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#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#include "../../datastructures/sparseTable.cpp"
#include "../LCA_sparse.cpp"
mt19937 rd(0);
void test(const vector<vector<int>> &old_adj, int root) {
int n = old_adj.size();
vector<int> perm(n);
iota(perm.begin(), perm.end(), 0);
ranges::shuffle(perm, rd);
vector<vector<int>> adj(n);
for (int i = 0; i < n; i++) {
auto &a = adj[perm[i]] = old_adj[i];
for (int &v: a) v = perm[v];
ranges::shuffle(a, rd);
}
root = perm[root];
vector<int> parent(n);
function<void(int,int)> dfs = [&](int u, int p) {
parent[u] = p;
for (int v: adj[u]) if (v != p) dfs(v, u);
};
dfs(root, -1);
function<bool(int, int)> is_ancestor = [&](int u, int v) {
while (v != -1 && u != v) v = parent[v];
return u == v;
};
function<int(int)> depth = [&](int v) {
int r = 0;
while ((v = parent[v]) != -1) r++;
return r;
};
LCA lca;
lca.init(adj, root);
for (int i = 0; i < n; i++) assert(lca.getDepth(i) == depth(i));
uniform_int_distribution<int> distrib(0, n-1);
for (int i = 0; i < 1000; i++) {
int u = distrib(rd);
int v = distrib(rd);
int l = lca.getLCA(u, v);
assert(is_ancestor(l, u));
assert(is_ancestor(l, v));
for (int p = parent[l]; int c: adj[l]) {
if (c == p) continue;
assert(!is_ancestor(c, u) || !is_ancestor(c, v));
}
}
}
int main() {
{
// Single vertex
vector<vector<int>> adj(1);
test(adj, 0);
}
{
// Path
vector<vector<int>> adj(100);
for (int i = 1; i < 100; i++) {
adj[i-1].push_back(i);
adj[i].push_back(i-1);
}
test(adj, 0);
test(adj, 99);
test(adj, 40);
}
{
// Random
vector<vector<int>> adj(1000);
for (int i = 1; i < 1000; i++) {
uniform_int_distribution<int> distrib(0, i-1);
int p = distrib(rd);
adj[p].push_back(i);
adj[i].push_back(p);
}
test(adj, 0);
test(adj, 300);
test(adj, 600);
test(adj, 900);
}
}
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