Software Engineer

You are given an array “arr'' of integers. Your task is to find the contiguous subarray within the array which has the largest product of its elements. You have to report this maximum product.

An array c is a subarray of array d if c can be obtained from d by deletion of several elements from the beginning and several elements from the end.

For e.g.- The non-empty subarrays of an array [1,2,3] will be- [1],[2],[3],[1,2],[2,3],[1,2,3]. 

For Example:

If arr = {-3,4,5}.
All the possible non-empty contiguous subarrays of “arr” are {-3}, {4}, {5}, {-3,4}, {4,5} and {-3,4,5}.
The product of these subarrays are -3, 4, 5, -12, 20 and -60 respectively.
The maximum product is 20. Hence, the answer is 20.

Follow Up:

Can you solve this in linear time and constant space complexity?

You have been given a matrix of ‘N’ rows and ‘M’ columns filled up with integers. Find the minimum sum that can be obtained from a path which from cell (x,y) and ends at the top left corner (1,1).

From any cell in a row, we can move to the right, down or the down right diagonal cell. So from a particular cell (row, col), we can move to the following three cells:

Down: (row+1,col)
Right: (row, col+1)
Down right diagonal: (row+1, col+1)

You have a binary tree of 'N' unique nodes and a Start node from where the tree will start to burn. Given that the Start node will always exist in the tree, your task is to print the time (in minutes) that it will take to burn the whole tree.

It is given that it takes 1 minute for the fire to travel from the burning node to its adjacent node and burn down the adjacent node.

For Example :

For the given binary tree: [1, 2, 3, -1, -1, 4, 5, -1, -1, -1, -1]
Start Node: 3

    1
   / \
  2   3
     / \
    4   5

Output: 2

Explanation :
In the zeroth minute, Node 3 will start to burn.

After one minute, Nodes (1, 4, 5) that are adjacent to 3 will burn completely.

After two minutes, the only remaining Node 2 will be burnt and there will be no nodes remaining in the binary tree. 

So, the whole tree will burn in 2 minutes.

Desing Singleton Class, Questions on OOPS indepth and Some SQL questoins on Group By, Joins

You have been given a Binary Tree where the value of each node is either 0 or 1. Your task is to return the same Binary Tree but all of its subtrees that don't contain a 1 have been removed.

Note :

A subtree of a node X is X, plus every node that is a descendant of X.

For Example :

Look at the below example to see a Binary Tree pruning.
Input: [1, 1, 1, 0, 1, 0, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]

Output: [1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1]

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

You are given a string 's', and a dictionary of words 'dict' containing 'n' words. Your task is to add spaces in 's' to form valid sentences, where each word is a word from the dictionary.

You need to return all possible sentences that can be formed using the given dictionary.

Note :

The same word from a dictionary can be used as many times as possible to make sentences.