SDE - Intern

You are given a chessboard consisting of ‘N’ rows and ’M’ columns. Rows are numbered from 0 to ‘N-1’ and columns are numbered from 0 to ‘M-1’. Cell(i, j) is the cell at the intersection of the ith row and the jth column.

A knight is a chess piece that can move from cell (x1, y1) to the cell (x2, y2) if one of the following conditions is met:

|x1−x2| = 2 and |y1−y2| = 1, or

|x1−x2| = 1 and |y1−y2| = 2.

A knight cannot move outside the chessboard.

Initially a knight is placed at the cell(0, 0) of this chessboard, Moving according to the rules of chess, the knight must visit each cell exactly once. Find out the order of each cell in which they are visited.

Note :

1. There are multiple possible orders in which a knight can visit each cell of the chessboard exactly once. You can find any valid order.
2. It may be possible that there is no possible order to visit each cell exactly once. In that case, return a matrix having all the values equal to -1. 

Example :

Consider an 8*8 chessboard, one possible order for visiting each cell exactly once is shown in the image below. Numbers in cells indicate the move number of the Knight. 

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.

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