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avl_tree.cpp
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avl_tree.cpp
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// iran
#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
template <typename T>
class AVL {
int s = 0;
struct node {
T val;
node *ch[2];
int dep, size;
node(T v, node* l = nullptr, node* r = nullptr) : val(v), dep(1), size(1) {
ch[0] = l; ch[1] = r;
}
};
int depth(node *t) { return t == nullptr ? 0 : t->dep; }
int count(node *t) { return t == nullptr ? 0 : t->size; }
node *update(node *t) {
t->dep = max(depth(t->ch[0]), depth(t->ch[1])) + 1;
t->size = count(t->ch[0]) + count(t->ch[1]) + 1;
return t;
}
node *rotate(node *t, int b) {
node *s = t->ch[1 - b];
t->ch[1 - b] = s->ch[b];
s->ch[b] = t;
t = update(t);
s = update(s);
return s;
}
node *fetch(node *t) {
if (t == nullptr) return t;
if (depth(t->ch[0]) - depth(t->ch[1]) == 2) {
if (depth(t->ch[0]->ch[1]) > depth(t->ch[0]->ch[0])) {
t->ch[0] = rotate(t->ch[0], 0);
}
t = rotate(t, 1);
}
else if (depth(t->ch[0]) - depth(t->ch[1]) == -2) {
if (depth(t->ch[1]->ch[0]) > depth(t->ch[1]->ch[1])) {
t->ch[1] = rotate(t->ch[1], 1);
}
t = rotate(t, 0);
}
return t;
}
node *insert(node *t, int k, T v) {
if (t == nullptr) return new node(v);
int c = count(t->ch[0]), b = (k > c);
t->ch[b] = insert(t->ch[b], k - (b ? (c + 1) : 0), v);
update(t);
return fetch(t);
}
node *erase(node *t) {
if (t == nullptr) return nullptr;
if (t->ch[0] == nullptr && t->ch[1] == nullptr) {
delete t;
return nullptr;
}
if (t->ch[0] == nullptr || t->ch[1] == nullptr) {
node *res = t->ch[t->ch[0] == nullptr];
delete t;
return res;
}
node *res = new node(find(t->ch[1], 0)->val, t->ch[0], erase(t->ch[1], 0));
delete t;
return fetch(update(res));
}
node *erase(node *t, int k) {
if (t == nullptr) return nullptr;
int c = count(t->ch[0]);
if (k < c) {
t->ch[0] = erase(t->ch[0], k);
t = update(t);
}
else if (k > c) {
t->ch[1] = erase(t->ch[1], k - (c + 1));
t = update(t);
}
else {
t = erase(t);
}
return fetch(t);
}
node *find(node *t, int k) {
if (t == nullptr) return t;
int c = count(t->ch[0]);
return k < c ? find(t->ch[0], k) : k == c ? t : find(t->ch[1], k - (c + 1));
}
int cnt(node *t, T v) {
if (t == nullptr) return 0;
if (t->val < v) return count(t->ch[0]) + 1 + cnt(t->ch[1], v);
if (t->val == v) return count(t->ch[0]);
return cnt(t->ch[0], v);
}
node *root;
public:
AVL() : root(nullptr) {}
void insert(T val) {
root = insert(root, cnt(root, val), val);
s++;
}
// 0-indexed
T get_kth_small(int k) {
assert(k < s);
return find(root, k)->val;
}
// 0-indexed
void erase_kth_small(int k) {
assert(k < s);
root = erase(root, k);
s--;
}
// 0-indexed
T get_kth_big(int k) {
assert(k < s);
return get_kth_small(s - 1 - k);
}
// 0-indexed
void erase_kth_big(int k) {
assert(k < s);
erase_kth_small(s - 1 - k);
}
int count(T val) {
return cnt(root, val);
}
int size() {
return s;
}
bool empty() {
return s == 0;
}
int count_lt(T val) {
int l = -1, r = s;
while (r - l > 1) {
int m = (l + r) / 2;
if (get_kth_small(m) < val) {
l = m;
} else {
r = m;
}
}
return r;
}
int count_le(T val) {
int l = -1, r = s;
while (r - l > 1) {
int m = (l + r) / 2;
if (get_kth_small(m) <= val) {
l = m;
} else {
r = m;
}
}
return r;
}
int count_gt(T val) {
int l = -1, r = s;
while (r - l > 1) {
int m = (l + r) / 2;
if (get_kth_big(m) > val) {
l = m;
} else {
r = m;
}
}
return r;
}
int count_ge(T val) {
int l = -1, r = s;
while (r - l > 1) {
int m = (l + r) / 2;
if (get_kth_big(m) >= val) {
l = m;
} else {
r = m;
}
}
return r;
}
void erase(T val) {
int kth = count_lt(val);
assert(get_kth_small(kth) == val);
erase_kth_small(kth);
}
};
int main() {
int n;
cin >> n;
AVL<i64> avl;
for (int i = 0; i < n; i++) {
int cmd;
cin >> cmd;
if (cmd > 0) {
int k;
cin >> k;
avl.insert(k);
} else if (cmd < 0) {
int k;
cin >> k;
avl.erase(k);
} else {
int k;
cin >> k;
cout << avl.get_kth_big(k - 1) << endl;
}
}
}