[洛谷P3380]【模板】二逼平衡树（树套树）

题目大意：有$5$种操作：

1. $1;l;r;k：$查询$k$在区间$[l,r]$内的排名
2. $2;l;r;k：$查询区间$[l,r]$内排名为$k$的值
3. $3;pos;k：$把第$pos$为上的数值改为$k$
4. $4;l;r;k：$查询$k$在区间$[l,r]$内的前驱
5. $5;l;r;k：$查询$k$在区间$[l,r]$内的后继

题解：树套树，权值线段树套平衡树

卡点：$TLE$卡了一会（我好菜啊）

C++ Code：

#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cctype>

//#define ONLINE_JUDGE
namespace __IO {
	namespace R {
		int x;
		#ifdef ONLINE_JUDGE
		#define M (1 << 24)
		char op[M], *ch = op;
		inline void begin() {
			fread(op, 1, M, stdin);
		}
		inline int read() {
			while (isspace(*ch)) ch++;
			for (x = *ch & 15, ch++; isdigit(*ch); ch++) x = x * 10 + (*ch & 15);
			return x;
		}
		#undef M
		#else
		int ch;
		inline int read() {
			ch = getchar();
			while (isspace(ch)) ch = getchar();
			for (x = ch & 15, ch = getchar(); isdigit(ch); ch = getchar()) x = x * 10 + (ch & 15);
			return x;
		}
		#endif
	}

	namespace W {
		#ifdef ONLINE_JUDGE
		#define M (1 << 24)
		char op[M], *ch = op - 1;
		inline void end() {
			fwrite(op, 1, ch - op + 1, stdout);
		}
		inline void write(int x) {
			if (x > 9) write(x / 10);
			*++ch = x % 10 ^ 48;
		}
		#undef M
		#else
		inline void write(int x) {
			if (x > 9) write(x / 10);
			putchar(x % 10 ^ 48);
		}
		#endif
	}
}
using __IO::R::read;
using __IO::W::write;

#define maxn 50010
#define N (maxn * 50)
const int inf = 0x7fffffff, maxl = 0, maxr = 1e8;

namespace Treap {
	int lc[N], rc[N], V[N], pri[N], sz[N];
	int res, idx, ta, tb, tmp;

	inline int nw(int x) {
		V[++idx] = x, sz[idx] = 1, pri[idx] = rand();
		return idx;
	}
	inline int update(int rt) {
		sz[rt] = sz[lc[rt]] + sz[rc[rt]] + 1;
		return rt;
	}

	void split(int rt, int k, int &x, int &y) {
		if (!rt) x = y = 0;
		else {
			if (V[rt] <= k) split(rc[rt], k, rc[rt], y), x = update(rt);
			else split(lc[rt], k, x, lc[rt]), y = update(rt);
		}
	}
	int merge(int x, int y) {
		if (!x || !y) return x | y;
		if (pri[x] < pri[y]) {rc[x] = merge(rc[x], y); return update(x);}
		else {lc[y] = merge(x, lc[y]); return update(y);}
	}
	
	void insert(int &rt, int x) {
		if (!rt) rt = nw(x);
		else {
			split(rt, x, ta, tb);
			rt = merge(ta, merge(nw(x), tb));
		}
	}
	void erase(int &rt, int x) {
		split(rt, x, ta, tb);
		split(ta, x - 1, ta, tmp);
		rt = merge(ta, tb);
	}
	int gtrnk(int &rt, int l, int r) {
		split(rt, l - 1, ta, tb);
		split(tb, r, tmp, tb);
		res = sz[tmp];
		rt = merge(ta, merge(tmp, tb));
		return res;
	}
}

namespace SgT {
	int lc[N], rc[N], rt[N], idx;
	int root;
	
	int pos, num;
	void __insert(int &rt, int l, int r) {
		if (!rt) rt = ++idx;
		Treap::insert(SgT::rt[rt], pos);
		if (l == r) return ;
		int mid = l + r >> 1;
		if (num <= mid) __insert(lc[rt], l, mid);
		else __insert(rc[rt], mid + 1, r);
	}
	void insert(int __pos, int __num) {
		pos = __pos, num = __num;
		__insert(root, maxl, maxr);
	}

	void __erase(int rt, int l, int r) {
		Treap::erase(SgT::rt[rt], pos);
		if (l == r) return ;
		int mid = l + r >> 1;
		if (num <= mid) __erase(lc[rt], l, mid);
		else __erase(rc[rt], mid + 1, r);
	}
	void erase(int __pos, int __num) {
		pos = __pos, num = __num;
		__erase(root, maxl, maxr);
	}
	
	int L, R, val;
	int __gtrnk(int rt, int l, int r) {
		if (l == r) return 1;
		int mid = l + r >> 1;
		if (val <= mid) return __gtrnk(lc[rt], l, mid);
		else return Treap::gtrnk(SgT::rt[lc[rt]], L, R) + __gtrnk(rc[rt], mid + 1, r);
	}
	int gtrnk(int __L, int __R, int __val) {
		L = __L, R = __R, val = __val;
		return __gtrnk(root, maxl, maxr);
	}

	int __gtkth(int rt, int l, int r, int k) {
		if (l == r) return l;
		int mid = l + r >> 1, tmp = Treap::gtrnk(SgT::rt[lc[rt]], L, R);
		if (tmp >= k) return __gtkth(lc[rt], l, mid, k);
		else return __gtkth(rc[rt], mid + 1, r, k - tmp);
	}
	int gtkth(int __L, int __R, int k) {
		L = __L, R = __R;
		return __gtkth(root, maxl, maxr, k);
	}

	int pre(int L, int R, int x) {
		int k = gtrnk(L, R, x);
		if (k == 1) {
			#ifdef ONLINE_JUDGE
			*++__IO::W::ch = '-';
			#else
			putchar('-');
			#endif
			return inf;
		}
		else return gtkth(L, R, k - 1);
	}
	int nxt(int L, int R, int x) {
		int k = gtrnk(L, R, x + 1);
		if (k > R - L + 1) return inf;
		else return gtkth(L, R, k);
	}
}

int n, m, V[maxn];
int main() {
//	freopen("LG3380.in", "r", stdin);
//	freopen("LG3380.txt", "w", stdout);
	#ifdef ONLINE_JUDGE
	__IO::R::begin();
	#endif
	srand(20040826);
	n = read(), m = read();
	for (int i = 1; i <= n; i++) {
		V[i] = read();
		SgT::insert(i, V[i]);
	}
	while (m --> 0) {
		int op = read(), l = read(), r = read(), k;
		if (op != 3) k = read();
		switch (op) {
			case 1:
				write(SgT::gtrnk(l, r, k));
				#ifdef ONLINE_JUDGE
				*++__IO::W::ch = '
';
				#else
				putchar('
');
				#endif
				break;
			case 2:
				write(SgT::gtkth(l, r, k));
				#ifdef ONLINE_JUDGE
				*++__IO::W::ch = '
';
				#else
				putchar('
');
				#endif
				break;
			case 3:
				SgT::erase(l, V[l]);
				V[l] = r;
				SgT::insert(l, V[l]);
				break;
			case 4:
				write(SgT::pre(l, r, k));
				#ifdef ONLINE_JUDGE
				*++__IO::W::ch = '
';
				#else
				putchar('
');
				#endif
				break;
			case 5:
				write(SgT::nxt(l, r, k));
				#ifdef ONLINE_JUDGE
				*++__IO::W::ch = '
';
				#else
				putchar('
');
				#endif
				break;
		}
	}
	#ifdef ONLINE_JUDGE
	__IO::W::end();
	#endif
	return 0;
}