注意事项:

  1. 函数 precidnexid 不能使用 splay 的,因为替罪羊树有空点。

Luogu P3369 【模板】普通平衡树

代码:

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#include<bits/stdc++.h>
using namespace std;
const int MAXn = 1e5;
const int INF = 0x3f3f3f3f;
const int NINF = 0xc0c0c0c0;

template <typename T>
inline void read(T &a) {
char c;for (c = getchar(); (c < '0' || c > '9') && c != '-'; c = getchar());bool f = c == '-';T x = f ? 0 : (c ^ '0');for (c = getchar(); c >= '0' && c <= '9'; c = getchar()) {x = x * 10 + (c ^ '0');}a = f ? -x : x;
}
template <typename T, typename ...Argv>
inline void read(T &a, Argv &...argv) {
read(a), read(argv...);
}

double thr = 0.75;
int cntnd, root, ls[MAXn + 10], rs[MAXn + 10];
int val[MAXn + 10], cnt[MAXn + 10], sizcnt[MAXn + 10], siznd[MAXn + 10], sizdel[MAXn + 10];
inline void pushup(int id) {
sizcnt[id] = cnt[id] + sizcnt[ls[id]] + sizcnt[rs[id]];
siznd[id] = 1 + siznd[ls[id]] + siznd[rs[id]];
sizdel[id] = (cnt[id] == 0) + sizdel[ls[id]] + sizdel[rs[id]];
}
inline int needrb(int id) {
return max(siznd[ls[id]], siznd[rs[id]]) >= thr * siznd[id] ||
sizdel[id] >= thr * siznd[id];
}
int cntino, ino[MAXn + 10];
void traversal(int id) {
if (id == 0) return;
traversal(ls[id]);
if (cnt[id]) ino[++cntino] = id;
traversal(rs[id]);
}
int build(int le, int ri) {
if (le > ri) return 0;
int mid = (le + ri) >> 1, id = ino[mid];
ls[id] = build(le, mid - 1);
rs[id] = build(mid + 1, ri);
pushup(id);
return id;
}
int rebuild(int id) {
cntino = 0;
traversal(id);
return build(1, cntino);
}
int cntpa, pa[MAXn + 10];
int find(int v) {
cntpa = 0;
int id = root;
while (id) {
pa[++cntpa] = id;
if (v == val[id]) break;
else if (v < val[id]) id = ls[id];
else id = rs[id];
}
if (id == 0) pa[++cntpa] = id;
return id;
}
void pushuppa() {
for (int i = cntpa; i; --i) {
pushup(pa[i]);
}
}
void rebuildpa() {
for (int i = 1; i <= cntpa; ++i) {
if (needrb(pa[i])) {
if (i == 1) root = rebuild(pa[i]);
else if (pa[i] == ls[pa[i - 1]]) ls[pa[i - 1]] = rebuild(pa[i]);
else rs[pa[i - 1]] = rebuild(pa[i]);
break;
}
}
}
void insert(int v) {
int id = find(v);
if (id == 0) {
pa[cntpa] = id = ++cntnd;
val[id] = v;
if (pa[cntpa - 1] == 0) root = id;
else if (v < val[pa[cntpa - 1]]) ls[pa[cntpa - 1]] = id;
else rs[pa[cntpa - 1]] = id;
}
++cnt[id];
pushuppa();
rebuildpa();
}
void delet(int v) {
int id = find(v);
if (cnt[id]) {
--cnt[id];
pushuppa();
rebuildpa();
}
}
int valtorank(int v) {
int ans = 1, id = root;
while (id) {
if (v < val[id]) {
id = ls[id];
} else if (v == val[id]) {
ans += sizcnt[ls[id]];
break;
} else {
ans += sizcnt[ls[id]] + cnt[id];
id = rs[id];
}
}
return ans;
}
int ranktoid(int rk) {
int id = root;
while (true) {
if (rk <= sizcnt[ls[id]]) {
id = ls[id];
} else if (rk <= sizcnt[ls[id]] + cnt[id]) {
break;
} else {
rk -= sizcnt[ls[id]] + cnt[id];
id = rs[id];
}
}
return id;
}
int precid(int v) {
return ranktoid(valtorank(v) - 1);
}
int nexid(int v) {
return ranktoid(valtorank(v + 1));
}

int n;
signed main() {
read(n);
for (int i = 1, opt, x; i <= n; ++i) {
read(opt, x);
if (opt == 1) {
insert(x);
} else if (opt == 2) {
delet(x);
} else if (opt == 3) {
printf("%d\n", valtorank(x));
} else if (opt == 4) {
printf("%d\n", val[ranktoid(x)]);
} else if (opt == 5) {
printf("%d\n", val[precid(x)]);
} else {
printf("%d\n", val[nexid(x)]);
}
}
return 0;
}