SDE - Intern

You are given an integer ‘N’ , calculate and print the sum of :

LCM(1,N) + LCM(2,N) + .. + LCM(N,N) 

where LCM(i,n) denotes the Least Common Multiple of the integers ‘i’ and ‘N’.

Given a binary tree, return the vertical order traversal of the values of the nodes of the given tree.

For each node at position (X, Y), (X-1, Y-1) will be its left child position while (X+1, Y-1) will be the right child position.

Running a vertical line from X = -infinity to X = +infinity, now whenever this vertical line touches some nodes, we need to add those values of the nodes in order starting from top to bottom with the decreasing ‘Y’ coordinates.

Note:

If two nodes have the same position, then the value of the node that is added first will be the value that is on the left side.

For example:

For the binary tree in the image below.

The vertical order traversal will be {2, 7, 5, 2, 6, 5, 11, 4, 9}.

Derive merge sort complexity.

Different methods to obtain fibonacci series , Space complexity of fibonacci recursion.

Create a stack data structure that allows operations such as push (adding an element), pop (removing the top element), top (retrieving the top element), and also provides a way to retrieve the minimum element in constant time.

Implement the following public functions :

1. push(data) :
This function should take one argument of type integer. It pushes the element into the stack and returns nothing.

2. pop() :
It pops the element from the top of the stack and returns nothing.

3. top() :
It returns the element being kept at the top of the stack.

4.  getMin() :
It returns the smallest element present in the stack.

Operations Performed on the Stack:

Query-1(Denoted by an integer 1): Pushes integer data to the stack. (push function)

Query-2(Denoted by an integer 2): Pops the data kept at the top of the stack. (pop function)

Query-3(Denoted by an integer 3): Fetches and returns the data being kept at the top of the stack. (top function)

Query-4(Denoted by an integer 4): Returns the smallest element present in the stack. (getMin() function)