結果
| 問題 |
No.1442 I-wate Shortest Path Problem
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-03-26 21:46:51 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,146 ms / 3,000 ms |
| コード長 | 10,543 bytes |
| コンパイル時間 | 4,929 ms |
| コンパイル使用メモリ | 226,832 KB |
| 最終ジャッジ日時 | 2025-01-19 22:15:29 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 25 |
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) (x)
#endif
template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1> struct ShortestPath {
int V, E;
bool single_positive_weight;
T wmin, wmax;
std::vector<std::vector<std::pair<int, T>>> to;
ShortestPath(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0), to(V) {}
void add_edge(int s, int t, T w) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
to[s].emplace_back(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);
}
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, INF);
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, 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 (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;
}
};
// lowest common ancestor (LCA) class for undirected weighted tree
// 無向重み付きグラフの最小共通祖先
// <https://yukicoder.me/submissions/392383>
struct UndirectedWeightedTree {
using T = long long; // Arbitrary data structure (operator+, operator- must be defined)
int INVALID = -1;
int V, lgV;
int E;
int root;
std::vector<std::vector<std::pair<int, int>>> adj; // (nxt_vertex, edge_id)
// vector<pint> edge; // edges[edge_id] = (vertex_id, vertex_id)
std::vector<T> weight; // w[edge_id]
std::vector<int> par; // parent_vertex_id[vertex_id]
std::vector<int> depth; // depth_from_root[vertex_id]
std::vector<T> acc_weight; // w_sum_from_root[vertex_id]
void _fix_root_dfs(int now, int prv, int prv_edge_id) {
par[now] = prv;
if (prv_edge_id != INVALID) acc_weight[now] = acc_weight[prv] + weight[prv_edge_id];
for (auto nxt : adj[now])
if (nxt.first != prv) {
depth[nxt.first] = depth[now] + 1;
_fix_root_dfs(nxt.first, now, nxt.second);
}
}
UndirectedWeightedTree() = default;
UndirectedWeightedTree(int N) : V(N), E(0), adj(N) {
lgV = 1;
while (1 << lgV < V) lgV++;
}
void add_edge(int u, int v, T w) {
adj[u].emplace_back(v, E);
adj[v].emplace_back(u, E);
// edge.emplace_back(u, v);
weight.emplace_back(w);
E++;
}
void fix_root(int r) {
root = r;
par.resize(V);
depth.resize(V);
depth[r] = 0;
acc_weight.resize(V);
acc_weight[r] = 0;
_fix_root_dfs(root, INVALID, INVALID);
}
std::vector<std::vector<int>> doubling;
void doubling_precalc() {
doubling.assign(lgV, std::vector<int>(V));
doubling[0] = par;
for (int d = 0; d < lgV - 1; d++)
for (int i = 0; i < V; i++) {
if (doubling[d][i] == INVALID)
doubling[d + 1][i] = INVALID;
else
doubling[d + 1][i] = doubling[d][doubling[d][i]];
}
}
int kth_parent(int x, int k) {
if (depth[x] < k) return INVALID;
for (int d = 0; d < lgV; d++) {
if (x == INVALID) return INVALID;
if (k & (1 << d)) x = doubling[d][x];
}
return x;
}
int lowest_common_ancestor(int u, int v) {
if (depth[u] > depth[v]) std::swap(u, v);
v = kth_parent(v, depth[v] - depth[u]);
if (u == v) return u;
for (int d = lgV - 1; d >= 0; d--) {
if (doubling[d][u] != doubling[d][v]) u = doubling[d][u], v = doubling[d][v];
}
return par[u];
}
T path_length(int u, int v) {
// Not distance, but the sum of weights
int r = lowest_common_ancestor(u, v);
return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]);
}
};
int main() {
int N, K;
cin >> N >> K;
UndirectedWeightedTree tree(N);
ShortestPath<lint> graph(N + K);
REP(i, N - 1) {
int a, b, c;
cin >> a >> b >> c;
a--, b--;
graph.add_edge(a, b, c);
graph.add_edge(b, a, c);
tree.add_edge(a, b, c);
}
tree.fix_root(0);
tree.doubling_precalc();
vector<int> P;
vector<vector<lint>> ds;
REP(k, K) {
int m, p;
cin >> m >> p;
while (m--) {
int x;
cin >> x;
x--;
graph.add_edge(N + k, x, 0);
graph.add_edge(x, N + k, p);
}
P.push_back(p);
}
REP(k, K) {
graph.Dijkstra(N + k);
ds.push_back(graph.dist);
}
vector<vector<lint>> ddd(K, vector<lint>(K));
REP(i, K) REP(j, K) ddd[i][j] = ds[i][N + j];
REP(_, 3) REP(i, K) REP(j, K) REP(k, K) chmin(ddd[j][k], ddd[j][i] + ddd[i][k]);
int Q;
cin >> Q;
while (Q--) {
int u, v;
cin >> u >> v;
u--, v--;
lint ret = tree.path_length(u, v);
REP(i, K) chmin(ret, ds[i][u] + ds[i][v] + P[i]);
REP(i, K) REP(j, K) {
chmin(ret, ds[i][u] + ds[j][v] + ddd[i][j] + P[i]);
}
cout << ret << '\n';
}
}