Software Engineer

Given a row-wise sorted matrix having N number of rows and M number of columns. Your task is to find the median of the given matrix.

Note :

Assume that the size of the matrix N*M is always odd.

You are given an undirected, connected and weighted graph G(V, E), consisting of V number of vertices (numbered from 0 to V-1) and E number of edges.

Find and print the total weight of the Minimum Spanning Tree (MST) using Kruskal's algorithm.

By definition, a minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

You have been given a sorted array of length ‘N’. You need to construct a balanced binary search tree from the array. If there can be more than one possible tree, then you can return any.

Note:

1. A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height by no more than 1.

2. A binary search tree is a binary tree data structure, with the following properties
    a. The left subtree of any node contains nodes with value less than the node’s value.
    b. The right subtree of any node contains nodes with values equal to or greater than the node’s value.
    c. Right, and left subtrees are also binary search trees.

Example:

Below tree, is a balanced binary search tree

Below tree is not a balanced tree as the height of the left subtree and right subtree of node ‘5’ differs by more than 1. Moreover, the tree is also not a BST as node ‘2’ is less than node ‘3’ but ‘2’ is the right child of ‘3’.

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.

Ninja owns a garden in the city of Ninjago. To prevent trespassers, he must fence the garden, but he is busy and asked you to help him.

You are given an array ‘Trees’ of size ‘N’ denoting the coordinates of each tree.

You want to impress Ninja by creating a circular fence such that all the trees lie either inside the fence or on the boundary of the fence. To minimize the cost you have to build the smallest possible fence. Find the coordinates of the centre and also find the radius of this circular fence.

Note :

Answers with a relative error of less than or equal to 10 ^ -5 are acceptable.

For Example :

If N = 3 and the trees are present at (0, 0), (1, 0) and (2, 0)
Then building a circle with (0, 0) and (2, 0) as diametric endpoints will result in the formation of the smallest circle enclosing all the trees.
Therefore we will return the centre as (1, 0) and radius equal to 1. 

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