点分治学习笔记 / 洛谷 P3806【点分治】

点分治算法实际上可以分成几个步骤：

Step $1$：将经过当前的根节点的路径处理好。

Step $2$：找到当前子树的重心。

Step $3$：由于树可以自由变换根节点，所以用重心来替换根节点，进行优化。

Step $4$：删除根节点。

Step $5$：递归枚举儿子节点。

由于某些原因，洛谷模板题需要提前预处理。

#include 

using namespace std;

const int N = 1e4 + 10;
int e[N << 1], ne[N << 1], w[N << 1], h[N], idx = 0;
int q[N];
bool vis[N], ans[N], jud[10000010];
int mx[N], sz[N], td[N], dis[N];
int n, m, root = 1, sumtree, cnt;

int reader()
{
  int opt = 1, x;
  char ch;
  while (!isdigit(ch = getchar()))
    if (ch == '-')
      opt = -1;
  x = ch - '0';
  while (isdigit(ch = getchar()))
    x = (x << 3) + (x << 1) + (ch ^ 48);
  return x * opt;
}

void init_edge()
{
  memset (h, -1, sizeof h);
  idx = 0;
}

void add_edge(int u, int v, int c)
{
  e[idx] = v;
  ne[idx] = h[u];
  w[idx] = c;
  h[u] = idx ++;
}

void get_bc(int u, int fa)
{
  sz[u] = 1;
  mx[u] = 0;
  for (int i = h[u]; ~i; i = ne[i])
  {
    int v = e[i];
    if (v != fa && !vis[v])
    {
      get_bc(v, u);
      sz[u] += sz[v];
      mx[u] = max(mx[u], sz[v]);
    }
  }
  mx[u] = max(mx[u], sumtree - sz[u]);
  if (mx[u] < mx[root])
    root = u;
}

void get_real_bc()
{
  get_bc(1, 0);
  get_bc(root, 0);
}

void get_dis(int u, int fa)
{
  td[++ cnt] = dis[u];
  for (int i = h[u]; ~i; i = ne[i])
  {
    int v = e[i];
    if (!vis[v] && v != fa)
    {
      dis[v] = dis[u] + w[i];
      get_dis(v, u);
    }
  }
}

void solve(int u)
{
  queue <int> que;
  for (int i = h[u]; ~i; i = ne[i])
  {
    int v = e[i];
    if (!vis[v])
    {
      cnt = 0;
      dis[v] = w[i];
      get_dis(v, u);
      for (int j = 1; j <= cnt; j ++)
        for (int k = 1; k <= m; k ++)
          if (q[k] >= td[j])
            ans[k] |= jud[q[k] - td[j]];
      for (int j = 1; j <= cnt; j ++)
        if (td[j] <= 1e7)
          que.push(td[j]);
      for (int j = 1; j <= cnt; j ++)
        if (td[j] <= 1e7)
          jud[td[j]] = true;
    }
  }
  while (que.size())
  {
    jud[que.front()] = false;
    que.pop();
  }
}

void initfs(int u)
{
  vis[u] = jud[0] = true;
  solve(u);
  for (int i = h[u]; ~i; i = ne[i])
  {
    int v = e[i];
    if (!vis[v])
    {
      mx[root = 0] = sumtree = sz[v];
      get_bc(v, 0);
      get_bc(root, 0);
      initfs(root);
    }
  }
}

int main()
{
  init_edge();
  n = reader(), m = reader();
  for (int i = 1; i < n; i ++)
  {
    int u = reader(), v = reader(), w = reader();
    add_edge(u, v, w);
    add_edge(v, u, w);
  }
  for (int i = 1; i <= m; i ++)
    q[i] = reader();
  mx[root = 0] = sumtree = n;
  get_real_bc();
  initfs(root);
  for (int i = 1; i <= m; i ++)
    if (ans[i])
      cout << "AYE\n";
    else
      cout << "NAY\n";
  return 0;
}

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