Software Engineer

You have been given a Binary Tree of 'n' nodes, where the nodes have integer values. Your task is to return its postorder traversal.

For Example:

For the given tree below,
Postorder traversal for the given tree will be [4, 5, 2, 3, 1]. Hence, the answer is [4, 5, 2, 3, 1].

You are given a 2-D array 'MATRIX' of dimensions N x M, of integers. You need to return the spiral path of the matrix.

Example Of Spiral Path:

Low-level design for a library system in a city.

High-level design related to a project I worked on at my previous organization.

You are given the root node of a binary tree consisting of ‘N’ nodes. Your task is to return its preorder traversal. The preorder traversal of a binary tree is defined as a process of traversing each node in the following manner-:

1- Visit the root node.
2- Traverse all nodes in the left subtree of the root node.
3- Traverse all the nodes in the right subtree of the root node.

For Example:

For the given tree below,
Preorder traversal for the given tree will be [1, 2, 4, 5, 3]. Hence, the answer is [1, 2, 4, 5, 3].

Example:

Elements are in the level order form. The input consists of values of nodes separated by a single space in a single line. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

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

Explanation :
Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. 

The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.

The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree. 

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

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