- Prepare
- Data Structures
- Trees
- Swap Nodes [Algo]

# Swap Nodes [Algo]

# Swap Nodes [Algo]

A binary tree is a tree which is characterized by one of the following properties:

- It can be empty (null).
- It contains a root node only.
- It contains a root node with a left subtree, a right subtree, or both. These subtrees are also binary trees.

*In-order* traversal is performed as

- Traverse the left subtree.
- Visit root.
- Traverse the right subtree.

For this in-order traversal, start from the left child of the root node and keep exploring the left subtree until you reach a leaf. When you reach a leaf, back up to its parent, check for a right child and visit it if there is one. If there is not a child, you've explored its left and right subtrees fully. If there is a right child, traverse its left subtree then its right in the same manner. Keep doing this until you have traversed the entire tree. You will only store the values of a node as you visit when one of the following is true:

- it is the first node visited, the first time visited
- it is a leaf, should only be visited once
- all of its subtrees have been explored, should only be visited once while this is true
- it is the root of the tree, the first time visited

**Swapping:** Swapping subtrees of a node means that if initially node has left subtree `L`

and right subtree `R`

, then after swapping, the left subtree will be `R`

and the right subtree, `L`

.

For example, in the following tree, we swap children of node `1`

.

```
Depth
1 1 [1]
/ \ / \
2 3 -> 3 2 [2]
\ \ \ \
4 5 5 4 [3]
```

In-order traversal of left tree is `2 4 1 3 5`

and of right tree is `3 5 1 2 4`

.

**Swap operation**:

We define depth of a node as follows:

- The root node is at depth
*1*. - If the depth of the parent node is
`d`

, then the depth of current node will be`d+1`

.

Given a tree and an integer, `k`

, in one operation, we need to swap the subtrees of all the nodes at each depth `h`

, where `h ∈ [k, 2k, 3k,...]`

. In other words, if `h`

is a multiple of `k`

, swap the left and right subtrees of that level.

You are given a tree of `n`

nodes where nodes are indexed from `[1..n]`

and it is rooted at `1`

. You have to perform `t`

swap operations on it, and after each swap operation print the in-order traversal of the current state of the tree.

**Function Description**

Complete the *swapNodes* function in the editor below. It should return a two-dimensional array where each element is an array of integers representing the node indices of an in-order traversal after a swap operation.

swapNodes has the following parameter(s):

- *indexes*: an array of integers representing index values of each , beginning with , the first element, as the root.

- *queries*: an array of integers, each representing a value.

**Input Format**

The first line contains `n`

, number of nodes in the tree.

Each of the next `n`

lines contains two integers, `a b`

, where `a`

is the index of left child, and `b`

is the index of right child of *i ^{th}* node.

**Note:** `-1`

is used to represent a null node.

The next line contains an integer, `t`

, the size of .

Each of the next `t`

lines contains an integer , each being a value .

**Output Format**

For each `k`

, perform the swap operation and store the indices of your in-order traversal to your result array. After all swap operations have been performed, return your result array for printing.

**Constraints**

- Either or
- Either or
- The index of a non-null child will always be greater than that of its parent.

**Sample Input 0**

```
3
2 3
-1 -1
-1 -1
2
1
1
```

**Sample Output 0**

```
3 1 2
2 1 3
```

**Explanation 0**

As nodes *2* and *3* have no children, swapping will not have any effect on them. We only have to swap the child nodes of the root node.

```
1 [s] 1 [s] 1
/ \ -> / \ -> / \
2 3 [s] 3 2 [s] 2 3
```

**Note:** `[s]`

indicates that a swap operation is done at this depth.

**Sample Input 1**

```
5
2 3
-1 4
-1 5
-1 -1
-1 -1
1
2
```

**Sample Output 1**

```
4 2 1 5 3
```

**Explanation 1**

Swapping child nodes of node *2* and *3* we get

```
1 1
/ \ / \
2 3 [s] -> 2 3
\ \ / /
4 5 4 5
```

**Sample Input 2**

```
11
2 3
4 -1
5 -1
6 -1
7 8
-1 9
-1 -1
10 11
-1 -1
-1 -1
-1 -1
2
2
4
```

**Sample Output 2**

```
2 9 6 4 1 3 7 5 11 8 10
2 6 9 4 1 3 7 5 10 8 11
```

**Explanation 2**

Here we perform swap operations at the nodes whose depth is either *2* or *4* for and then at nodes whose depth is *4* for .

```
1 1 1
/ \ / \ / \
/ \ / \ / \
2 3 [s] 2 3 2 3
/ / \ \ \ \
/ / \ \ \ \
4 5 -> 4 5 -> 4 5
/ / \ / / \ / / \
/ / \ / / \ / / \
6 7 8 [s] 6 7 8 [s] 6 7 8
\ / \ / / \ \ / \
\ / \ / / \ \ / \
9 10 11 9 11 10 9 10 11
```