結果
| 問題 |
No.1320 Two Type Min Cost Cycle
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2020-12-17 00:27:33 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 316 ms / 2,000 ms |
| コード長 | 12,643 bytes |
| コンパイル時間 | 2,525 ms |
| コンパイル使用メモリ | 224,004 KB |
| 最終ジャッジ日時 | 2025-01-17 02:10:21 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 57 |
ソースコード
#include <bits/stdc++.h>
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) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#else
#define dbg(x) {}
#endif
template <typename T> struct ShortestPath {
int V, E;
int INVALID = -1;
std::vector<std::vector<std::pair<int, T>>> to;
ShortestPath() = default;
ShortestPath(int V) : V(V), E(0), to(V) {}
void add_edge(int s, int t, T len) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
to[s].emplace_back(t, len);
E++;
}
std::vector<T> dist;
std::vector<int> prev;
// Dijkstra algorithm
// Complexity: O(E log E)
void Dijkstra(int s) {
assert(0 <= s and s < V);
dist.assign(V, std::numeric_limits<T>::max());
dist[s] = 0;
prev.assign(V, INVALID);
using P = std::pair<T, int>;
std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
pq.emplace(0, s);
while (!pq.empty()) {
T d;
int v;
std::tie(d, v) = pq.top();
pq.pop();
if (dist[v] < d) continue;
for (auto nx : to[v]) {
T dnx = d + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
pq.emplace(dnx, nx.first);
}
}
}
}
// Bellman-Ford algorithm
// Complexity: O(VE)
bool BellmanFord(int s, int nb_loop) {
assert(0 <= s and s < V);
dist.assign(V, std::numeric_limits<T>::max());
dist[s] = 0;
prev.assign(V, INVALID);
for (int l = 0; l < nb_loop; l++) {
bool upd = false;
for (int v = 0; v < V; v++) {
if (dist[v] == std::numeric_limits<T>::max()) continue;
for (auto nx : to[v]) {
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;
}
void ZeroOneBFS(int s) {
assert(0 <= s and s < V);
dist.assign(V, std::numeric_limits<T>::max());
dist[s] = 0;
prev.assign(V, INVALID);
std::deque<int> que;
que.push_back(s);
while (!que.empty()) {
int v = que.front();
que.pop_front();
for (auto nx : to[v]) {
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
if (nx.second) {
que.push_back(nx.first);
} else {
que.push_front(nx.first);
}
}
}
}
}
// Warshall-Floyd algorithm
// Complexity: O(E + V^3)
std::vector<std::vector<T>> dist2d;
void WarshallFloyd() {
dist2d.assign(V, std::vector<T>(V, std::numeric_limits<T>::max()));
for (int i = 0; i < V; i++) {
dist2d[i][i] = 0;
for (auto p : to[i]) dist2d[i][p.first] = min(dist2d[i][p.first], p.second);
}
for (int k = 0; k < V; k++) {
for (int i = 0; i < V; i++) {
if (dist2d[i][k] = std::numeric_limits<T>::max()) continue;
for (int j = 0; j < V; j++) {
if (dist2d[k][j] = std::numeric_limits<T>::max()) continue;
dist2d[i][j] = min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
}
}
}
}
};
// Shortest cycle detection of UNDIRECTED SIMPLE graphs
// Assumption: only two types of edges are permitted: weight = 0 or W ( > 0)
// Complexity: O(E)
// Verified: <https://codeforces.com/contest/1325/problem/E>
struct ShortestCycle01 {
int V, E;
int INVALID = -1;
std::vector<std::vector<std::pair<int, int>>> to; // (nxt, weight)
ShortestCycle01() = default;
ShortestCycle01(int V) : V(V), E(0), to(V) {}
void add_edge(int s, int t, int len) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
assert(len >= 0);
to[s].emplace_back(t, len);
to[t].emplace_back(s, len);
E++;
}
std::vector<lint> dist;
std::vector<int> prev;
// Find minimum length simple cycle which passes vertex `v`
// - return: (LEN, (a, b))
// - LEN: length of the shortest cycles if exists, numeric_limits<int>::max() otherwise.
// - the cycle consists of vertices [v, ..., prev[prev[a]], prev[a], a, b, prev[b], prev[prev[b]], ..., v]
std::pair<lint, std::pair<int, int>> Solve(int v) {
assert(0 <= v and v < V);
dist.assign(V, std::numeric_limits<lint>::max());
dist[v] = 0;
prev.assign(V, -1);
using P = pair<lint, pint>;
std::priority_queue<P, vector<P>, greater<P>> bfsq;
std::vector<std::pair<std::pair<int, int>, int>> add_edge;
bfsq.emplace(0, pint(v, -1));
while (!bfsq.empty()) {
auto [wnow, pp] = bfsq.top();
auto [now, prv] = pp;
bfsq.pop();
for (auto nxt : to[now])
if (nxt.first != prv) {
if (dist[nxt.first] == std::numeric_limits<lint>::max()) {
dist[nxt.first] = dist[now] + nxt.second;
prev[nxt.first] = now;
bfsq.emplace(dist[nxt.first], pint(nxt.first, now));
} else {
add_edge.emplace_back(std::make_pair(now, nxt.first), nxt.second);
}
}
}
lint minimum_cycle = std::numeric_limits<lint>::max();
int s = -1, t = -1;
for (auto edge : add_edge) {
int a = edge.first.first, b = edge.first.second;
lint L = dist[a] + dist[b] + edge.second;
if (L < minimum_cycle) minimum_cycle = L, s = a, t = b;
}
return std::make_pair(minimum_cycle, std::make_pair(s, t));
}
};
// struct ShortestCycleOfUndirectedGraph {
// int V, E;
// std::vector<std::vector<std::pair<int, int>>> to;
// ShortestCycleOfUndirectedGraph(int N) : V(N), E(0), to(N) {}
// void add_edge(int s, int t, int len) {
// assert(0 <= s and s < V);
// assert(0 <= t and t < V);
// assert(len >= 0);
// to[s].emplace_back(t, len);
// to[t].emplace_back(s, len);
// E++;
// }
// std::array<std::vector<long long>, 2> dist;
// std::array<std::vector<int>, 2> prev;
// long long solve(int v) {
// assert(0 <= v and v < V);
// dist[0].assign(V, std::numeric_limits<long long>::max() / 2);
// dist[1].assign(V, std::numeric_limits<long long>::max() / 2);
// prev[0].assign(V, -1);
// prev[1].assign(V, -1);
// using P = std::pair<long long, int>;
// std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
// while (!pq.empty()) {
// long long wnow = pq.top().first;
// int now = pq.top().second;
// pq.pop();
// if (dist[1][now] < wnow) continue;
// for (const auto nxtp : to[now]) {
// int nxt = nxtp.first;
// if (prev1[now] != nxt and chmin(dist1[nxt], dist1[now] + nxtp.second)) prev1[nxt] =
// }
// }
// }
// };
void solve_dir(int N, int M) {
vector<vector<pint>> to(N);
while (M--) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
to[u].emplace_back(v, w);
}
lint ret = 1e18;
REP(s, N) {
ShortestPath<lint> graph(N + 1);
REP(i, N) for (auto [j, w] : to[i]) {
graph.add_edge(i, j, w);
if (j == s) graph.add_edge(i, N, w);
}
graph.Dijkstra(s);
if (graph.dist[N] < 1e18) chmin(ret, graph.dist[N]);
}
cout << (ret < 1e18 ? ret : -1) << '\n';
}
int main()
{
int T, N, M;
cin >> T >> N >> M;
lint ret = 1e18;
if (T == 1)
solve_dir(N, M);
else {
ShortestCycle01 graph(N);
while (M--) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
graph.add_edge(u, v, w);
}
REP(i, N) {
chmin<lint>(ret, graph.Solve(i).first);
dbg(ret);
dbg(graph.dist);
dbg(graph.prev);
}
cout << (ret < 1e18 ? ret : -1) << '\n';
}
}