | AC | 2 ms
5,248 KB |
| testcase_11 | AC | 2 ms
5,248 KB |
| testcase_12 | AC | 2 ms
5,248 KB |
| testcase_13 | AC | 2 ms
5,248 KB |
| testcase_14 | AC | 2 ms
5,248 KB |
| testcase_15 | AC | 2 ms
5,248 KB |
| testcase_16 | AC | 2 ms
5,248 KB |
| testcase_17 | AC | 1 ms
5,248 KB |
| testcase_18 | AC | 1 ms
5,248 KB |
| testcase_19 | AC | 2 ms
5,248 KB |
| testcase_20 | AC | 1 ms
5,248 KB |
| testcase_21 | AC | 2 ms
5,248 KB |
| testcase_22 | AC | 2 ms
5,248 KB |
| testcase_23 | AC | 2 ms
5,248 KB |
| testcase_24 | AC | 2 ms
5,248 KB |
| testcase_25 | AC | 2 ms
5,248 KB |
| testcase_26 | AC | 2 ms
5,248 KB |
| testcase_27 | AC | 2 ms
5,248 KB |
| testcase_28 | AC | 2 ms
5,248 KB |
| testcase_29 | AC | 2 ms
5,248 KB |
| testcase_30 | AC | 2 ms
5,248 KB |
| testcase_31 | AC | 2 ms
5,248 KB |
| testcase_32 | AC | 2 ms
5,248 KB |
| testcase_33 | WA | - |
| testcase_34 | WA | - |
| testcase_35 | AC | 2 ms
5,248 KB |
| testcase_36 | AC | 2 ms
5,248 KB |
| testcase_37 | AC | 2 ms
5,248 KB |
| testcase_38 | AC | 2 ms
5,248 KB |
| testcase_39 | AC | 2 ms
5,248 KB |
| testcase_40 | AC | 176 ms
39,140 KB |
| testcase_41 | AC | 140 ms
38,108 KB |
| testcase_42 | AC | 80 ms
23,856 KB |
| testcase_43 | AC | 129 ms
30,032 KB |
| testcase_44 | AC | 167 ms
38,024 KB |
| testcase_45 | AC | 169 ms
38,244 KB |
| testcase_46 | AC | 140 ms
35,932 KB |
| testcase_47 | AC | 77 ms
22,060 KB |
| testcase_48 | AC | 109 ms
26,960 KB |
| testcase_49 | AC | 142 ms
33,284 KB |
| testcase_50 | AC | 124 ms
32,324 KB |
| testcase_51 | AC | 96 ms
26,268 KB |
| testcase_52 | AC | 133 ms
34,580 KB |
| testcase_53 | AC | 165 ms
37,700 KB |
| testcase_54 | AC | 82 ms
23,016 KB |
| testcase_55 | AC | 233 ms
51,292 KB |
| testcase_56 | AC | 240 ms
46,280 KB |
| testcase_57 | AC | 222 ms
48,564 KB |
| testcase_58 | AC | 215 ms
55,212 KB |
| testcase_59 | AC | 201 ms
49,212 KB |
| testcase_60 | AC | 236 ms
54,092 KB |
| testcase_61 | AC | 280 ms
51,512 KB |
| testcase_62 | AC | 271 ms
57,500 KB |
| testcase_63 | AC | 299 ms
52,964 KB |
| testcase_64 | AC | 199 ms
51,932 KB |
| testcase_65 | AC | 149 ms
30,104 KB |
| testcase_66 | AC | 136 ms
30,180 KB |
| testcase_67 | AC | 138 ms
31,948 KB |
| testcase_68 | AC | 346 ms
52,012 KB |
| testcase_69 | AC | 205 ms
39,456 KB |
| testcase_70 | AC | 284 ms
52,000 KB |
| testcase_71 | AC | 112 ms
25,992 KB |
| testcase_72 | AC | 237 ms
41,972 KB |
| testcase_73 | AC | 292 ms
50,640 KB |
| testcase_74 | AC | 253 ms
47,968 KB |
| testcase_75 | AC | 38 ms
19,320 KB |
| testcase_76 | AC | 30 ms
15,568 KB |
| testcase_77 | AC | 191 ms
37,376 KB |
| testcase_78 | AC | 236 ms
41,220 KB |
| testcase_79 | AC | 22 ms
12,208 KB |
| testcase_80 | AC | 31 ms
13,852 KB |
| testcase_81 | AC | 52 ms
23,700 KB |
| testcase_82 | AC | 64 ms
25,824 KB |
| testcase_83 | AC | 106 ms
29,780 KB |
| 61_evil_bias_nocross_01.txt | AC | 172 ms
38,884 KB |
| 61_evil_bias_nocross_02.txt | AC | 149 ms
37,852 KB |
| 61_evil_bias_nocross_03.txt | AC | 71 ms
23,592 KB |
| 61_evil_bias_nocross_04.txt | AC | 111 ms
29,276 KB |
| 61_evil_bias_nocross_05.txt | AC | 143 ms
37,384 KB |
| 61_evil_bias_nocross_06.txt | AC | 164 ms
38,724 KB |
| 61_evil_bias_nocross_07.txt | AC | 89 ms
26,148 KB |
| 61_evil_bias_nocross_08.txt | AC | 141 ms
34,192 KB |
| 61_evil_bias_nocross_09.txt | AC | 140 ms
35,904 KB |
| 61_evil_bias_nocross_10.txt | AC | 73 ms
22,636 KB |
| 61_evil_bias_nocross_11.txt | AC | 97 ms
28,480 KB |
| 61_evil_bias_nocross_12.txt | AC | 159 ms
33,248 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 <numeric>
#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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
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
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;
}
};
struct Problem {
int N1, N2, N3;
vector<pint> edges;
int s() const { return N1 + N2 + N3; }
int t() const { return s() + 1; }
pint get_v(int vid) const {
if (vid < N1) return {0, vid};
if (vid < N1 + N2) return {1, vid - N1};
if (vid < N1 + N2 + N3) return {2, vid - N1 - N2};
exit(1);
}
int convert_to(int did, int i) const {
if (did == 0) return i;
if (did == 1) return i + N1;
if (did == 2) return i + N1 + N2;
exit(1);
}
};
Problem truncate(const Problem &p) {
vector dels(3, vector<int>());
dels.at(0).assign(p.N1, 0);
dels.at(1).assign(p.N2, 0);
dels.at(2).assign(p.N3, 0);
for (auto [u, v] : p.edges) {
if (u > v) swap(u, v);
const auto [du, iu] = p.get_v(u);
if (v == p.s() or v == p.t()) {
if (v == p.s()) {
// ++dels.at(du).front();
// --dels.at(du).at(iu);
} else {
// ++dels.at(du).at(iu);
}
} else {
const auto [dv, iv] = p.get_v(v);
if (du == dv) {
++dels.at(du).at(min(iu, iv));
--dels.at(du).at(max(iu, iv));
}
}
}
for (auto &v : dels) { FOR(i, 1, v.size()) v.at(i) += v.at(i - 1); }
vector<vector<int>> alives(3);
REP(d, 3) {
REP(i, dels.at(d).size()) {
if (!dels.at(d).at(i)) alives.at(d).push_back(i);
}
}
Problem ret;
ret.N1 = alives.at(0).size();
ret.N2 = alives.at(1).size();
ret.N3 = alives.at(2).size();
for (auto [u, v] : p.edges) {
if (u > v) swap(u, v);
if (v == p.s() or v == p.t()) {
const auto [du, iu] = p.get_v(u);
int ju = arglb(alives.at(du), iu);
if (v == p.s()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.s());
if (v == p.t()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.t());
} else {
const auto [du, iu] = p.get_v(u);
const auto [dv, iv] = p.get_v(v);
int ju = arglb(alives.at(du), iu);
int jv = arglb(alives.at(dv), iv);
if (du == dv and ju == jv) continue;
ret.edges.emplace_back(ret.convert_to(du, ju), ret.convert_to(dv, jv));
}
}
ret.edges = sort_unique(ret.edges);
return ret;
}
struct Rect {
int xl, xr;
int yl, yr;
lint area() const {
lint xw = max(0, xr - xl);
lint yw = max(0, yr - yl);
return xw * yw;
}
Rect bottom_left(int x, int y) { return Rect{xl, min(xr, x), yl, min(yr, y)}; }
Rect top_right(int x, int y) { return Rect{max(xl, x), xr, max(yl, y), yr}; }
template <class OStream> friend OStream &operator<<(OStream &os, const Rect &x) {
return os << "(" << x.xl << "," << x.xr << "," << x.yl << "," << x.yr << ")";
}
};
lint solve(const Problem &p) {
vector<vector<int>> switch13(p.N3 + 1), switch23(p.N3 + 1);
multiset<int> xubs, yubs;
xubs.insert(p.N1 + 1);
yubs.insert(p.N2 + 1);
int xlb = 0, ylb = 0, zlb = 0, zub = 1 << 26;
vector<pint> rectv12s;
rectv12s.emplace_back(p.N1 + 1, p.N2 + 1);
for (auto [u, v] : p.edges) {
if (u > v) swap(u, v);
const auto [du, iu] = p.get_v(u);
if (v == p.s() or v == p.t()) {
if (v == p.s()) {
if (du == 0) chmax(xlb, iu + 1);
if (du == 1) chmax(ylb, iu + 1);
if (du == 2) chmax(zlb, iu + 1);
} else {
if (du == 0) xubs.insert(iu + 1);
if (du == 1) yubs.insert(iu + 1);
if (du == 2) chmin(zub, iu + 1);
}
} else {
const auto [dv, iv] = p.get_v(v);
assert(du != dv);
if (du == 0 and dv == 1) {
rectv12s.emplace_back(iu + 1, iv + 1);
} else if (du == 0 and dv == 2) {
switch13.at(iv).push_back(iu + 1);
xubs.insert(iu + 1);
} else if (du == 1 and dv == 2) {
switch23.at(iv).push_back(iu + 1);
yubs.insert(iu + 1);
} else {
// exit(1);
}
}
}
dbg(rectv12s);
vector<Rect> rects;
rects.push_back(Rect{0, p.N1 + 1, 0, p.N2 + 1});
for (auto [x, y] : sort_unique(rectv12s)) {
if (rects.empty()) continue;
auto last = rects.back();
rects.pop_back();
while (rects.size() and rects.back().yl >= y) rects.pop_back();
if (rects.size()) {
rects.back() = rects.back().bottom_left(x, y);
if (!rects.back().area()) rects.pop_back();
}
rects.push_back(last.bottom_left(x, y));
if (!rects.back().area()) rects.pop_back();
rects.push_back(last.top_right(x, y));
if (!rects.back().area()) rects.pop_back();
}
vector<lint> area_sum{0};
vector<int> xrs, yrs;
for (auto r : rects) {
auto tmp = area_sum.back() + r.area();
area_sum.push_back(tmp);
xrs.push_back(r.xr);
yrs.push_back(r.yr);
}
dbg(make_tuple(rects));
dbg(area_sum);
auto calc_area_bottomleft = [&](int x, int y) -> lint {
int i = min(arglb(xrs, x), arglb(yrs, y));
lint ret = area_sum.at(i);
if (i < int(rects.size())) ret += rects.at(i).bottom_left(x, y).area();
return ret;
};
lint ret = 0;
REP(z, p.N3 + 1) {
int xub = *xubs.cbegin();
int yub = *yubs.cbegin();
if (z >= zlb and z <= zub and xlb < xub and ylb < yub) {
ret += calc_area_bottomleft(xub, yub) + calc_area_bottomleft(xlb, ylb);
ret -= calc_area_bottomleft(xub, ylb) + calc_area_bottomleft(xlb, yub);
}
for (int x : switch13.at(z)) {
xubs.erase(xubs.lower_bound(x));
chmax(xlb, x);
}
for (int y : switch23.at(z)) {
yubs.erase(yubs.lower_bound(y));
chmax(ylb, y);
}
}
return ret;
}
// MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible
// with C++11 Reference: <https://atcoder.github.io/ac-library/production/document_ja/maxflow.html>
template <class Cap> struct mf_graph {
struct simple_queue_int {
std::vector<int> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const int &t) { payload.push_back(t); }
int &front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
mf_graph() : _n(0) {}
mf_graph(int n) : _n(n), g(n) {}
int add_edge(int from, int to, Cap cap) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
int m = int(pos.size());
pos.push_back({from, int(g[from].size())});
int from_id = int(g[from].size());
int to_id = int(g[to].size());
if (from == to) to_id++;
g[from].push_back(_edge{to, to_id, cap});
g[to].push_back(_edge{from, from_id, 0});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
};
edge get_edge(int i) {
int m = int(pos.size());
assert(0 <= i && i < m);
auto _e = g[pos[i].first][pos[i].second];
auto _re = g[_e.to][_e.rev];
return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result;
for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
return result;
}
void change_edge(int i, Cap new_cap, Cap new_flow) {
int m = int(pos.size());
assert(0 <= i && i < m);
assert(0 <= new_flow && new_flow <= new_cap);
auto &_e = g[pos[i].first][pos[i].second];
auto &_re = g[_e.to][_e.rev];
_e.cap = new_cap - new_flow;
_re.cap = new_flow;
}
std::vector<int> level, iter;
simple_queue_int que;
void _bfs(int s, int t) {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
que.clear();
que.push(s);
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto e : g[v]) {
if (e.cap == 0 || level[e.to] >= 0) continue;
level[e.to] = level[v] + 1;
if (e.to == t) return;
que.push(e.to);
}
}
}
Cap _dfs(int v, int s, Cap up) {
if (v == s) return up;
Cap res = 0;
int level_v = level[v];
for (int &i = iter[v]; i < int(g[v].size()); i++) {
_edge &e = g[v][i];
if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
Cap d = _dfs(e.to, s, std::min(up - res, g[e.to][e.rev].cap));
if (d <= 0) continue;
g[v][i].cap += d;
g[e.to][e.rev].cap -= d;
res += d;
if (res == up) return res;
}
level[v] = _n;
return res;
}
Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
Cap flow(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
level.assign(_n, 0), iter.assign(_n, 0);
que.clear();
Cap flow = 0;
while (flow < flow_limit) {
_bfs(s, t);
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
Cap f = _dfs(t, s, flow_limit - flow);
if (!f) break;
flow += f;
}
return flow;
}
std::vector<bool> min_cut(int s) {
std::vector<bool> visited(_n);
simple_queue_int que;
que.push(s);
while (!que.empty()) {
int p = que.front();
que.pop();
visited[p] = true;
for (auto e : g[p]) {
if (e.cap && !visited[e.to]) {
visited[e.to] = true;
que.push(e.to);
}
}
}
return visited;
}
void dump_graphviz(std::string filename = "maxflow") const {
std::ofstream ss(filename + ".DOT");
ss << "digraph{\n";
for (int i = 0; i < _n; i++) {
for (const auto &e : g[i]) {
if (e.cap > 0) ss << i << "->" << e.to << "[label=" << e.cap << "];\n";
}
}
ss << "}\n";
ss.close();
return;
}
int _n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
bool check_infeasible(const Problem &p) {
const int gs = p.s(), gt = p.t();
mf_graph<int> mf(gt + 1);
REP(i, p.N1 - 1) mf.add_edge(i, i + 1, 1);
REP(i, p.N2 - 1) mf.add_edge(p.N1 + i, p.N1 + i + 1, 1);
REP(i, p.N3 - 1) mf.add_edge(p.N1 + p.N2 + i, p.N1 + p.N2 + i + 1, 1);
if (p.N1) mf.add_edge(gs, 0, 1);
if (p.N2) mf.add_edge(gs, p.N1, 1);
if (p.N3) mf.add_edge(gs, p.N1 + p.N2, 1);
if (p.N1) mf.add_edge(p.N1 - 1, gt, 1);
if (p.N2) mf.add_edge(p.N1 + p.N2 - 1, gt, 1);
if (p.N3) mf.add_edge(p.N1 + p.N2 + p.N3 - 1, gt, 1);
for (auto [u, v] : p.edges) mf.add_edge(u, v, 1), mf.add_edge(v, u, 1);
auto f = mf.flow(gs, gt, 4);
return f == 4;
// shortest_path<int> graph(gt + 1);
// REP(i, p.N1 - 1) graph.add_edge(i + 1, i, 1);
// REP(i, p.N2 - 1) graph.add_edge(p.N1 + i + 1, p.N1 + i, 1);
// REP(i, p.N3 - 1) graph.add_edge(p.N1 + p.N2 + i + 1, p.N1 + p.N2 + i, 1);
// if (p.N1) graph.add_edge(0, gs, 1);
// if (p.N2) graph.add_edge(p.N1, gs, 1);
// if (p.N3) graph.add_edge(p.N1 + p.N2, gs, 1);
// for (auto [u, v] : p.edges) {
// if (u == p.s()) graph.add_edge(gs, v, 1);
// if (v == p.s()) graph.add_edge(gs, u, 1);
// }
// graph.solve(gs);
// shortest_path<int> graph2(gt + 1);
// REP(i, p.N1 - 1) graph2.add_edge(i, i + 1, 1);
// REP(i, p.N2 - 1) graph2.add_edge(p.N1 + i, p.N1 + i + 1, 1);
// REP(i, p.N3 - 1) graph2.add_edge(p.N1 + p.N2 + i, p.N1 + p.N2 + i + 1, 1);
// if (p.N1) graph2.add_edge(gt, p.N1 - 1, 1);
// if (p.N2) graph2.add_edge(gt, p.N1 + p.N2 - 1, 1);
// if (p.N3) graph2.add_edge(gt, p.N1 + p.N2 + p.N3 - 1, 1);
// for (auto [u, v] : p.edges) {
// if (u == p.t()) graph2.add_edge(gt, v, 1);
// if (v == p.t()) graph2.add_edge(gt, u, 1);
// }
// graph2.solve(gt);
// REP(i, gt + 1) {
// if (graph.dist[i] + graph2.dist[i] <= 1 << 28) return true;
// }
// return false;
}
int main() {
int M;
Problem problem;
cin >> problem.N1 >> problem.N2 >> problem.N3 >> M;
while (M--) {
int u, v;
cin >> u >> v;
--u, --v;
if (u > v) swap(u, v);
if (u == problem.s() and v == problem.t()) {
puts("0");
return 0;
}
problem.edges.emplace_back(u, v);
}
if (check_infeasible(problem)) {
dbg("infeasible");
puts("0");
return 0;
}
problem = truncate(problem);
if (!problem.N1 or !problem.N2 or !problem.N3) {
puts("0");
return 0;
}
cout << solve(problem) << endl;
}