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 bed+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.
- 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
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 ith node.
Note:
-1
is used to represent a null node.
The next line contains an integer,
Each of the next
t
, the size of .Each of the next
t
lines contains an integer , each being a value .
Output Format
For each
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
Swap Nodes [Algo] - Hacker Rank Solution
For every depth we need to store the nodes that have depth , this can be easily implemented using one dfs.
Now, for each query we will run the loop for , and since we have already stored the nodes at depth for every we can easily swap their left and right child.
Problem Setter's code:
import java.io.*;
import java.util.*;
public class Solution {
class node {
node left, right;
int data;
node(int x) {
this.data = x;
this.left = this.right = null;
}
}
void inorder(node t) {
if(t == null) return;
inorder(t.left);
System.out.print(t.data + " ");
inorder(t.right);
}
void dfs(node t, int y) {
if(t == null) return;
// add node label (at depth y) to the arraylist depth at index y
depth[y].add(t.data);
dfs(t.left, y + 1);
dfs(t.right, y + 1);
}
node tree[];
ArrayList<Integer> depth[];
void solve() {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
tree = new node[n + 1];
depth = new ArrayList[n + 1];
for(int i = 1; i <= n; i++) {
tree[i] = new node(i);
depth[i] = new ArrayList<>();
}
for(int i = 1; i <= n; i++) {
int l = sc.nextInt();
int r = sc.nextInt();
if(l != -1) {
tree[i].left = tree[l];
}
if(r != -1) {
tree[i].right = tree[r];
}
}
dfs(tree[1], 1);
int t = sc.nextInt();
while(t-- > 0) {
int k = sc.nextInt();
int h = k;
while(h <= n) {
// swap children of each node at depth h
for(int d : depth[h]) {
node temp = tree[d].left;
tree[d].left = tree[d].right;
tree[d].right = temp;
}
// h is all the possible multiples of k where we have to swap nodes
h += k;
}
inorder(tree[1]);
System.out.println();
}
}
public static void main(String[] args) {
new Solution().solve();
}
}
editorial copy paste
ReplyDeletewe need explanation about implementation
ReplyDeletelearn dfs and bfs in binary search tree.Hope this helps
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