Score : $600$ points

问题描述

给定一个由 $1,2,\ldots,N$ 构成的排列 $P=(P_1,P_2,\ldots,P_N)$，以及一个整数 $X$。

另外，还给出了 $Q$ 个查询。第 $i$ 个查询表示为一个三元组 $(C_i,L_i,R_i)$。每个查询对排列 $P$ 执行以下操作：

• 若 $C_i=1$：将 $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ 按升序排序。
• 若 $C_i=2$：将 $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ 按降序排序。

在按照给定顺序执行完所有查询之后，在最终的排列 $P$ 中找到满足 $P_i=X$ 的 $i$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Given is a permutation $P=(P_1,P_2,\ldots,P_N)$ of $1,2,\ldots,N$, and an integer $X$.

Additionally, $Q$ queries are given. The $i$-th query is represented as a triple of numbers $(C_i,L_i,R_i)$. Each query does the following operation on the permutation $P$.

• If $C_i=1$: sort $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ in ascending order.
• If $C_i=2$: sort $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ in descending order.

In the final permutation $P$ after executing all queries in the given order, find $i$ such that $P_i=X$.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq Q \leq 2\times 10^5$
• $1 \leq X \leq N$
• $(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$.
• $1 \leq C_i \leq 2$
• $1 \leq L_i \leq R_i \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $Q$ $X$

$P_1$ $P_2$ $\ldots$ $P_N$

$C_1$ $L_1$ $R_1$

$C_2$ $L_2$ $R_2$

$\vdots$

$C_Q$ $L_Q$ $R_Q$

Output

Print the answer.

Sample Input 1

5 2 1
1 4 5 2 3
1 3 5
2 1 3

Sample Output 1

3

Initially, the permutation is $P=[1,4,5,2,3]$. The queries change it as follows.

• $1$-st query sorts the $3$-rd through $5$-th elements in ascending order, making $P=[1,4,2,3,5]$.
• $2$-nd query sorts the $1$-st through $3$-rd elements in descending order, making $P=[4,2,1,3,5]$.

In the final permutation, we have $P_3=1$, so $3$ should be printed.

Sample Input 2

7 3 3
7 5 3 1 2 4 6
1 1 7
2 3 6
2 5 7

Sample Output 2

7

The final permutation is $P=[1,2,6,5,7,4,3]$.

update @ 2024/3/10 10:16:27