A14198. Phoenix and Bits
编程题
普及/提高-
知识点
题目描述
Phoenix loves playing with bits — specifically, by using the bitwise operations AND, OR, and XOR. He has $n$ integers $a_1, a_2, \dots, a_n$ , and will perform $q$ of the following queries:
1. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ AND $x$ ;
2. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ OR $x$ ;
3. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ XOR $x$ ;
4. output how many distinct integers $a_i$ where $l \le a_i \le r$ .
For each query, Phoenix is given $l$ , $r$ , and $x$ . Note that he is considering the values of the numbers, not their indices.
1. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ AND $x$ ;
2. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ OR $x$ ;
3. replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ XOR $x$ ;
4. output how many distinct integers $a_i$ where $l \le a_i \le r$ .
For each query, Phoenix is given $l$ , $r$ , and $x$ . Note that he is considering the values of the numbers, not their indices.
输入格式
The first line contains two integers $n$ and $q$ ( $1 \le n \le 2 \cdot 10^5$ ; $1 \le q \le 10^5$ ) — the number of integers and the number of queries, respectively.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i < 2^{20}$ ) — the integers that Phoenix starts with.
The next $q$ lines contain the queries. For each query, the first integer of each line is $t$ ( $1 \le t \le 4$ ) — the type of query.
If $t \in \{1, 2, 3\}$ , then three integers $l_i$ , $r_i$ , and $x_i$ will follow ( $0 \le l_i, r_i, x_i < 2^{20}$ ; $l_i \le r_i$ ).
Otherwise, if $t=4$ , two integers $l_i$ and $r_i$ will follow ( $0 \le l_i \le r_i < 2^{20}$ ).
It is guaranteed that there is at least one query where $t=4$ .
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i < 2^{20}$ ) — the integers that Phoenix starts with.
The next $q$ lines contain the queries. For each query, the first integer of each line is $t$ ( $1 \le t \le 4$ ) — the type of query.
If $t \in \{1, 2, 3\}$ , then three integers $l_i$ , $r_i$ , and $x_i$ will follow ( $0 \le l_i, r_i, x_i < 2^{20}$ ; $l_i \le r_i$ ).
Otherwise, if $t=4$ , two integers $l_i$ and $r_i$ will follow ( $0 \le l_i \le r_i < 2^{20}$ ).
It is guaranteed that there is at least one query where $t=4$ .
输出格式
Print the answer for each query where $t=4$ .
输入输出样例
输入 #1
5 6 5 4 3 2 1 1 2 3 2 4 2 5 3 2 5 3 4 1 6 2 1 1 8 4 8 10
输出 #1
3 2 1
输入 #2
6 7 6 0 2 3 2 7 1 0 4 3 2 6 8 4 4 0 7 3 2 5 3 1 0 1 2 4 0 3 4 2 7
输出 #2
5 1 2
说明/提示
In the first example:
- For the first query, $2$ is replaced by $2$ AND $2 = 2$ and $3$ is replaced with $3$ AND $2 = 2$ . The set of numbers is $\{1, 2, 4, 5\}$ .
- For the second query, there are $3$ distinct numbers between $2$ and $5$ : $2$ , $4$ , and $5$ .
- For the third query, $2$ is replaced by $2$ XOR $3 = 1$ , $4$ is replaced by $4$ XOR $3 = 7$ , and $5$ is replaced by $5$ XOR $3 = 6$ . The set of numbers is $\{1, 6, 7\}$ .
- For the fourth query, there are $2$ distinct numbers between $1$ and $6$ : $1$ and $6$ .
- For the fifth query, $1$ is replaced by $1$ OR $8 = 9$ . The set of numbers is $\{6, 7, 9\}$ .
- For the sixth query, there is one distinct number between $8$ and $10$ : $9$ .
- For the first query, $2$ is replaced by $2$ AND $2 = 2$ and $3$ is replaced with $3$ AND $2 = 2$ . The set of numbers is $\{1, 2, 4, 5\}$ .
- For the second query, there are $3$ distinct numbers between $2$ and $5$ : $2$ , $4$ , and $5$ .
- For the third query, $2$ is replaced by $2$ XOR $3 = 1$ , $4$ is replaced by $4$ XOR $3 = 7$ , and $5$ is replaced by $5$ XOR $3 = 6$ . The set of numbers is $\{1, 6, 7\}$ .
- For the fourth query, there are $2$ distinct numbers between $1$ and $6$ : $1$ and $6$ .
- For the fifth query, $1$ is replaced by $1$ OR $8 = 9$ . The set of numbers is $\{6, 7, 9\}$ .
- For the sixth query, there is one distinct number between $8$ and $10$ : $9$ .