倍增LCA受到启发的一题

#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10, INF = 0x3f3f3f3f;
vector<int>g[N];
int n, m;
char s[N];
int fa[N][20];
int dep[N];
bool dp[N][20][2];//i走2^j步有没有经过1,0 转移方程 g[i,j,op]|=g[i,j-1,op]|g[fa[i,j-1],j-1,op];
int book[N];
int k;
void bfs(int root)
{
  memset(dep, 0x3f, sizeof(dep));
  dep[root] = 1;
  dep[0] = 0;
  queue<int>q;
  q.push(root);
  while (q.size())
  {
    int t = q.front();
    q.pop();
    for (auto x : g[t])
    {
      if (dep[x] > dep[t] + 1)
      {
        dep[x] = dep[t] + 1;
        q.push(x);
        fa[x][0] = t;
        dp[x][0][book[t]] = 1;
        for (int i = 1; i <= k; i++)
        {
          fa[x][i] = fa[fa[x][i - 1]][i - 1];
          dp[x][i][1] |= (dp[x][i - 1][1] | dp[fa[x][i - 1]][i - 1][1]);
          dp[x][i][0] |= (dp[x][i - 1][0] | dp[fa[x][i - 1]][i - 1][0]);
        }
      }
    }
  }
}
bool lca(int a, int b, bool f)
{
  if (dep[a] < dep[b]) swap(a, b);
  bool res = 0;
  for (int i = k; i >= 0; i--)
  {
    if (dep[fa[a][i]] >= dep[b])
    {
      res |= dp[a][i][f];
      a = fa[a][i];
    }
  }
  if (a == b)
  {
    return res;
  }
  for (int i = k; i >= 0; i--)
  {
    if (fa[a][i] != fa[b][i])
    {
      res |= dp[a][i][f];
      res |= dp[b][i][f];
      a = fa[a][i];
      b = fa[b][i];
    }
  }
  res |= dp[a][0][f];
  res |= dp[b][0][f];
  return res;
}
void solve()
{
  cin >> n >> m;
  cin >> s + 1;
  k = (int)(log(n) / log(2)) + 1;
  for (int i = 1; i <= n; i++)
  {
    if (s[i] == 'H') book[i] = 1;
    for (int j = 0; j <= k; j++)
      dp[i][j][book[i]] = 1;
  }
  for (int i = 1; i < n; i++)
  {
    int a, b;
    cin >> a >> b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  bfs(1);
  for (int i = 1; i <= m; i++)
  {
    int x, y;
    char t;
    bool f = 0;
    cin >> x >> y >> t;
    if (t == 'H') f = 1;
    if (x == y)
    {
      cout << (book[x] == f);
    }
    else
    {
      bool res = lca(x, y, f);
      cout << res;
    }
  }
}
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int __ = 1;
  //cin>>__;
  while (__--)
  {
    solve();
  }
  return 0;
}