Software Development

Given an integer ‘N’ representing the number of pairs of parentheses, Find all the possible combinations of balanced parentheses with the given number of pairs of parentheses.

Note :

Conditions for valid parentheses:
1. All open brackets must be closed by the closing brackets.

2. Open brackets must be closed in the correct order.

For Example :

()()()() is a valid parentheses.
)()()( is not a valid parentheses.

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:

You are a student of Netaji Subhas Institute of Technology. You have to take ‘N’ number of courses labelled from 1 to N to complete your B.Tech Degree.

Some courses may have prerequisites, for example, to take course 1 you have to first take course 2, which is expressed as a pair: [1, 2]. Now, your task is to find is it possible for you to finish all courses.

Note: There are no duplicate pairs in the prerequisites array.

For example-

If N = 2 and prerequisite = [[1, 2]]. Then, there are a total of 2 courses you need to take. To take course 1 you need to finish course 2. So, it is possible to complete all courses. 

You are given a 'Binary Tree'.

Return the bottom view of the binary tree.

Note :

1. A node will be in the bottom-view if it is the bottom-most node at its horizontal distance from the root. 

2. The horizontal distance of the root from itself is 0. The horizontal distance of the right child of the root node is 1 and the horizontal distance of the left child of the root node is -1. 

3. The horizontal distance of node 'n' from root = horizontal distance of its parent from root + 1, if node 'n' is the right child of its parent.

4. The horizontal distance of node 'n' from root = horizontal distance of its parent from the root - 1, if node 'n' is the left child of its parent.

5. If more than one node is at the same horizontal distance and is the bottom-most node for that horizontal distance, including the one which is more towards the right.

Example:

Input: Consider the given Binary Tree:

Output: 4 2 6 3 7

Explanation:
Below is the bottom view of the binary tree.

1 is the root node, so its horizontal distance = 0.
Since 2 lies to the left of 0, its horizontal distance = 0-1= -1
3 lies to the right of 0, its horizontal distance = 0+1 = 1
Similarly, horizontal distance of 4 = Horizontal distance of 2 - 1= -1-1=-2
Horizontal distance of 5 = Horizontal distance of 2 + 1=  -1+1 = 0
Horizontal distance of 6 = 1-1 =0
Horizontal distance of 7 = 1+1 = 2

The bottom-most node at a horizontal distance of -2 is 4.
The bottom-most node at a horizontal distance of -1 is 2.
The bottom-most node at a horizontal distance of 0 is 5 and 6. However, 6 is more towards the right, so 6 is included.
The bottom-most node at a horizontal distance of 1 is 3.
The bottom-most node at a horizontal distance of 2 is 7.

Hence, the bottom view would be 4 2 6 3 7

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Given a binary tree, convert this binary tree into its mirror tree.

A binary tree is a tree in which each parent node has at most two children.

Mirror of a Tree: Mirror of a Binary Tree T is another Binary Tree M(T) with left and right children of all non-leaf nodes interchanged.

Note:

1. Make in-place changes, that is, modify the nodes given a binary tree to get the required mirror tree.

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Design a data structure that stores a mapping of a key to a given value and supports the following operations in constant time.

1. INSERT(key, value): Inserts an integer value to the data structure against a string type key if not already present. If already present, it updates the value of the key with the new one. This function will not return anything.

2. DELETE(key): Removes the key from the data structure if present. It doesn't return anything.

3. SEARCH(key): It searches for the key in the data structure. In case it is present, return true. Otherwise, return false.

4. GET(key): It returns the integer value stored against the given key. If the key is not present, return -1. 

5. GET_SIZE(): It returns an integer value denoting the size of the data structure. 

6. IS_EMPTY(): It returns a boolean value, denoting whether the data structure is empty or not. 

Note :

1. Key is always a string value.
2. Value can never be -1.

Operations Performed :

First(Denoted by integer value 1):  Insertion to the Data Structure. It is done in a pair of (key, value).

Second(Denoted by integer value 2):  Deletion of a key from the Data Structure.

Third(Denoted by integer value 3): Search a given key in the Data Structure.

Fourth(Denoted by integer value 4): Retrieve the value for a given key from the Data Structure.

Fifth(Denoted by integer value 5): Retrieve the size of the Data Structure.

Sixth(Denoted by integer value 6): Retrieve whether the Data Structure is empty or not.

Two pipes, A and B, can fill a cistern in 37 minutes and 45 minutes, respectively. Both pipes are opened. The cistern will be filled in just half an hour if B is turned off after.

Egg dropping Puzzle:

The following is a description of an instance of the famous egg drop puzzle involving N = 2 eggs and a K = 36-floor building.

Suppose we wish to determine which floors in a 36-story building are safe to drop eggs from and which will cause the eggs to break upon landing. We make a few assumptions:

• An egg that survives a fall can be used again.
• A broken egg must be discarded.
• The effect of a fall is the same for all eggs.
• If an egg breaks when dropped from a certain floor, it would also break if dropped from any higher floor.
• If an egg survives a fall from a certain floor, it would also survive a fall from any lower floor.
• It is not ruled out that the first-floor window may break an egg, nor is it ruled out that the 36th-floor window may not.

If only one egg is available and we want to be certain of obtaining the correct result, the experiment can be conducted in only one way:
Drop the egg from the first floor; if it survives, drop it from the second floor, and continue upward until it breaks. In the worst case, this method may require 36 drops.

Now, suppose two eggs are available. What is the minimum number of egg drops required to guarantee determining the critical floor in all cases?

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