SDE - 1

Formula to find the area of an inscribed circle:∏ /{4} * a^2 where a is the side of a square in which a circle is inscribed.

This can be solved using recursion. 
Steps :
(1) Call Mirror for left-subtree i.e., Mirror(left-subtree)
(2) Call Mirror for right-subtree i.e., Mirror(right-subtree)
(3) Swap left and right subtrees.
temp = left->subtree
left->subtree = right->subtree
right->subtree = temp

Worst-case Time complexity is O(n) 
Auxiliary space complexity : O(h) where h is the height of the tree.

This problem can be solved using recursion. In this approach, we will start form last element of both the strings. If elements at the last matches then we will decrement length of both the string else we will decrement the length of either of the string.

lcs(s1, s2, n, m):
	if n == 0 or m == 0:
		return 0
	if s1[n-1] == s2[m - 1]:
		return 1 + lcs(s1, s2, n-1, m-1)
	else:
		return max(lcs(s1, s2, n-1, m), lcs(s1, s2, n, m-1))

But this approach would result in TLE for longer test cases. It can be optimized using dynamic programming.

In the top down approach, we make a table of size [m+1][n+1] where m and n are the length of the strings. The intermediate row and column of the table indicates what will be the value of the longest common subsequence if its called for the smaller inputs.

if s1[i - 1] == s2[j - 1]:
	dp[i][j] = dp[i - 1][j - 1] + 1
else:
	dp[i][j] = max(dp[i][j - 1], dp[i - 1][j])

Inorder Traversal using Recursion
Algorithm Inorder(tree)
1. Traverse the left subtree, i.e., call Inorder(left-subtree)
2. Visit the root.
3. Traverse the right subtree, i.e., call Inorder(right-subtree)

Inorder traversal of tree without recursion
Inorder traversal requires that we print the leftmost node first and the right most node at the end. 
So basically for each node we need to go as far as down and left as possible and then we need to come back and go right. So the steps would be : 
1. Start with the root node. 
2. Push the node in the stack and visit it's left child.
3. Repeat step 2 while node is not NULL, if it's NULL then pop the topmost node from the stack and print it.
4. Now move to node's right child and repeat step 1
5. Repeat the above steps while node is not NULL and stack is not empty

The recursive approach involves direct implementation of mathematical recurrence formula. 
F(n) = F(n-1)+F(n-2)
Pseudocode :
fibonacci(n):
if(n<=1)
return n;
return fibonacci(n-1) + fibonacci(n-2)

This is an exponential approach. 
It can be optimized using dynamic programming. Maintain an array that stores all the calculated fibonacci numbers so far and return the nth fibonacci number at last. This approach will take O(n) time complexity and O(n) auxiliary space.

Views in SQL are kind of virtual tables. A view also has rows and columns as they are in a real table in the database. We can create a view by selecting fields from one or more tables present in the database. A View can either have all the rows of a table or specific rows based on certain condition.

B Trees, B+ Trees

1. Domain constraints
Domain constraints can be defined as the definition of a valid set of values for an attribute.
The data type of domain includes string, character, integer, time, date, currency, etc. The value of the attribute must be available in the corresponding domain.

2. Entity integrity constraints
The entity integrity constraint states that primary key value can't be null.
This is because the primary key value is used to identify individual rows in relation and if the primary key has a null value, then we can't identify those rows. A table can contain a null value other than the primary key field.

3.3. Referential Integrity Constraints
A referential integrity constraint is specified between two tables.
In the Referential integrity constraints, if a foreign key in Table 1 refers to the Primary Key of Table 2, then every value of the Foreign Key in Table 1 must be null or be available in Table 2.

4. Key constraints
Keys are the entity set that is used to identify an entity within its entity set uniquely.
An entity set can have multiple keys, but out of which one key will be the primary key. A primary key can contain a unique and null value in the relational table.

SDLC is a process followed for a software project, within a software organization. It consists of a detailed plan describing how to develop, maintain, replace and alter or enhance specific software. The life cycle defines a methodology for improving the quality of software and the overall development process.

A typical Software Development Life Cycle consists of the following stages −

Stage 1: Planning and Requirement Analysis
Requirement analysis is the most important and fundamental stage in SDLC. It is performed by the senior members of the team with inputs from the customer, the sales department, market surveys and domain experts in the industry. This information is then used to plan the basic project approach and to conduct product feasibility study in the economical, operational and technical areas. Planning for the quality assurance requirements and identification of the risks associated with the project is also done in the planning stage. The outcome of the technical feasibility study is to define the various technical approaches that can be followed to implement the project successfully with minimum risks.

Stage 2: Defining Requirements
Once the requirement analysis is done the next step is to clearly define and document the product requirements and get them approved from the customer or the market analysts. This is done through an SRS (Software Requirement Specification) document which consists of all the product requirements to be designed and developed during the project life cycle.

Stage 3: Designing the Product Architecture
SRS is the reference for product architects to come out with the best architecture for the product to be developed. Based on the requirements specified in SRS, usually more than one design approach for the product architecture is proposed and documented in a DDS - Design Document Specification. This DDS is reviewed by all the important stakeholders and based on various parameters as risk assessment, product robustness, design modularity, budget and time constraints, the best design approach is selected for the product.
A design approach clearly defines all the architectural modules of the product along with its communication and data flow representation with the external and third party modules (if any). The internal design of all the modules of the proposed architecture should be clearly defined with the minutest of the details in DDS.

Stage 4: Building or Developing the Product
In this stage of SDLC the actual development starts and the product is built. The programming code is generated as per DDS during this stage. If the design is performed in a detailed and organized manner, code generation can be accomplished without much hassle.
Developers must follow the coding guidelines defined by their organization and programming tools like compilers, interpreters, debuggers, etc. are used to generate the code. Different high level programming languages such as C, C++, Pascal, Java and PHP are used for coding. The programming language is chosen with respect to the type of software being developed.

Stage 5: Testing the Product
This stage is usually a subset of all the stages as in the modern SDLC models, the testing activities are mostly involved in all the stages of SDLC. However, this stage refers to the testing only stage of the product where product defects are reported, tracked, fixed and retested, until the product reaches the quality standards defined in the SRS.

Stage 6: Deployment in the Market and Maintenance
Once the product is tested and ready to be deployed it is released formally in the appropriate market. Sometimes product deployment happens in stages as per the business strategy of that organization. The product may first be released in a limited segment and tested in the real business environment (UAT- User acceptance testing).
Then based on the feedback, the product may be released as it is or with suggested enhancements in the targeting market segment. After the product is released in the market, its maintenance is done for the existing customer base.

The Agile methodology is a way to manage a project by breaking it up into several phases. It involves constant collaboration with stakeholders and continuous improvement at every stage. Once the work begins, teams cycle through a process of planning, executing, and evaluating. Continuous collaboration is vital, both with team members and project stakeholders.

Agile methodologies overview
The Agile Manifesto of Software Development put forth a groundbreaking mindset on delivering value and collaborating with customers when it was created in 2001. Agile's four main values are :
1) Individuals and interactions over processes and tools
2) Working software over comprehensive documentation
3) Customer collaboration over contract negotiation
4) Responding to change over following a plan

Factorial can be calculated using following recursive formula: 

n! = n * (n-1)!

n! = 1 if n = 0 or n = 1

Factorial can also be calculated iteratively as recursion can be costly for large numbers. 

Factorial(n)
{
	//Initialise a variable res = 1
	long long res=1
	for (i = 2 to i <= n) do :
		res = res* i
	return res
}

Tip 1 : The cross questioning can go intense some time, think before you speak.

Tip 2 : Be open minded and answer whatever you are thinking, in these rounds I feel it is important to have opinion.

Tip 3 : Context of questions can be switched, pay attention to the details. It is okay to ask questions in these round, like what are the projects currently the company is investing, which team you are mentoring. How all is the work environment etc.