F.小Z的樹遷移
思路
賽事沒想出來如何做,可以發現,對於一個節點u,走d步所走的最遠距離即為 深度為depthu+d且位於u的子樹之中的節點距離根節點距離的最大值 再減去節點u距離根節點的距離即為結果
當我們查詢時該如何做?
第一步,我們先給每個節點按照dfs序進行編號,這樣保證了同一子樹的節點的編號在\(l-r\)的一個連續區間內
第二步,把每個節點存進對應的深度容器中,當我們處理一個查詢時,查詢的深度即為depth[u]+d,我們找到對應深度容器,由於容器中滿足條件的點為一段連續的區間,我們可以透過二分查詢這段區間的首尾
第三步,預處理st表維護區間最大值
注意:處理二分邊界條件
牛客官方題解
程式碼
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using piii = pair<int, pii>;
using pll = pair<ll, ll>;
using plll = pair<ll, pll>;
using plii = pair<ll, pii>;
#define fi first
#define se second
const int INF = 0x3f3f3f3f;
const ull mod1 = (1ull << 61) - 1, mod2 = 1e9 + 7;
const ull base1 = 131, base2 = 13331;
// mt19937 rnd(time(0));
const int mod = 998244353;
void solve() {
int n;
cin >> n;
vector<vector<pii>> g(n + 1);
for (int i = 1; i < n; i++) {
int a, b, w;
cin >> a >> b >> w;
g[a].push_back({b, w}), g[b].push_back({a, w});
}
vector<int> depth(n + 1), siz(n + 1);
vector<vector<pair<int, ll>>> tups(n + 1);
vector<ll> dist(n + 1), dfn(n + 1);
int cnt = 0;
auto dfs = [&](auto&& self, int u, int fa) -> void {
dfn[u] = ++cnt;
depth[u] = depth[fa] + 1;
siz[u] = 1;
for (auto [y, w] : g[u]) {
if (y == fa)
continue;
dist[y] = dist[u] + w;
self(self, y, u);
siz[u] += siz[y];
}
};
dfs(dfs, 1, 0);
for (int i = 1; i <= n; i++) {
tups[depth[i]].push_back({dfn[i], dist[i]});
}
for (int i = 1; i <= n; i++) {
auto& v = tups[i];
sort(v.begin(), v.end());
}
vector<vector<vector<ll>>> sts(n + 1);
for (int i = 1; i <= n; i++) {
int len = tups[i].size();
auto& v = sts[i];
auto& data = tups[i];
if (len) {
int flen = log2(len) + 1;
v.resize(len);
for (int j = 0; j < len; j++)
v[j].resize(flen);
for (int j = 0; j < flen; j++) {
for (int k = 0; k + (1 << j) - 1 < len; k++) {
if (j == 0)
v[k][j] = data[k].se;
else {
v[k][j] = max(v[k][j - 1], v[k + (1 << j - 1)][j - 1]);
}
}
}
}
}
auto get = [&](int l, int r, int dep) {
auto& v = sts[dep];
int k = log2(r - l + 1);
// cout<<l<<" "<<r<<" "<<v.size()<<" "<<dep<<" "<<k<<endl;
// cout<<v[0].size()<<endl;
return max(v[l][k], v[r - (1 << k) + 1][k]);
};
int q;
cin >> q;
while (q--) {
int u, d;
cin >> u >> d;
int dep = depth[u] + d;
if (dep > n) {
cout << -1 << endl;
continue;
}
int bg = dfn[u], ed = dfn[u] + siz[u] - 1;
auto& v = tups[dep];
if (v.size() == 0) {
cout << -1 << endl;
continue;
}
int l1 = 0, r1 = v.size() - 1;
while (l1 < r1) {
int mid = l1 + r1 >> 1;
if (v[mid].fi >= bg)
r1 = mid;
else
l1 = mid + 1;
}
int l2 = 0, r2 = v.size() - 1;
while (l2 < r2) {
int mid = l2 + r2 + 1 >> 1;
if (v[mid].fi <= ed)
l2 = mid;
else
r2 = mid - 1;
}
if (l2 < l1) {
cout << -1 << endl;
continue;
}
auto tt = v.front().fi;
if (v.size() == 1 && (tt < bg || tt > ed)) {
cout << -1 << endl;
continue;
}
cout << get(l1, l2, dep) - dist[u] << endl;
}
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
int _ = 1;
// cin >> _;
while (_--) {
solve();
}
return 0;
}