LCA_with_prefix_precomputation.cpp

// Problem :
// https://www.hackerearth.com/practice/algorithms/dynamic-programming/2-dimensional/practice-problems/algorithm/killjee-and-saraff-35617645/

#include "bits/stdc++.h"
#define sz(x) (int)(x.size())
using namespace std;

const int N = 2e5 + 5, LG = 19;

int tim = 0;
int parent[LG][N];
int tin[N], tout[N], level[N];
std::vector<int> g[N];
int n, q, pref[N];
bool prime[N];

void dfs(int k, int par, int lvl) {
  tin[k] = ++tim;
  parent[0][k] = par;
  level[k] = lvl;
  for (auto it : g[k]) {
    if (it == par)
      continue;
    dfs(it, k, lvl + 1);
  }
  tout[k] = tim;
}

void precompute() {
  for (int i = 1; i < LG; i++)
    for (int j = 1; j <= n; j++)
      if (parent[i - 1][j])
        parent[i][j] = parent[i - 1][parent[i - 1][j]];
}

int LCA(int u, int v) {
  if (level[u] < level[v])
    swap(u, v);
  int diff = level[u] - level[v];
  for (int i = LG - 1; i >= 0; i--) {
    if ((1 << i) & diff) {
      u = parent[i][u];
    }
  }
  if (u == v)
    return u;
  for (int i = LG - 1; i >= 0; i--) {
    if (parent[i][u] && parent[i][u] != parent[i][v]) {
      u = parent[i][u];
      v = parent[i][v];
    }
  }
  return parent[0][u];
}

void dfs2(int node, int par, int cnt) {
  pref[node] = cnt;
  for (int child : g[node])
    if (child != par) {
      dfs2(child, node, cnt + prime[child]);
    }
}

int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);

  fill(prime + 2, prime + N, true);
  for (int i = 2; i < N; i++)
    if (prime[i]) {
      for (int j = 2 * i; j < N; j += i)
        prime[j] = false;
    }

  cin >> n;
  for (int i = 1, u, v; i < n; i++) {
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  dfs(1, 0, 1);
  precompute();
  dfs2(1, 0, 0);

  cin >> q;
  while (q--) {
    int u, v;
    cin >> u >> v;
    int L = LCA(u, v);
    int ans = pref[u] + pref[v] - 2 * pref[L] + (prime[L]);
    cout << ans << '\n';
  }
}