P6329 【模板】点分树 | 震波[点分树]

点分树就是按照点分治的过程建出来，然后容斥一下.jpg

// powered by c++11
// by Isaunoya
#include <bits/stdc++.h>

#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)
#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

using namespace std;
using db = double;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;

#define pii pair<int, int>
#define fir first
#define sec second

template <class T>

void cmax(T& x, const T& y) {
  if (x < y) x = y;
}

template <class T>

void cmin(T& x, const T& y) {
  if (x > y) x = y;
}

#define all(v) v.begin(), v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back

template <class T>

void sort(vector<T>& v) {
  sort(all(v));
}

template <class T>

void reverse(vector<T>& v) {
  reverse(all(v));
}

template <class T>

void unique(vector<T>& v) {
  sort(all(v)), v.erase(unique(all(v)), v.end());
}

void reverse(string& s) { reverse(s.begin(), s.end()); }

const int io_size = 1 << 23 | 233;
const int io_limit = 1 << 22;
struct io_in {
  char ch;
#ifndef __WIN64
  char getchar() {
    static char buf[io_size], *p1 = buf, *p2 = buf;

    return (p1 == p2) && (p2 = (p1 = buf) + fread(buf, 1, io_size, stdin), p1 == p2) ? EOF : *p1++;
  }
#endif
  io_in& operator>>(char& c) {
    for (c = getchar(); isspace(c); c = getchar())
      ;

    return *this;
  }
  io_in& operator>>(string& s) {
    for (s.clear(); isspace(ch = getchar());)
      ;

    if (!~ch) return *this;

    for (s = ch; !isspace(ch = getchar()) && ~ch; s += ch)
      ;

    return *this;
  }

  io_in& operator>>(char* str) {
    char* cur = str;
    while (*cur) *cur++ = 0;

    for (cur = str; isspace(ch = getchar());)
      ;
    if (!~ch) return *this;

    for (*cur = ch; !isspace(ch = getchar()) && ~ch; *++cur = ch)
      ;

    return *++cur = 0, *this;
  }

  template <class T>

  void read(T& x) {
    bool f = 0;
    while ((ch = getchar()) < 48 && ~ch) f ^= (ch == 45);

    x = ~ch ? (ch ^ 48) : 0;
    while ((ch = getchar()) > 47) x = x * 10 + (ch ^ 48);
    x = f ? -x : x;
  }

  io_in& operator>>(int& x) { return read(x), *this; }

  io_in& operator>>(ll& x) { return read(x), *this; }

  io_in& operator>>(uint& x) { return read(x), *this; }

  io_in& operator>>(ull& x) { return read(x), *this; }

  io_in& operator>>(db& x) {
    read(x);
    bool f = x < 0;
    x = f ? -x : x;
    if (ch ^ '.') return *this;

    double d = 0.1;
    while ((ch = getchar()) > 47) x += d * (ch ^ 48), d *= .1;
    return x = f ? -x : x, *this;
  }
} in;

struct io_out {
  char buf[io_size], *s = buf;
  int pw[233], st[233];

  io_out() {
    set(7);
    rep(i, pw[0] = 1, 9) pw[i] = pw[i - 1] * 10;
  }

  ~io_out() { flush(); }

  void io_chk() {
    if (s - buf > io_limit) flush();
  }

  void flush() { fwrite(buf, 1, s - buf, stdout), fflush(stdout), s = buf; }

  io_out& operator<<(char c) { return *s++ = c, *this; }

  io_out& operator<<(string str) {
    for (char c : str) *s++ = c;
    return io_chk(), *this;
  }

  io_out& operator<<(char* str) {
    char* cur = str;
    while (*cur) *s++ = *cur++;
    return io_chk(), *this;
  }

  template <class T>

  void write(T x) {
    if (x < 0) *s++ = '-', x = -x;

    do {
      st[++st[0]] = x % 10, x /= 10;
    } while (x);

    while (st[0]) *s++ = st[st[0]--] ^ 48;
  }

  io_out& operator<<(int x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ll x) { return write(x), io_chk(), *this; }

  io_out& operator<<(uint x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ull x) { return write(x), io_chk(), *this; }

  int len, lft, rig;

  void set(int _length) { len = _length; }

  io_out& operator<<(db x) {
    bool f = x < 0;
    x = f ? -x : x, lft = x, rig = 1. * (x - lft) * pw[len];
    return write(f ? -lft : lft), *s++ = '.', write(rig), io_chk(), *this;
  }
} out;

const int maxn = 2e5 + 52;

struct smt {
  int ls[maxn << 7], rs[maxn << 7], val[maxn << 7];
  int rt[maxn], frt[maxn], cnt;
	// rt_i 这棵线段树存的是离 i 节点的距离/权值
	// frt_i 这棵线段树存的是离 fa_i 这个节点的距离/权值
	 
  smt() { cnt = 0; }

  void upd(int& p, int l, int r, int x, int v) {
    if (!p) p = ++cnt;
    val[p] += v;
    if (l == r) {
      return;
    }
    int mid = l + r >> 1;
    if (x <= mid) {
      upd(ls[p], l, mid, x, v);
    } else {
      upd(rs[p], mid + 1, r, x, v);
    }
  }

  int qry(int p, int a, int b, int l, int r) {
    if (!p) {
      return 0;
    }
    if (a <= l && r <= b) {
      return val[p];
    }
    int mid = l + r >> 1, ans = 0;
    if (a <= mid) {
      ans += qry(ls[p], a, b, l, mid);
    }
    if (b > mid) {
      ans += qry(rs[p], a, b, mid + 1, r);
    }
    return ans;
  }
} smt;

vector<int> g[maxn];
pii st[maxn][22];
int dfn[maxn], idx = 0, dep[maxn];
void dfs(int u, int fa) {
  st[dfn[u] = ++idx][0] = pii(dep[u], u);
  for (int v : g[u])
    if (v ^ fa) {
      dep[v] = dep[u] + 1;
      dfs(v, u);
      st[++idx][0] = pii(dep[u], u);
    }
}

int mx[maxn], sz[maxn], vis[maxn], tot, rt;
void getroot(int u, int fa) {
  sz[u] = 1, mx[u] = 0;
  for (int v : g[u])
    if (!vis[v] && v ^ fa) {
      getroot(v, u);
      sz[u] += sz[v];
      cmax(mx[u], sz[v]);
    }
  cmax(mx[u], tot - sz[u]);
  if (mx[u] < mx[rt]) rt = u;
}

int d[maxn], mxd;
void getdis(int u, int fa) {
  cmax(mxd, d[u] = d[fa] + 1);
  for (int v : g[u])
    if (!vis[v] && v ^ fa) {
      getdis(v, u);
    }
}

int qwq[maxn], fa[maxn];
void solve(int u) {
  vis[u] = 1, mxd = 0;
  getdis(u, 0), qwq[u] = mxd;
  for (int v : g[u]) {
    if (!vis[v]) {
      tot = sz[v], rt = 0;
      getroot(v, 0);
      fa[rt] = u, solve(rt);
    }
  }
}

int lg[maxn];
int lca(int x, int y) {
  if ((x = dfn[x]) > (y = dfn[y])) {
    x ^= y ^= x ^= y;
  }
  int len = lg[y - x + 1];
  return min(st[x][len], st[y - (1 << len) + 1][len]).second;
}
int dis(int x, int y) { return dep[x] + dep[y] - (dep[lca(x, y)] << 1); }

int n, m;
int val[maxn];

void change(int x, int v) {
  int now = x;
  while (now) {
    smt.upd(smt.rt[now], 0, qwq[now], dis(now, x), v);
    if (fa[now]) {
      smt.upd(smt.frt[now], 0, qwq[fa[now]], dis(fa[now], x), v);
    }
    now = fa[now];
  }
}

int qry(int x, int k) {
  int ans = 0, now = x;
  while (now) {
    if (dis(now, x) <= k) {
      ans += smt.qry(smt.rt[now], 0, k - dis(now, x), 0, qwq[now]);
      // 你只能加上离 now 不超过 k - dis(now,x) 的点 
    }
    if (fa[now] && dis(x, fa[now]) <= k) {
      ans -= smt.qry(smt.frt[now], 0, k - dis(fa[now], x), 0, qwq[fa[now]]);
      // 减掉离 fa[now] 不超过 k - dis(fa[now],x) 的点，做容斥
    }
    now = fa[now];
  }
  return ans;
}

signed main() {
  // code begin.
  in >> n >> m;
  rep(i, 1, n) { in >> val[i]; }
  rep(i, 2, n) {
    int u, v;
    in >> u >> v;
    g[u].pb(v), g[v].pb(u);
  }
  dfs(1, 0);
  rep(i, 2, idx) lg[i] = lg[i >> 1] + 1;
  rep(j, 1, lg[idx]) {
    rep(i, 1, idx - (1 << j) + 1) st[i][j] = min(st[i][j - 1], st[i + (1 << j - 1)][j - 1]);
  }
  mx[rt = 0] = 1e9, tot = n;
  getroot(1, 0), solve(rt);
  rep(i, 1, n) {
    int now = i;
    while (now) {
      smt.upd(smt.rt[now], 0, qwq[now], dis(now, i), val[i]); 
      if (fa[now]) {
        smt.upd(smt.frt[now], 0, qwq[fa[now]], dis(fa[now], i), val[i]);
      }
      now = fa[now];
    }
  }
  int ans = 0;
  while (m--) {
    int opt, x, y;
    in >> opt >> x >> y;
    x ^= ans, y ^= ans;
    if (!opt) {
      out << (ans = qry(x, y)) << '
';
    } else {
      change(x, y - val[x]), val[x] = y;
    }
  }
  return 0;
  // code end.
}