/*
full solution using centroid decomposition and a segment tree ~ O(Qlog^2N)
Author: Erik Sünderhauf
*/
#include <bits/stdc++.h>
#define sz(x) (int)(x).size()
using namespace std;
typedef long long ll;
const int N = 1e6 + 5;
const int LG = 18;
vector<int> adj[N];
struct segtree {
int n;
vector<int> ch, seg;
segtree() {}
void upd(int l, int r, int k, int x, int v) {
if (r < x || x < l) return;
if (x <= l && r <= x) {
seg[k] += v;
return;
}
int m = (l+r) / 2;
upd(l, m, k*2, x, v);
upd(m+1, r, k*2+1, x, v);
seg[k] = seg[k*2] + seg[k*2+1];
}
int qry(int l, int r, int k, int x) {
if (r < x) return 0;
if (x <= l) return seg[k];
int m = (l+r) / 2;
return qry(l, m, k*2, x) + qry(m+1, r, k*2+1, x);
}
void upd(int t) {
int i = lower_bound(ch.begin(), ch.end(), t) - ch.begin();
upd(0, n-1, 1, i, 1);
}
int qry(int t) {
int i = lower_bound(ch.begin(), ch.end(), t) - ch.begin();
return qry(0, n-1, 1, i);
}
void init() {
seg.resize(4*n);
fill(seg.begin(), seg.end(), 0);
}
} seg[N];
// start lca
int lca_par[LG][N], depth[N];
int jump(int u, int d) {
if (d < 0)
return u;
for (int i = 0; i < LG; i++)
if (d >> i & 1)
u = lca_par[i][u];
return u;
}
int lca(int u, int v) {
if (depth[u] > depth[v])
swap(u, v);
v = jump(v, depth[v] - depth[u]);
if (u == v)
return u;
for (int i = LG-1; i >= 0; i--)
if (lca_par[i][u] != lca_par[i][v])
u = lca_par[i][u], v = lca_par[i][v];
return lca_par[0][u];
}
void dfs(int u, int p) {
for (int v: adj[u]) if (v != p) {
depth[v] = depth[u] + 1;
lca_par[0][v] = u;
dfs(v, u);
}
}
// end lca
// start centroid decomposition
int s[N], par[N], vis[N], cd_depth[N];
int getSz(int u, int p) {
s[u] = 1;
for (int v: adj[u])
if (v != p && !vis[v])
s[u] += getSz(v, u);
return s[u];
}
int findCen(int u, int p, int n) {
for (int v: adj[u])
if (v != p && !vis[v] && s[v] > n/2)
return findCen(v, u, n);
return u;
}
void decompose(int c, int p) {
c = findCen(c, -1, getSz(c, -1));
par[c] = p;
cd_depth[c] = ~p ? cd_depth[p] + 1 : 0;
vis[c] = 1;
for (int v: adj[c])
if (!vis[v])
decompose(v, c);
vis[c] = 0;
}
// end centroid decomposition
// start hld
int hvy[N], root[N];
int init_hld(int u, int p) {
s[u] = 1;
hvy[u] = -1;
root[u] = u;
for (int v: adj[u]) {
if (v != p) {
s[u] += init_hld(v, u);
if (hvy[u] < 0 || s[hvy[u]] < s[v])
hvy[u] = v;
}
}
return s[u];
}
// end hld
int hi[N][2], lo[N]; // walk up using edges with (decreasing / increasing) indices or down using edges with decreasing indices
int ind[N], curt = 0; // time when u and lca_par[0][u] where connected
void init(int n, vector<pair<int,int>> e) {
for (auto [u, v]: e) {
adj[u].push_back(v);
adj[v].push_back(u);
}
// cd
decompose(1, -1);
for (int i = 1; i <= n; i++) {
for (int j: adj[i]) {
if (cd_depth[j] > cd_depth[i])
seg[i].n++;
}
seg[i].init();
}
// lca
dfs(1, -1);
for (int i = 1; i < LG; i++)
for (int j = 1; j <= n; j++)
lca_par[i][j] = lca_par[i-1][lca_par[i-1][j]];
// hld
init_hld(1, -1);
for (int i = 1; i <= n; i++)
if (lca_par[0][i] == 0 || hvy[lca_par[0][i]] != i)
for (int j = i; j != -1; j = hvy[j])
root[j] = i;
for (int i = 1; i <= n; i++)
hi[i][0] = hi[i][1] = i, ind[i] = N+1, lo[i] = i;
}
int lower(int u, int v) {
return depth[u] > depth[v] ? v : u;
}
int higher(int u, int v) {
return depth[u] < depth[v] ? v : u;
}
// last node on the path from u to v
int last_node(int u, int v) {
if (u == v)
return u;
int l = lca(u, v);
if (l != v)
return lca_par[0][v];
return jump(u, depth[u] - depth[l] - 1);
}
// last node on the path from u to v
int first_node(int u, int v) {
return last_node(v, u);
}
// when was this edge created?
int get_ind(int u, int v) {
return u == v ? 0 : ind[higher(u, v)];
}
// is there a path from v to u where the indices of all edges increase
bool data(int u, int v) {
if (u == v)
return 1;
int l = lca(u, v);
if (lower(hi[u][0], l) != hi[u][0]) // walk down using increasing labels
return 0;
int x = v, y = -1;
while (root[x] != root[l])
y = root[x], x = lca_par[0][root[x]];
// there is a light edge on the path from v to l -> we updated the whole subtree containing v already
if (x != v && lower(hi[v][1], x) != hi[v][1])
return 0;
// we have to walk from x to l over heavy edges and we might have to check a light edge
if (higher(lo[l], x) != lo[l] || (x != l && y != -1 && get_ind(y, x) > ind[x]))
return 0;
int pu = last_node(u, l), pv = last_node(v, l);
return u == l || v == l || ind[pu] > ind[pv];
}
void xchg(int u, int v) {
++curt;
if (cd_depth[u] > cd_depth[v])
swap(u, v);
if (depth[u] > depth[v])
swap(u, v);
ind[v] = curt;
hi[v][0] = hi[u][0];
if (hvy[u] != v) {
function<void(int,int,int)> mrk = [&](int x, int y, int t) {
hi[x][1] = u;
for (int z: adj[x])
if (z != y && get_ind(x, z) < t)
mrk(z, x, get_ind(x, z));
};
mrk(v, u, curt);
} else {
lo[u] = lo[v];
}
if (cd_depth[u] > cd_depth[v])
swap(u, v);
seg[u].ch.push_back(curt);
// update segment tree
int c = u;
while (c > 0) {
if (data(u, c)) { // walk from c to u and then over the new edge
int fst = first_node(c, u);
if (fst == c)
fst = v;
int t = get_ind(c, fst);
seg[c].upd(t);
}
c = par[c];
}
}
int count(int u) {
int c = u, r = 0;
while (c > 0) {
if (data(c, u)) {
int lst = last_node(u, c);
int t = get_ind(lst, c) + 1;
r += seg[c].qry(t) + 1;
}
c = par[c];
}
return r;
}
int main() {
int n, q; cin >> n >> q;
vector<pair<int,int>> e(n-1);
vector<array<int,3>> qr(n+q-1);
for (int i = 0, j = 0; i < n+q-1; i++) {
char t; int u, v = 0; cin >> t >> u;
assert(t != 'C');
qr[i] = {t == 'C' ? 2 : (t == 'S' ? 0 : 1), u, v};
if (t == 'S')
e[j++] = make_pair(u, v);
}
init(n, e);
for (int i = 0; i < n+q-1; i++) {
int t = qr[i][0], u = qr[i][1], v = qr[i][2];
if (t == 0) {
xchg(u, v);
} else if (t == 1) {
bool b = data(u, v);
cout << (b ? "yes\n" : "no\n");
} else {
int d = count(u);
cout << d << "\n";
}
}
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3572 ms |
80064 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3572 ms |
80064 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3521 ms |
80164 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3521 ms |
80164 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3579 ms |
80084 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3579 ms |
80084 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3538 ms |
80076 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3538 ms |
80076 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3537 ms |
80140 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3537 ms |
80140 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3569 ms |
80168 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
3569 ms |
80168 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
