SDE - 1

You are given a sorted array of ‘N’ distinct integers that are in the Arithmetic Progression sequence except for one element which is missing from the sequence. You have to find that missing number from the given sequence.

Note:

1. A sequence [arr0, arr1,…, arr(n-1)] is called an Arithmetic progression if for each 'i' ( 0 ≤ i < n - 1) the value arr[i+1] − arr[i] is the same. 
2. There is exactly one missing number in the given sequence.
3. All the numbers present in the sequence are distinct.
4. It is the guarantee that the first and last elements of the sequence are not missing elements.

Follow Up

The overall run time complexity should be O(log(N)).

You are given a Binary Tree of 'n' nodes.

The Top view of the binary tree is the set of nodes visible when we see the tree from the top.

Find the top view of the given binary tree, from left to right.

Example :

Input: Let the binary tree be:

Output: [10, 4, 2, 1, 3, 6]

Explanation: Consider the vertical lines in the figure. The top view contains the topmost node from each vertical line.

You are given a directed graph having ‘N’ nodes. A matrix ‘EDGES’ of size M x 2 is given which represents the ‘M’ edges such that there is an edge directed from node EDGES[i][0] to node EDGES[i][1].

Find whether the graph contains a cycle or not, return true if a cycle is present in the given directed graph else return false.

For Example :

In the following directed graph has a cycle i.e. B->C->E->D->B.

Note :

1. The cycle must contain at least two nodes.
2. It is guaranteed that the given graph has no self-loops in the graph.
3. The graph may or may not be connected.
4. Nodes are numbered from 1 to N.
5. Your solution will run on multiple test cases. If you are using global variables make sure to clear them.

You have been given an undirected graph with 'N' vertices and 'M' edges. The vertices are labelled from 1 to 'N'.

Your task is to find if the graph contains a cycle or not.

A path that starts from a given vertex and ends at the same vertex traversing the edges only once is called a cycle.

Example :

In the below graph, there exists a cycle between vertex 1, 2 and 3. 

Note:

1. There are no parallel edges between two vertices.

2. There are no self-loops(an edge connecting the vertex to itself) in the graph.

3. The graph can be disconnected.

For Example :

Input: N = 3 , Edges =  [[1, 2], [2, 3], [1, 3]].
Output: Yes

Explanation : There are a total of 3 vertices in the graph. There is an edge between vertex 1 and 2, vertex 2 and 3 and vertex 1 and 3. So, there exists a cycle in the graph. 

You have been given a matrix of ‘N’ rows and ‘M’ columns filled up with integers. Find the minimum sum that can be obtained from a path which from cell (x,y) and ends at the top left corner (1,1).

From any cell in a row, we can move to the right, down or the down right diagonal cell. So from a particular cell (row, col), we can move to the following three cells:

Down: (row+1,col)
Right: (row, col+1)
Down right diagonal: (row+1, col+1)

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out the minimum no. of races which are required to get the top 3 horses.