SDE - 1

You are given an arbitrary unweighted rooted tree which consists of N nodes, 0 to N - 1. Your task is to find the largest distance between two nodes in the tree.

The distance between two nodes is the number of edges in a path between the nodes (there will always be a unique path between any pair of nodes since it is a tree).

Note :

Use zero-based indexing for the nodes.

The tree is always rooted at 0.

Given a singly linked list of 'N' nodes. The objective is to determine the middle node of a singly linked list. However, if the list has an even number of nodes, we return the second middle node.

Note:

1. If the list is empty, the function immediately returns None because there is no middle node to find.
2. If the list has only one node, then the only node in the list is trivially the middle node, and the function returns that node.

You are given a starting position for a rat which is stuck in a maze at an initial point (0, 0) (the maze can be thought of as a 2-dimensional plane). The maze would be given in the form of a square matrix of order 'N' * 'N' where the cells with value 0 represent the maze’s blocked locations while value 1 is the open/available path that the rat can take to reach its destination. The rat's destination is at ('N' - 1, 'N' - 1). Your task is to find all the possible paths that the rat can take to reach from source to destination in the maze. The possible directions that it can take to move in the maze are 'U'(up) i.e. (x, y - 1) , 'D'(down) i.e. (x, y + 1) , 'L' (left) i.e. (x - 1, y), 'R' (right) i.e. (x + 1, y).

Note:

Here, sorted paths mean that the expected output should be in alphabetical order.

For Example:

Given a square matrix of size 4*4 (i.e. here 'N' = 4):
1 0 0 0
1 1 0 0
1 1 0 0
0 1 1 1 
Expected Output:
DDRDRR DRDDRR 
i.e. Path-1: DDRDRR and Path-2: DRDDRR

The rat can reach the destination at (3, 3) from (0, 0) by two paths, i.e. DRDDRR and DDRDRR when printed in sorted order, we get DDRDRR DRDDRR.

You are given a positive integer ‘n’.

Your task is to find and return its square root. If ‘n’ is not a perfect square, then return the floor value of sqrt(n).

Example:

Input: ‘n’ = 7

Output: 2

Explanation:
The square root of the number 7 lies between 2 and 3, so the floor value is 2.

You are given an integer 'N'. For a given 'N' x 'N' chessboard, find a way to place 'N' queens such that no queen can attack any other queen on the chessboard.

A queen can be killed when it lies in the same row, or same column, or the same diagonal of any of the other queens. You have to print all such configurations.