<模板> 树套树

提交地址: 洛谷P3380 二逼平衡树

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#include <bits/stdc++.h>
#define reg register
#define lc t[x].ch[0]
#define rc t[x].ch[1]
using namespace std;
const int MaxN = 50010;
const int inf = 2147483647;
int n, m, tot;
int a[MaxN];
struct node
{
int ch[2];
int cnt, size, val, rnd;
};
node t[MaxN << 5];
struct treap
{
int l, r, root;
void update(int x) { t[x].size = t[lc].size + t[rc].size + t[x].cnt; }
void rotate(int &x, int c)
{
int s = t[x].ch[c];
t[x].ch[c] = t[s].ch[c ^ 1];
t[s].ch[c ^ 1] = x;
update(x);
update(x = s);
}
void insert(int &x, int val)
{
if (!x)
{
x = ++tot;
t[x].cnt = t[x].size = 1;
t[x].rnd = rand(), t[x].val = val;
return;
}
t[x].size++;
if (t[x].val == val)
{
++t[x].cnt;
return;
}
int c = val > t[x].val;
insert(t[x].ch[c], val);
if (t[x].rnd > t[t[x].ch[c]].rnd)
rotate(x, c);
}
void del(int &x, int val)
{
if (!x)
return;
if (t[x].val == val)
{
if (t[x].cnt > 1)
{
t[x].cnt--, t[x].size--;
return;
}
bool c = t[lc].rnd > t[rc].rnd;
if (lc == 0 || rc == 0)
x = lc + rc;
else
rotate(x, c), del(x, val);
}
else
--t[x].size, del(t[x].ch[t[x].val < val], val);
}
int rank(int x, int val)
{
if (!x)
return 0;
if (t[x].val == val)
return t[lc].size;
if (t[x].val > val)
return rank(lc, val);
else
return t[lc].size + t[x].cnt + rank(rc, val);
}
int query_val(int x, int val)
{
while (1)
{
if (val <= t[lc].size)
x = lc;
else if (val > t[lc].size + t[x].cnt)
val -= t[lc].size + t[x].cnt, x = rc;
else
return t[x].val;
}
}
int query_pre(int x, int val)
{
if (!x)
return -inf;
if (t[x].val >= val)
return query_pre(lc, val);
else
return cmax(t[x].val, query_pre(rc, val));
}
int query_sub(int x, int val)
{
if (!x)
return inf;
if (t[x].val <= val)
return query_sub(rc, val);
else
return cmin(t[x].val, query_sub(lc, val));
}
};
treap tr[MaxN << 2];
struct tree
{
void build(int id, int l, int r)
{
tr[id].l = l, tr[id].r = r;
for (int i = l; i <= r; i++)
tr[id].insert(tr[id].root, a[i]);
if (l == r)
return;
int mid = (l + r) >> 1;
build(id << 1, l, mid);
build(id << 1 | 1, mid + 1, r);
}
int query_rank(int id, int l, int r, int val)
{
if (tr[id].l > r || tr[id].r < l)
return 0;
if (l <= tr[id].l && tr[id].r <= r)
{
int ans = tr[id].rank(tr[id].root, val);
return ans;
}
int ans = 0;
ans += query_rank(id << 1, l, r, val);
ans += query_rank(id << 1 | 1, l, r, val);
return ans;
}
int query_val(int l, int r, int k)
{
int L = 0, R = 1e8;
while (L < R)
{
int mid = (L + R + 1) >> 1;
if (query_rank(1, l, r, mid) + 1 <= k)
L = mid;
else
R = mid - 1;
}
return L;
}
void modify(int id, int pos, int val)
{
if (pos < tr[id].l || tr[id].r < pos)
return;
tr[id].del(tr[id].root, a[pos]);
tr[id].insert(tr[id].root, val);
if (tr[id].l == tr[id].r)
return;
modify(id << 1, pos, val);
modify(id << 1 | 1, pos, val);
}
int query_pre(int id, int l, int r, int val)
{
if (tr[id].l > r || tr[id].r < l)
return -inf;
if (l <= tr[id].l && tr[id].r <= r)
return tr[id].query_pre(tr[id].root, val);
int ans = max(query_pre(id << 1, l, r, val), query_pre(id << 1 | 1, l, r, val));
return ans;
}
int query_sub(int id, int l, int r, int val)
{
if (tr[id].l > r || tr[id].r < l)
return inf;
if (l <= tr[id].l && tr[id].r <= r)
return tr[id].query_sub(tr[id].root, val);
int ans = min(query_sub(id << 1, l, r, val), query_sub(id << 1 | 1, l, r, val));
return ans;
}
} T;
inline int read()
{
int x = 0;
char ch = getchar();
while (ch > '9' || ch < '0')
ch = getchar();
while (ch <= '9' && ch >= '0')
x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar();
return x;
}
int main()
{
srand(19260817);
int n = read(), m = read();
for (int i = 1; i <= n; i++)
a[i] = read();
int op;
T.build(1, 1, n);
for (int i = 1; i <= m; i++)
{
op = read();
int l, r, val, pos;
if (op == 3)
{
pos = read(), val = read();
T.modify(1, pos, val);
a[pos] = val;
continue;
}
l = read(), r = read(), val = read();
if (op == 1)
printf("%d\n", T.query_rank(1, l, r, val) + 1);
else if (op == 2)
printf("%d\n", T.query_val(l, r, val));
else if (op == 4)
printf("%d\n", T.query_pre(1, l, r, val));
else if (op == 5)
printf("%d\n", T.query_sub(1, l, r, val));
}
return 0;
}
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