Problem
给你一张图，点的权值，边和几个操作:
D x: 删除第x条边
Q x y: 询问包含x的联通块中权值第y大的权值
C x y: 将x这个点的权值改为y
Solution
一看就要离线处理，把所有操作都倒过来
然后删除操作变为加边操作
Notice
记得: 是改完以后再把点一个一个加入Treap中！！
Code
非旋转Treap
#pragma GCC optimize(2)
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define sqz main
#define ll long long
#define reg register int
#define rep(i, a, b) for (reg i = a; i <= b; i++)
#define per(i, a, b) for (reg i = a; i >= b; i--)
#define travel(i, u) for (reg i = head[u]; i; i = edge[i].next)
const int INF = 1e9, N = 3000000;
const double eps = 1e-6, phi = acos(-1.0);
ll mod(ll a, ll b) {if (a >= b || a < 0) a %= b; if (a < 0) a += b; return a;}
ll read(){ ll x = 0; int zf = 1; char ch; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
if (ch == '-') zf = -1, ch = getchar(); while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); return x * zf;}
void write(ll y) { if (y < 0) putchar('-'), y = -y; if (y > 9) write(y / 10); putchar(y % 10 + '0');}
struct Node
{
int num1, num2, type;
}Q[N + 5];
int point = 0, fa[N + 5], Root[N + 5], T[N + 5], From[N + 5], To[N + 5], Flag[N + 5];
struct node
{
int Val[N + 5], Level[N + 5], Size[N + 5], Son[2][N + 5], Num[N + 5];
inline void up(int u)
{
Size[u] = Size[Son[0][u]] + Size[Son[1][u]] + 1;
}
int Newnode(int v)
{
int u = ++point;
Val[u] = v, Level[u] = rand();
Son[0][u] = Son[1][u] = 0, Size[u] = 1;
return u;
}
int Merge(int X, int Y)
{
if (X * Y == 0) return X + Y;
if (Level[X] < Level[Y])
{
Son[1][X] = Merge(Son[1][X], Y);
up(X); return X;
}
else
{
Son[0][Y] = Merge(X, Son[0][Y]);
up(Y); return Y;
}
}
void Split(int u, int t, int &x, int &y)
{
if (!u)
{
x = y = 0;
return;
}
if (Val[u] <= t) x = u, Split(Son[1][u], t, Son[1][u], y);
else y = u, Split(Son[0][u], t, x, Son[0][u]);
up(u);
}
int Find_num(int u, int v)
{
if (!u) return 0;
if (v <= Size[Son[0][u]]) return Find_num(Son[0][u], v);
else if (v <= Size[Son[0][u]] + 1) return u;
else return Find_num(Son[1][u], v - Size[Son[0][u]] - 1);
}
void Insert(int &u, int v)
{
int t = Newnode(v), x, y;
Split(u, v, x, y);
u = Merge(Merge(x, t), y);
}
void Delete(int &u, int v)
{
int x, y, z;
Split(u, v, x, z), Split(x, v - 1, x, y);
u = Merge(Merge(x, Merge(Son[0][y], Son[1][y])), z);
}
}Treap;
int Find(int x)
{
if (fa[x] != x) fa[x] = Find(fa[x]);
return fa[x];
}
void Union(int u, int v)
{
if (Treap.Size[Root[u]] < Treap.Size[Root[v]]) swap(u, v);
while (Treap.Size[Root[v]])
{
int t = Treap.Find_num(Root[v], 1);
Treap.Insert(Root[u], Treap.Val[t]);
Treap.Delete(Root[v], Treap.Val[t]);
}
fa[v] = u;
Root[v] = 0;
}
int sqz()
{
int n, m, cas = 0;
while (~scanf("%d %d", &n, &m) && (n || m))
{
point = 0;
rep(i, 1, n) T[i] = read(), fa[i] = i, Root[i] = 0;
rep(i, 1, m) From[i] = read(), To[i] = read(), Flag[i] = 0;
int q = 0; char op[5];
while (scanf("%s", op) && op[0] != 'E')
{
q++;
if (op[0] == 'D')
Q[q].num1 = read(), Flag[Q[q].num1] = 1, Q[q].type = 0;
else
{
Q[q].num1 = read(), Q[q].num2 = read();
if (op[0] == 'C') swap(T[Q[q].num1], Q[q].num2), Q[q].type = 1;
else Q[q].type = 2;
}
}
rep(i, 1, n) Treap.Insert(Root[i], T[i]);
rep(i, 1, m)
if (!Flag[i])
{
int u = Find(From[i]), v = Find(To[i]);
if (u != v) Union(u, v);
}
ll ans = 0; int tot = 0;
per(i, q, 1)
{
if (Q[i].type == 0)
{
int u = Find(From[Q[i].num1]), v = Find(To[Q[i].num1]);
if (u != v) Union(u, v);
}
else if (Q[i].type == 1)
{
int u = Find(Q[i].num1);
Treap.Delete(Root[u], T[Q[i].num1]);
Treap.Insert(Root[u], Q[i].num2);
T[Q[i].num1] = Q[i].num2;
}
else
{
int u = Find(Q[i].num1);
int t = Treap.Find_num(Root[u], Treap.Size[Root[u]] - Q[i].num2 + 1);
if (t != -INF) ans += Treap.Val[t];
tot++;
}
}
printf("Case %d: %.6f
", ++cas, ans * 1.0 / tot);
}
return 0;
}
旋转Treap
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define sqz main
#define ll long long
#define reg register int
#define rep(i, a, b) for (reg i = a; i <= b; i++)
#define per(i, a, b) for (reg i = a; i >= b; i--)
#define travel(i, u) for (reg i = head[u]; i; i = edge[i].next)
const int INF = 1e9, N = 3000000;
const double eps = 1e-6, phi = acos(-1.0);
ll mod(ll a, ll b) {if (a >= b || a < 0) a %= b; if (a < 0) a += b; return a;}
ll read(){ ll x = 0; int zf = 1; char ch; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
if (ch == '-') zf = -1, ch = getchar(); while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); return x * zf;}
void write(ll y) { if (y < 0) putchar('-'), y = -y; if (y > 9) write(y / 10); putchar(y % 10 + '0');}
struct Node
{
int num1, num2, type;
}Q[N + 5];
int point = 0, fa[N + 5], Root[N + 5], T[N + 5], From[N + 5], To[N + 5], Flag[N + 5];
struct node
{
int Val[N + 5], Level[N + 5], Size[N + 5], Son[2][N + 5], Num[N + 5];
inline void up(int u)
{
Size[u] = Size[Son[0][u]] + Size[Son[1][u]] + Num[u];
}
inline void Newnode(int &u, int v)
{
u = ++point;
Level[u] = rand(), Val[u] = v;
Size[u] = Num[u] = 1, Son[0][u] = Son[1][u] = 0;
}
inline void Lturn(int &x)
{
int y = Son[1][x]; Son[1][x] = Son[0][y], Son[0][y] = x;
up(x); up(y); x = y;
}
inline void Rturn(int &x)
{
int y = Son[0][x]; Son[0][x] = Son[1][y], Son[1][y] = x;
up(x); up(y); x = y;
}
void Insert(int &u, int t)
{
if (u == 0)
{
Newnode(u, t);
return;
}
Size[u]++;
if (t == Val[u]) Num[u]++;
else if (t > Val[u])
{
Insert(Son[0][u], t);
if (Level[Son[0][u]] < Level[u]) Rturn(u);
}
else if (t < Val[u])
{
Insert(Son[1][u], t);
if (Level[Son[1][u]] < Level[u]) Lturn(u);
}
}
void Delete(int &u, int t)
{
if (!u) return;
if (Val[u] == t)
{
if (Num[u] > 1)
{
Num[u]--, Size[u]--;
return;
}
if (Son[0][u] * Son[1][u] == 0) u = Son[0][u] + Son[1][u];
else if (Level[Son[0][u]] < Level[Son[1][u]]) Rturn(u), Delete(u, t);
else Lturn(u), Delete(u, t);
}
else if (t > Val[u]) Size[u]--, Delete(Son[0][u], t);
else Size[u]--, Delete(Son[1][u], t);
}
int Find_num(int u, int t)
{
if (!u) return -INF;
if (t <= Size[Son[0][u]]) return Find_num(Son[0][u], t);
else if (t <= Size[Son[0][u]] + Num[u]) return Val[u];
else return Find_num(Son[1][u], t - Size[Son[0][u]] - Num[u]);
}
}Treap;
int Find(int x)
{
if (fa[x] != x) fa[x] = Find(fa[x]);
return fa[x];
}
void Union(int u, int v)
{
if (Treap.Size[Root[u]] < Treap.Size[Root[v]]) swap(u, v);
while (Treap.Size[Root[v]])
{
int t = Treap.Find_num(Root[v], 1);
Treap.Insert(Root[u], t);
Treap.Delete(Root[v], t);
}
fa[v] = u;
Root[v] = 0;
}
int sqz()
{
int n, m, cas = 0;
while (~scanf("%d %d", &n, &m) && (n || m))
{
point = 0;
rep(i, 1, n) T[i] = read(), fa[i] = i, Root[i] = 0;
rep(i, 1, m) From[i] = read(), To[i] = read(), Flag[i] = 0;
int q = 0; char op[5];
while (scanf("%s", op) && op[0] != 'E')
{
q++;
if (op[0] == 'D')
Q[q].num1 = read(), Flag[Q[q].num1] = 1, Q[q].type = 0;
else
{
Q[q].num1 = read(), Q[q].num2 = read();
if (op[0] == 'C') swap(T[Q[q].num1], Q[q].num2), Q[q].type = 1;
else Q[q].type = 2;
}
}
rep(i, 1, n) Treap.Insert(Root[i], T[i]);
rep(i, 1, m)
if (!Flag[i])
{
int u = Find(From[i]), v = Find(To[i]);
if (u != v) Union(u, v);
}
ll ans = 0; int tot = 0;
per(i, q, 1)
{
if (Q[i].type == 0)
{
int u = Find(From[Q[i].num1]), v = Find(To[Q[i].num1]);
if (u != v) Union(u, v);
}
else if (Q[i].type == 1)
{
int u = Find(Q[i].num1);
Treap.Delete(Root[u], T[Q[i].num1]);
Treap.Insert(Root[u], Q[i].num2);
T[Q[i].num1] = Q[i].num2;
}
else
{
int u = Find(Q[i].num1);
int t = Treap.Find_num(Root[u], Q[i].num2);
if (t != -INF) ans += t;
tot++;
}
}
printf("Case %d: %.6f
", ++cas, ans * 1.0 / tot);
}
return 0;
}