hzwer说替罪羊树好写代码短，然而我写完改了两天，和二逼平衡树一样长…
#include <queue>
using namespace std;
class Scapegoat_Tree{
private :
int ch[101000][2], fa[101000], sz[101000], key[101000], rep[101000];
int cnt, len, root, tmp[101000];
double a;
queue<int> Q;
public :
inline void init(double _a) {
a = _a;
cnt = root = 0;
while (!Q.empty()) Q.pop();
}
inline int newnode() {
int ret;
if (Q.empty()) ret = ++ cnt;
else ret = Q.front(), Q.pop();
fa[ret] = ch[ret][0] = ch[ret][1] = rep[ret] = key[ret] = sz[ret] = 0;
return ret;
}
inline bool balance(int x) {
return ((double)max(sz[ch[x][0]], sz[ch[x][1]]) <= (double)sz[x] * a);
}
inline int pos_max_element() {
int p = root;
while (ch[p][1]) p = ch[p][1];
return p;
}
inline int pos_min_element() {
int p = root;
while (ch[p][0]) p = ch[p][0];
return p;
}
inline void output(int x) {
if (ch[x][0]) output(ch[x][0]);
tmp[++ len] = x;
if (ch[x][1]) output(ch[x][1]);
}
inline int build(int l, int r) {
if (l > r) return 0;
int mid = (l + r) >> 1, p = tmp[mid];
fa[ch[p][0] = build(l, mid - 1)] = p;
fa[ch[p][1] = build(mid + 1, r)] = p;
sz[p] = sz[ch[p][0]] + sz[ch[p][1]] + rep[p];
return p;
}
inline void rebuild(int x) {
len = 0; output(x);
int f = fa[x], ws = (x == ch[f][1]), u;
u = build(1, len);
fa[u] = f;
if (f) ch[f][ws] = u;
if (x == root) root = u;
}
inline void insert(int x) {
if (!root) {
key[root = newnode()] = x;
rep[root] = sz[root] = 1;
return;
}
int p = root;
while (x != key[p] && ch[p][key[p] < x]) {
sz[p] ++;
p = ch[p][key[p] < x];
}
sz[p] ++;
if (x == key[p]) rep[p] ++;
else {
int tp = newnode();
fa[tp] = p;
ch[p][key[p] < x] = tp;
rep[tp] = sz[tp] = 1;
key[tp] = x;
p = tp;
}
int rec = 0;
for (int i = p; i; i = fa[i])
if (!balance(i)) rec = i;
if (rec) rebuild(rec);
}
inline int find(int x) {
int p = root;
while (ch[p][key[p] < x] && key[p] != x) p = ch[p][key[p] < x];
return p;
}
inline void erase(int x) {
int p = find(x), rec = 0;
if (rep[p] > 1) {
rep[p] --;
sz[p] --;
for (int i = fa[p]; i; i = fa[i]) {
sz[i] --;
if (!balance(i)) rec = i;
}
if (rec) rebuild(rec);
}
else if (ch[p][0] && ch[p][1]) {
int tp = ch[p][0];
while (ch[tp][1]) tp = ch[tp][1];
Q.push(tp);
key[p] = key[tp];
rep[p] = rep[tp];
int son = ch[tp][0], ws = (ch[fa[tp]][1] == tp);
fa[ch[fa[tp]][ws] = son] = fa[tp];
for (int i = fa[tp]; i != p; i = fa[i]) {
sz[i] -= rep[tp];
if (!balance(i)) rec = i;
}
for (int i = p; i; i = fa[i]) {
sz[i] --;
if (!balance(i)) rec = i;
}
if (rec) rebuild(rec);
}
else {
int son = (ch[p][0] ? ch[p][0] : ch[p][1]), ws = (ch[fa[p]][1] == p);
fa[ch[fa[p]][ws] = son] = fa[p];
if (p == root) root = son;
Q.push(p);
for (int i = fa[p]; i; i = fa[i]) {
sz[i] --;
if (!balance(i)) rec = i;
}
if (rec) rebuild(rec);
}
}
inline int size() {
return sz[root];
}
inline int pred(int x) {
int p = root, ret = (int)-2e9 - 1e8;
while (ch[p][key[p] < x]) {
if (key[p] < x) ret = max(ret, key[p]);
p = ch[p][key[p] < x];
}
if (key[p] < x) ret = max(ret, key[p]);
return ret;
}
inline int succ(int x) {
int p = root, ret = (int)2e9 + 1e8;
while (ch[p][key[p] <= x]) {
if (key[p] > x) ret = min(ret, key[p]);
p = ch[p][key[p] <= x];
}
if (key[p] > x) ret = min(ret, key[p]);
return ret;
}
inline int rank_ord(int x) {
int p = root, ret = 0;
while (ch[p][key[p] < x] && key[p] != x) {
if (key[p] < x) ret += rep[p] + sz[ch[p][0]];
p = ch[p][key[p] < x];
}
if (key[p] == x) ret += sz[ch[p][0]];
return ret + 1;
}
inline int find_kth(int k) {
if (k > sz[root]) return key[pos_max_element()];
int p = root;
while (p) {
if (sz[ch[p][0]] < k && k <= sz[ch[p][0]] + rep[p]) return key[p];
if (k <= sz[ch[p][0]]) p = ch[p][0];
else {
k -= sz[ch[p][0]] + rep[p];
p = ch[p][1];
}
}
return key[p];
}
};