SDE - Intern

You are given an arbitrary tree consisting of 'N' nodes numbered from 0 to 'N' - 1. You need to find the total number of elements in all the subtrees of the given tree. In other words, given a generic tree, find the count of elements in the subtrees rooted at each node.

A subtree of a tree T is a tree S consisting of a node in T and all of its descendants in T. The subtree corresponding to the root node is the entire tree. For better understanding, refer to the image below:-

Note:

1. The tree will always be rooted at 0. 
2. You can return the count of nodes in any order.
3. The root of any subtree is also counted in the subtree thus the count of nodes in a subtree rooted at a leaf node is 
4. You can return the numbers in any order.

You are given a ‘Binary Tree’.

Return the level-order traversal of the Binary Tree.

Example:

Input: Consider the following Binary Tree:

Output: 
Following is the level-order traversal of the given Binary Tree: [1, 2, 3, 5, 6, 4]

We have a collection of 'N' stones, each stone has a positive integer weight.

On each turn, we choose the two heaviest stones and smash them together. Suppose the stones have weights 'x' and 'y' with 'x' <= 'y'. The result of this smash will be:

1. If 'x' == 'y', both stones are totally destroyed;

2. If 'x' != 'y', the stone of weight 'x' is totally destroyed, and the stone of weight 'y' has a new weight equal to 'y - x'.

In the end, there is at most 1 stone left. Return the weight of this stone or 0 if there are no stones left.

You are given an array of integers 'ARR' of length 'N' and an integer Target. Your task is to return all pairs of elements such that they add up to Target.

Note:

We cannot use the element at a given index twice.

Follow Up:

Try to do this problem in O(N) time complexity. 

You are given an 'N' * 'M' sized binary-valued matrix 'MAT, where 'N' is the number of rows and 'M' is the number of columns. You need to return the maximum size (area) of the submatrix which consists of all 1’s i.e. the maximum area of a submatrix in which each cell has only the value ‘1’.

In the above image, areas in green, red, and violet color are all submatrices of the original 4x4 matrix.

Note:

1. Binary valued matrix has only two values in each cell : 0 and 1.
2. A submatrix is a matrix formed by selecting certain rows and columns from a larger matrix.
3. The area of a matrix with 'h' rows and 'w' columns is equal to 'h' * 'w'.