Link-Cut-Tree题目泛做（为了对应自己的课件）

题目1：BZOJ 2049 洞穴勘测

#include <bits/stdc++.h>
#define L(x) c[x][0]
#define R(x) c[x][1]
 
using namespace std;
 
const int oo = 0x3f3f3f3f;
 
struct SplayTree{
  static const int N = 10000 + 5;
 
  int top, st[N];
  int fa[N], c[N][2], sum[N], mx[N], val[N];
  bool rev[N];
   
  bool isroot(int x){
    return L(fa[x]) != x && R(fa[x]) != x;
  }
 
  void pushdown(int x){
    int l = L(x), r = R(x);
 
    if(rev[x]){
      rev[x] ^= 1; rev[l] ^= 1; rev[r] ^= 1;
      swap(L(x), R(x));
    }
  }
 
  void pushup(int x){
    int l = L(x), r = R(x);
 
    sum[x] = sum[l] + sum[r] + val[x];
    mx[x] = max(val[x], max(mx[l], mx[r]));
  }
 
  void rotate(int x){
    int y = fa[x], z = fa[y], l, r;
 
    l = (L(y) == x) ^ 1; r = l ^ 1;
    if(!isroot(y))
      c[z][(L(z) == y) ^ 1] = x;
    fa[x] = z; fa[y] = x; fa[c[x][r]] = y;
    c[y][l] = c[x][r]; c[x][r] = y;
  }
 
  void splay(int x){
    top = 0;
    st[++ top] = x;
    for(int i = x; !isroot(i); i = fa[i])
      st[++ top] = fa[i];
    while(top) pushdown(st[top --]);
    while(!isroot(x)){
      int y = fa[x], z = fa[y];
 
      if(!isroot(y)){
        if(L(y) == x ^ L(z) == y) rotate(x);
        else rotate(y);
      }
      rotate(x);
    }
  }
}Splay;
 
struct LinkCutTree{
 
  void Access(int x){
    int t = 0;
 
    while(x){
      Splay.splay(x);
      Splay.R(x) = t;
      t = x; x = Splay.fa[x];
    }
  }
 
  void makeroot(int x){
    Access(x); Splay.splay(x); Splay.rev[x] ^= 1;
  }
 
  void link(int x, int y){
    makeroot(x); Splay.fa[x] = y; Splay.splay(x);
  }
 
  void cut(int x, int y){
    makeroot(x); Access(y); Splay.splay(y);
    Splay.L(y) = Splay.fa[x] = 0;
  }
 
  int findroot(int x){
    Access(x); Splay.splay(x);
    int y = x;
    while(Splay.L(y)) y = Splay.L(y);
 
    return y;
  }
}lct;
 
int n, m, x, y;
char str[10];
 
int main(){
  scanf("%d%d", &n, &m);
  for(int i = 1; i <= m; ++ i){
    scanf("%s%d%d", str, &x, &y);
 
    if(str[0] == 'C') lct.link(x, y);
    else if(str[0] == 'D') lct.cut(x, y);
    else{
      if(lct.findroot(x) == lct.findroot(y)) printf("Yes
");
      else printf("No
");
    }
  }
 
  return 0;
}

题目2： BZOJ 1180 OTOCI

#include <bits/stdc++.h>
#define L(x) c[x][0]
#define R(x) c[x][1]
 
using namespace std;
 
typedef long long ll;
const int N = 30000 + 5;
const int oo = 0x3f3f3f3f;
 
struct SplayTree{
  int fa[N], c[N][2];
  ll val[N], mx[N], sum[N];
  bool rev[N];
  int top, st[N];
 
  inline bool isroot(int x){
    return L(fa[x]) != x && R(fa[x]) != x;
  }
 
  void pushdown(int x){
    int l = L(x), r = R(x);
 
    if(rev[x]){
      rev[x] ^= 1; rev[l] ^= 1; rev[r] ^= 1;
      swap(L(x), R(x));
    }
  }
 
  void pushup(int x){
    int l = L(x), r = R(x);
 
    sum[x] = sum[l] + sum[r] + val[x];
    mx[x] = max(val[x], max(mx[l], mx[r]));
  }
 
  void rotate(int x){
    int y = fa[x], z = fa[y], l, r;
 
    l = (L(y) == x) ^ 1; r = l ^ 1;
    if(!isroot(y)){
      c[z][(L(z) == y) ^ 1] = x;
    }
    fa[x] = z; fa[y] = x; fa[c[x][r]] = y;
    c[y][l] = c[x][r]; c[x][r] = y;
    pushup(y); pushup(x);
  }
 
  void splay(int x){
    top = 0;
    st[++ top] = x;
 
    for(int i = x; !isroot(i); i = fa[i])
      st[++ top] = fa[i];
    while(top) pushdown(st[top --]);
    while(!isroot(x)){
      int y = fa[x], z = fa[y];
 
      if(!isroot(y)){
        if(L(y) == x ^ L(z) == y) rotate(x);
        else rotate(y);
      }
      rotate(x);
    }
  }
}Splay;
 
struct LinkCutTree{
  void Access(int x){
    int t = 0;
 
    while(x){
      Splay.splay(x);
      Splay.R(x) = t;
      t = x;
      Splay.pushup(x);
      x = Splay.fa[x];
    }
  }
 
  void makeroot(int x){
    Access(x); Splay.splay(x); Splay.rev[x] ^= 1;
  }
 
  void link(int x, int y){
    makeroot(x); Splay.fa[x] = y; Splay.splay(x);
  }
 
  void cut(int x, int y){
    makeroot(x); Access(y); Splay.splay(y);
    Splay.L(y) = Splay.fa[x] = 0;
  }
 
  int findroot(int x){
    Access(x); Splay.splay(x);
 
    int y = x;
 
    while(Splay.L(y)){
      y = Splay.L(y);
    }
 
    return y;
  }
}lct;
 
int n, m, x, y;
char str[20];
 
int main(){
  scanf("%d", &n);
  for(int i = 1; i <= n; ++ i){
    scanf("%lld", &Splay.val[i]);
    Splay.sum[i] = Splay.val[i];
  }
  scanf("%d", &m);
  for(int i = 1; i <= m; ++ i){
    scanf("%s%d%d", str, &x, &y);
 
    if(str[0] == 'b'){
      if(lct.findroot(x) == lct.findroot(y))
        puts("no");
      else{
        puts("yes"); lct.link(x, y);
      } 
    }
    else if(str[0] == 'e'){
      if(lct.findroot(x) != lct.findroot(y)){
        puts("impossible");
      }
      else{
        lct.makeroot(x); lct.Access(y); Splay.splay(y);
        printf("%lld
", Splay.sum[y]);
      }
    }
    else{
      lct.makeroot(x); Splay.val[x] = y; Splay.pushup(x);
    }
  }
 
  return 0;
}

题目3：BZOJ 3282 TREE

#include <bits/stdc++.h>
#define L(x) c[x][0]
#define R(x) c[x][1]
 
using namespace std;
 
const int N = 300000 + 5;
 
struct SplayTree{
  int fa[N], c[N][2], val[N], sum[N];
  bool rev[N];
  int top, st[N];
 
  inline bool isroot(int x){
    return L(fa[x]) != x && R(fa[x]) != x;
  }
 
  void pushup(int x){
    int l = L(x), r = R(x);
 
    sum[x] = sum[l] ^ sum[r] ^ val[x];
  }
  void pushdown(int x){
    int l = L(x), r = R(x);
 
    if(rev[x]){
      rev[x] ^= 1; rev[l] ^= 1; rev[r] ^= 1;
      swap(L(x), R(x));
    }
  }
  void rotate(int x){
    int y = fa[x], z = fa[y], l, r;
 
    l = (L(y) == x) ^ 1; r = l ^ 1;
 
    if(!isroot(y)){
      c[z][(L(z) == y) ^ 1] = x;
    }
    fa[y] = x; fa[x] = z; fa[c[x][r]] = y;
    c[y][l] = c[x][r]; c[x][r] = y;
    pushup(y); pushup(x);
  }
 
  void splay(int x){
    top = 0;
    st[++ top] = x;
    for(int i = x; !isroot(i); i = fa[i])
      st[++ top] = fa[i];
 
    while(top) pushdown(st[top --]);
    while(!isroot(x)){
      int y = fa[x], z = fa[y];
 
      if(!isroot(y)){
        if(L(y) == x ^ L(z) == y) rotate(x);
        else rotate(y);
      }
      rotate(x);
    }
  }
}Splay;
 
struct LinkCutTree{
  void Access(int x){
    int t = 0;
 
    while(x){
      Splay.splay(x);
      Splay.R(x) = t;
      t = x;
      Splay.pushup(x);
      x = Splay.fa[x];
    }
  }
 
  void makeroot(int x){
    Access(x); Splay.splay(x); Splay.rev[x] ^= 1;
  }
 
  int findroot(int x){
    Access(x); Splay.splay(x);
 
    int y = x;
 
    while(Splay.L(y)) y = Splay.L(y);
 
    return y;
  }
 
  void link(int x, int y){
    makeroot(x); Splay.fa[x] = y; Splay.splay(x);
  }
 
  void cut(int x, int y){
    makeroot(x); Access(y); Splay.splay(y);
    Splay.L(y) = Splay.fa[x] = 0;
  }
}lct;
 
int n, m;
int x, y, z;
 
int main(){
  scanf("%d%d", &n, &m);
  for(int i = 1; i <= n; ++ i){
    scanf("%d", &Splay.val[i]);
    Splay.sum[i] = Splay.val[i];
  }
  for(int i = 1; i <= m; ++ i){
    scanf("%d%d%d", &z, &x, &y);
 
    switch(z){
    case 0:{
      lct.makeroot(x); lct.Access(y); Splay.splay(y);
      printf("%d
", Splay.sum[y]);
      break;
    }
    case 1:{
      if(lct.findroot(x) != lct.findroot(y)){
        lct.link(x, y);
      }
      break;
    }
    case 2:{
      if(lct.findroot(x) == lct.findroot(y)){
        lct.cut(x, y);
      }
      break;
    }
    case 3:{
      lct.Access(x); Splay.splay(x); Splay.val[x] = y;
      Splay.pushup(x);
      break;
    }
    }
  }
 
  return 0;
}

题目4： HDU 4010 Query On The Trees

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <iostream>
#define L(x) c[x][0]
#define R(x) c[x][1]

using namespace std;

const int N = 300000 + 5;
const int oo = 0x3f3f3f3f;

int n, m, tot;
int first[N], nxt[N<<1];
int u[N<<1], v[N<<1];
int que[N<<1];

struct SplayTree{
  int fa[N], c[N][2], val[N], mx[N], add[N];
  bool rev[N];
  int top, st[N];

  inline bool isroot(int x){
    return L(fa[x]) != x && R(fa[x]) != x;
  }

  void pushup(int x){
    int l = L(x), r = R(x);
    
    mx[x] = max(mx[l], mx[r]);
    mx[x] = max(mx[x], val[x]);
  }
  
  void pushdown(int x){
    int l = L(x), r = R(x);

    if(rev[x]){
      rev[x] ^= 1; rev[l] ^= 1; rev[r] ^= 1;
      swap(L(x), R(x));
    }
    if(add[x]){
      if(l){
        add[l] += add[x]; mx[l] += add[x]; val[l] += add[x];
      }
      if(r){
        add[r] += add[x]; mx[r] += add[x]; val[r] += add[x];
      }
      add[x] = 0;
    }
  }

  void rotate(int x){
    int y = fa[x], z = fa[y], l, r;

    l = (L(y) == x) ^ 1; r = l ^ 1;
    if(!isroot(y)){
      c[z][L(z) == y ^ 1] = x;
    }
    fa[x] = z; fa[y] = x; fa[c[x][r]] = y;
    c[y][l] = c[x][r]; c[x][r] = y;
    pushup(y); pushup(x);
  }

  void splay(int x){
    top = 0;
    st[++ top] = x;
    for(int i = x; !isroot(i); i = fa[i])
      st[++ top] = fa[i];
    while(top) pushdown(st[top --]);
    while(!isroot(x)){
      int y = fa[x], z = fa[y];

      if(!isroot(y)){
        if(L(y) == x ^ L(z) == y) rotate(x);
        else rotate(y);
      }
      rotate(x);
    }
  }
}Splay;

struct LinkCutTree{
  void Access(int x){
    int t = 0;

    while(x){
      Splay.splay(x);
      Splay.R(x) = t;
      t = x;
      Splay.pushup(x);
      x = Splay.fa[x];
    }
  }
  void Add(int x, int y, int w){
    makeroot(x); Access(y); Splay.splay(y);
    Splay.add[y] += w; Splay.val[y] += w; 
    Splay.mx[y] += w; 
  }
  int findroot(int x){
    Access(x); Splay.splay(x);

    int y = x;

    while(Splay.L(y)){
      y = Splay.L(y);
    }

    return y;
  }

  void makeroot(int x){
    Access(x); Splay.splay(x); Splay.rev[x] ^= 1;
  }

  void cut(int x, int y){
    makeroot(x); Access(y); Splay.splay(y);
    Splay.L(y) = Splay.fa[Splay.L(y)] = 0; Splay.pushup(y);
  }

  void link(int x, int y){
    makeroot(x); Splay.fa[x] = y; Splay.splay(x);
  }
}lct;

void insert(int s, int t){
  ++ tot;
  u[tot] = s; v[tot] = t;
  nxt[tot] = first[s];
  first[s] = tot;
}

void bfs(){
  int head, tail;
  head = tail = 1;
  que[head] = 1;
  Splay.fa[1] = 0;
  
  while(head <= tail){
    int x = que[head];

    for(int i = first[x]; i; i = nxt[i]){
      if(v[i] != Splay.fa[x]){
        Splay.fa[v[i]] = x;
        que[++ tail] = v[i];
      }
    }
    ++ head;
  }
}

int main(){
  int flag, x, y, z;
  
  while(~scanf("%d", &n)){
    tot = 0;
    for(int i = 0; i <= n; ++ i){
      Splay.fa[i] = Splay.val[i] = Splay.add[i] = 0;
      Splay.rev[i] = false;
      Splay.mx[i] = -oo;
      Splay.c[i][0] = Splay.c[i][1] = 0;
      first[i] = 0;
    }
    for(int i = 1; i < n; ++ i){
      scanf("%d%d", &x, &y);
      insert(x, y); insert(y, x);
    }
    for(int i = 1; i <= n; ++ i){
      scanf("%d", &x);
      Splay.val[i] = Splay.mx[i] = x;
    }
    bfs();

    scanf("%d", &m);
    for(int i = 1; i <= m; ++ i){
      scanf("%d", &flag);
      switch(flag){
      case 1:{
        scanf("%d%d", &x, &y);
        if(lct.findroot(x) == lct.findroot(y))
          puts("-1");
        else
          lct.link(x, y);
        break;
      }
      case 2:{
        scanf("%d%d", &x, &y);
        if(lct.findroot(x) != lct.findroot(y) || x == y)
          puts("-1");
        else lct.cut(x, y);
        break;
      }
      case 3:{
        scanf("%d%d%d", &z, &x, &y);
        if(lct.findroot(x) != lct.findroot(y))
          puts("-1");
        else
          lct.Add(x, y, z);
        break;
      }
      case 4:{
        scanf("%d%d", &x, &y);
        if(lct.findroot(x) != lct.findroot(y))
          puts("-1");
        else{
          lct.makeroot(x); lct.Access(y); Splay.splay(y);
          printf("%d
", Splay.mx[y]);
        }
        break;
      }
      }
    }
    puts("");
  }

  return 0;
}