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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#946616 | #9805. Guide Map | ji_114514 | TL | 1ms | 5736kb | C++20 | 3.7kb | 2025-03-22 00:35:30 | 2025-03-22 00:35:31 |
Judging History
answer
#include<bits/stdc++.h>
#define ll long long
using namespace std;
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
struct DSU {
std::vector<int> f, siz;
DSU() {}
DSU(int n) {
init(n);
}
void init(int n) {
f.resize(n);
std::iota(f.begin(), f.end(), 0);
siz.assign(n, 1);
}
int find(int x) {
while (x != f[x]) {
x = f[x] = f[f[x]];
}
return x;
}
bool same(int x, int y) {
return find(x) == find(y);
}
bool merge(int x, int y) {
x = find(x);
y = find(y);
if (x == y) {
return false;
}
siz[x] += siz[y];
f[y] = x;
return true;
}
int size(int x) {
return siz[find(x)];
}
};
const int N = 2e5 + 10, mod = 998244353;
ll qmi(ll a, ll k) {
ll res = 1;
while (k) {
if (k & 1)res = res * a % mod;
k >>= 1;
a = a * a % mod;
}
return res;
}
int ln[N * 30], rn[N * 30], idx, cnt[N * 30], root[N];
void insert(int &u, int v, int l, int r, int x) {
u = ++idx;
cnt[u] = cnt[v] + 1, ln[u] = ln[v], rn[u] = rn[v];
if (l == r)return;
int mid = l + r >> 1;
if (x > mid)insert(rn[u], rn[v], mid + 1, r, x);
else insert(ln[u], ln[v], l, mid, x);
}
int query(int u, int v, int l, int r, int x, int y) {
if (l > y || r < x)return 0;
if (l >= x && r <= y)return cnt[u] - cnt[v];
int mid = l + r >> 1;
return query(ln[u], ln[v], l, mid, x, y) + query(rn[u], rn[v], mid + 1, r, x, y);
}
int n, rt, pa[N], dfn[N], sz[N], tot;
vector<int>e[N];
ll f[N], sum;
//就是个细节问题其实好说,自己的儿子比自己打也好说,不过好像是主席树写的有点问题说实话。
void dfs1(int u) {
if (pa[u]) {
e[u].erase(find(e[u].begin(), e[u].end(), pa[u]));
}
dfn[u] = ++tot, sz[u] = 1;
insert(root[dfn[u]], root[dfn[u] - 1], 1, n, u);
for (auto v : e[u]) {
pa[v] = u;
dfs1(v);
sz[u] += sz[v];
}
f[u] = query(root[dfn[u] + sz[u] - 1], root[dfn[u] - 1], 1, n, u + 1, n);
for (auto v : e[u])f[u] += f[v];//f[u] 做了个子树和
}
//换根将另外一边处理为对整棵树
//大概我们希望的就是以某个点为根,就是那个意思反正。
//比如一开始的f[root] 对答案的贡献大概就是 2^(f[root])
//然后我们需要的就是若干2的幂次和
void dfs2(int u) {
sum = (sum + qmi(2, f[u])) % mod;
//cout << u << ' ' << f[u] << "!\n";
for (auto v : e[u]) {
f[v] = f[u];
//还挺简单的说实话。
f[v] -= query(root[dfn[v] + sz[v] - 1], root[dfn[v] - 1], 1, n, u + 1, n);
f[v] += query(root[dfn[v] - 1], root[dfn[rt] - 1], 1, n, v + 1, n) + query(root[n], root[dfn[v] + sz[v] - 1], 1, n, v + 1, n);
dfs2(v);
}
}
ll base, res;
//然后这个dfs就动态更新答案就好了,反正要处理好base啥的
//都套用一个主席树算了,懒得写了
//突然意识到一个严重的问题,我们query的其实是指数对吧。
void dfs3(int u) {
res = (res + qmi(2, base) * sum) % mod;
// cout << u << ' ' << base << ' ' << sum << ' ' << res << endl;
for (auto v : e[u]) {
//进入加入贡献
ll temp = query(root[dfn[rt] + sz[rt]], root[dfn[rt] - 1], 1, n, v + 1, n);
base += temp;
dfs3(v);
base -= temp;
}
}
void solve()
{
cin >> n;
DSU dsu(n + 1);
for (int i = 0; i < n - 2; i++) {
int u, v; cin >> u >> v;
e[u].push_back(v);
e[v].push_back(u);
dsu.merge(u, v);
}
for (int i = 1; i <= n; i++) {
if (!dsu.same(i, 1)) {
rt = i;
break;
}
}
dfs1(1), dfs1(rt);
dfs2(rt);
if (sz[rt] == 1)res = (res + qmi(2, base)) % mod;
base = f[1] - (sz[1] - 1);
dfs3(1);
//不要注意漏判孤立点
cout << (res + mod) % mod << '\n';
}
int main()
{
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
int t = 1;
while (t--)solve();
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 5736kb
input:
4 1 4 2 3
output:
6
result:
ok 1 number(s): "6"
Test #2:
score: 0
Accepted
time: 1ms
memory: 5732kb
input:
2
output:
2
result:
ok 1 number(s): "2"
Test #3:
score: -100
Time Limit Exceeded
input:
4 1 2 1 3