洛谷P3871 [TJOI2010] 中位数 题解 FHQ Treap模板题

题目链接：https://www.luogu.com.cn/problem/P3871

解题思路：

FHQ Treap模板题，只涉及插入和 kth 操作。

示例程序：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
mt19937 rng(time(0));

struct Node {
	int ls, rs, key, pri, sz;
	Node() {}
	Node(int _key) { ls = rs = 0; key = _key; pri = rng(); sz = 1; }
} tr[maxn];
int rt, idx;

void push_up(int u) {
	int ls = tr[u].ls, rs = tr[u].rs;
	tr[u].sz = tr[ls].sz + tr[rs].sz + 1;
}

void split(int u, int x, int &L, int &R) {
	if (!u) {
		L = R = 0;
		return;
	}
	if (tr[u].key <= x) {
		L = u;
		split(tr[u].rs, x, tr[u].rs, R);
	}
	else {
		R = u;
		split(tr[u].ls, x, L, tr[u].ls);
	}
	push_up(u);
}

int merge(int L, int R) {
	if (!L || !R) return L + R;
	if (tr[L].pri > tr[R].pri) {
		tr[L].rs = merge(tr[L].rs, R);
		push_up(L);
		return L;
	}
	else {
		tr[R].ls = merge(L, tr[R].ls);
		push_up(R);
		return R;
	}
}

void ins(int x) {
	int L, R;
	split(rt, x, L, R);
	tr[++idx] = Node(x);
	rt = merge(merge(L, idx), R);
}

int kth(int u, int k) {
	while (u) {
		int sz = tr[tr[u].ls].sz;
		if (sz + 1 == k)
			return u;
		else if (sz >= k)
			u = tr[u].ls;
		else
			k -= sz + 1,
			u = tr[u].rs;
	}
	assert(1 == 0);
	return -1; // 不会到这一行
}

int n, m, x;
char op[5];

int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
        scanf("%d", &x);
        ins(x);
	}
	scanf("%d", &m);
	while (m--) {
        scanf("%s", op);
        if (op[0] == 'a') {
            scanf("%d", &x);
            ins(x);
        }
        else {
            int u = kth(rt, (idx+1)/2);
            printf("%d\n", tr[u].key);
        }
	}
	return 0;
}