結果
| 問題 |
No.1030 だんしんぐぱーりない
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2020-04-20 02:14:31 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 403 ms / 2,000 ms |
| コード長 | 8,999 bytes |
| コンパイル時間 | 3,686 ms |
| コンパイル使用メモリ | 218,132 KB |
| 最終ジャッジ日時 | 2025-01-09 21:50:44 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 40 |
コンパイルメッセージ
In member function ‘UndirectedWeightedTree& UndirectedWeightedTree::operator=(UndirectedWeightedTree&&)’,
inlined from ‘int main()’ at main.cpp:242:36:
main.cpp:17:8: warning: ‘<anonymous>.UndirectedWeightedTree::root’ may be used uninitialized [-Wmaybe-uninitialized]
17 | struct UndirectedWeightedTree
| ^~~~~~~~~~~~~~~~~~~~~~
main.cpp: In function ‘int main()’:
main.cpp:242:36: note: ‘<anonymous>’ declared here
242 | tree = UndirectedWeightedTree(N);
| ^
ソースコード
#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define REP(i, n) FOR(i,0,n)
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; }
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; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
// 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 int; // Arbitrary data structure (operator+, operator- must be defined)
int INVALID = -1;
int V, lgV;
int E;
int root;
vector<vector<pair<int, int>>> adj; // (nxt_vertex, edge_id)
// vector<pint> edge; // edges[edge_id] = (vertex_id, vertex_id)
vector<T> weight; // w[edge_id]
vector<int> par; // parent_vertex_id[vertex_id]
vector<int> depth; // depth_from_root[vertex_id]
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);
}
vector<vector<int>> doubling;
void doubling_precalc()
{
doubling.assign(lgV, 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]) 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]);
}
};
// Nonrecursive Segment Tree (point-update, range-get)
// - Conditions for operations:
// - datamerge: [TDATA, TDATA] -> TDATA, e(x, y) == e(y, x)
// - data2ret: [TDATA, TQUERY] -> TRET
// - retmerge: [TRET, TRET] -> TRET, g(defaultRET, x) == x, g(x, y) = g(y, x)
// - commutability f(e(x, y), q) == g(f(x, q), f(y, q))
template <typename TDATA, typename TRET, typename TQUERY>
struct NonrecursiveSegmentTree
{
int N;
TRET defaultRET;
virtual TDATA datamerge(const TDATA &, const TDATA &) = 0;
virtual TRET data2ret(const TDATA &, const TQUERY &) = 0;
virtual TRET retmerge(const TRET &, const TRET &) = 0;
std::vector<TDATA> data;
inline TDATA& at(int i) { return data[i]; }
inline void _merge(int i) { at(i) = datamerge(at(i << 1), at((i << 1) + 1)); }
void initialize(const std::vector<TDATA> &seq, TRET RET_ZERO) {
N = seq.size();
defaultRET = RET_ZERO;
data = seq;
data.insert(data.end(), seq.begin(), seq.end());
for (int i = N - 1; i; i--) _merge(i);
}
NonrecursiveSegmentTree() = default;
void update(int pos, const TDATA &x) {
assert(pos >= 0 and pos < N);
at(pos + N) = x;
for (int i = pos + N; i > 1;) i >>= 1, _merge(i);
}
// [l, r), 0-indexed
TRET get(int l, int r, TQUERY query = NULL) {
assert(l >= 0 and r <= N);
TRET retl = defaultRET, retr = defaultRET;
l += N, r += N;
while (l < r) {
if (l & 1) retl = retmerge(retl, data2ret(data[l++], query));
if (r & 1) retr = retmerge(data2ret(data[--r], query), retr);
l >>= 1, r >>= 1;
}
return retmerge(retl, retr);
}
// Calculate smallest r that satisfies g(f(x_l, q), ..., f(x_{r - 1}, q)) >= threshold
// Assumption: Monotonicity of g(x_l, ..., x_r) about r (l: fixed)
// Complexity: O(log N)
int binary_search(int l, const TRET &threshold, TQUERY query = NULL) {
std::stack<int> rs;
l += N;
int r = N * 2;
TRET retl = defaultRET;
if (threshold <= retl) return l - N;
while (l < r) {
if (l & 1) {
TRET ret_tmp = retmerge(retl, data2ret(data[l], query));
if (threshold <= ret_tmp) {
while (l * 2 < N * 2) {
ret_tmp = retmerge(retl, data2ret(data[l * 2], query));
if (threshold <= ret_tmp) l *= 2;
else retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
l++;
retl = ret_tmp;
}
if (r & 1) rs.push(--r);
l >>= 1, r >>= 1;
}
while (!rs.empty()) {
l = rs.top();
rs.pop();
TRET ret_tmp = retmerge(retl, data2ret(data[l], query));
if (threshold <= ret_tmp) {
while (l * 2 < N * 2) {
ret_tmp = retmerge(retl, data2ret(data[l * 2], query));
if (threshold <= ret_tmp) l *= 2;
else retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
retl = ret_tmp;
}
return N;
}
template<typename T1, typename T2, typename T3>
friend std::ostream &operator<<(std::ostream &os, NonrecursiveSegmentTree<T1, T2, T3> s) {
os << "[SegmentTree (len: " << s.N << ')';
for (int i = 0; i < s.N; i++) os << s.at(i + s.N) << ',';
os << "]";
return os;
}
};
UndirectedWeightedTree tree;
// Range Minimum Query
// - get: return min(x_l, ..., x_{r - 1})
struct RangeLCAQuery : public NonrecursiveSegmentTree<int, int, bool>
{
using T = int;
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T datamerge(const T &vl, const T &vr) override {
if (vl == -1) return vr;
if (vr == -1) return vl;
return tree.lowest_common_ancestor(vl, vr);
};
T data2ret(const T &v, const bool &q) override { return v; }
T retmerge(const T &vl, const T &vr) override { return datamerge(vl, vr); };
RangeLCAQuery(const std::vector<T> &seq) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, -1);
};
};
vector<vector<int>> to;
vector<int> C;
void dfs(int now, int par, int am)
{
chmax(C[now], am);
for (auto nxt : to[now]) if (nxt != par) dfs(nxt, now, C[now]);
}
int main()
{
int N, K, Q;
cin >> N >> K >> Q;
tree = UndirectedWeightedTree(N);
C.resize(N);
vector<int> A(K);
cin >> C >> A;
for (auto &a : A) a--;
to.resize(N);
REP(_, N - 1)
{
int e, f;
cin >> e >> f;
e--, f--;
tree.add_edge(e, f, 1);
to[e].push_back(f);
to[f].push_back(e);
}
tree.fix_root(0);
tree.doubling_precalc();
RangeLCAQuery lca(A);
dfs(0, -1, 0);
while (Q--)
{
int t;
cin >> t;
if (t == 1)
{
int X, Y;
cin >> X >> Y;
X--, Y--;
A[X] = Y;
lca.update(X, A[X]);
}
else
{
int L, R;
cin >> L >> R;
cout << C[lca.get(L - 1, R)] << '\n';
}
}
}