A11728. Full Binary Tree Queries
编程题
普及/提高-
知识点
题目描述
You have a full binary tree having infinite levels.
Each node has an initial value. If a node has value $x$ , then its left child has value $2·x$ and its right child has value $2·x+1$ .
The value of the root is $1$ .
You need to answer $Q$ queries.
There are $3$ types of queries:
1. Cyclically shift the values of all nodes on the same level as node with value $X$ by $K$ units. (The values/nodes of any other level are not affected).
2. Cyclically shift the nodes on the same level as node with value $X$ by $K$ units. (The subtrees of these nodes will move along with them).
3. Print the value of every node encountered on the simple path from the node with value $X$ to the root.
Positive $K$ implies right cyclic shift and negative $K$ implies left cyclic shift.
It is guaranteed that atleast one type $3$ query is present.
Each node has an initial value. If a node has value $x$ , then its left child has value $2·x$ and its right child has value $2·x+1$ .
The value of the root is $1$ .
You need to answer $Q$ queries.
There are $3$ types of queries:
1. Cyclically shift the values of all nodes on the same level as node with value $X$ by $K$ units. (The values/nodes of any other level are not affected).
2. Cyclically shift the nodes on the same level as node with value $X$ by $K$ units. (The subtrees of these nodes will move along with them).
3. Print the value of every node encountered on the simple path from the node with value $X$ to the root.
Positive $K$ implies right cyclic shift and negative $K$ implies left cyclic shift.
It is guaranteed that atleast one type $3$ query is present.
输入格式
The first line contains a single integer $Q$ ( $1<=Q<=10^{5}$ ).
Then $Q$ queries follow, one per line:
- Queries of type $1$ and $2$ have the following format: $T$ $X$ $K$ ( $1<=T<=2$ ; $1<=X<=10^{18}$ ; $0<=|K|<=10^{18}$ ), where $T$ is type of the query.
- Queries of type $3$ have the following format: $3$ $X$ ( $1<=X<=10^{18}$ ).
Then $Q$ queries follow, one per line:
- Queries of type $1$ and $2$ have the following format: $T$ $X$ $K$ ( $1<=T<=2$ ; $1<=X<=10^{18}$ ; $0<=|K|<=10^{18}$ ), where $T$ is type of the query.
- Queries of type $3$ have the following format: $3$ $X$ ( $1<=X<=10^{18}$ ).
输出格式
For each query of type $3$ , print the values of all nodes encountered in descending order.
输入输出样例
输入 #1
5 3 12 1 2 1 3 12 2 4 -1 3 8
输出 #1
12 6 3 1 12 6 2 1 8 4 2 1
输入 #2
5 3 14 1 5 -3 3 14 1 3 1 3 14
输出 #2
14 7 3 1 14 6 3 1 14 6 2 1
说明/提示
Following are the images of the first $4$ levels of the tree in the first test case:
Original:
 After query 1 2 1:
 After query 2 4 -1:
Original:
 After query 1 2 1:
 After query 2 4 -1:
