SDE - Intern

You are given two integers 'n' and 'm', the dimensions of a grid. The coordinates are from (0, 0) to (n - 1, m - 1).

The grid can only have values 0 and 1.

The value is 0 if there is water and 1 if there is land.

An island is a group of ‘1’s such that every ‘1’ has at least another ‘1’ sharing a common edge.

You are given an array 'queries' of size 'q'.

Each element in 'queries' contains two integers 'x' and 'y', referring to the coordinates in the grid.

Initially, the grid is filled with 0, which means only water and no land.

At each query, the value of 'grid' at (x, y) becomes 1, which means it becomes land.

Find out, after each query, the number of islands in the grid.

Example :

Input: 'n' = 3, 'm' = 4
'queries' = [[1, 1], [1, 2], [2, 3]]

Output: [1, 1, 2]

Explanation:

Initially, the grid was:
0 0 0 0
0 0 0 0
0 0 0 0

After query (1, 1):
0 0 0 0
0 1 0 0
0 0 0 0
There is one island having land (1, 1).

After query (1, 2):
0 0 0 0
0 1 1 0
0 0 0 0
Since (1, 1) and (1, 2) share a common edge, they form one island. So there is one island having lands (1, 1) and (1, 2).

After query (2, 3):
0 0 0 0
0 1 1 0
0 0 0 1
Now there are two islands, one having lands (1, 1) and (1, 2), and another having land (2, 3).

So the number of islands after each query is [1, 1, 2].

You are given three rods (numbered 1 to 3), and ‘N’ disks initially placed on the first rod, one on top of each other in increasing order of size ( the largest disk is at the bottom). You are supposed to move the ‘N’ disks to another rod(either rod 2 or rod 3) using the following rules and in less than 2 ^ (N) moves.

1. You can only move one disk in one move. 
2. You can not place a larger disk on top of a smaller disk.
3. You can only move the disk at the top of any rod.    

Note :

You may assume that initially, the size of the ‘i’th disk from the top of the stack is equal to ‘i’, i.e. the disk at the bottom has size ‘N’, the disk above that has size ‘N - 1’, and so on. The disk at the top has size 1.

Example :

You are given a 2D board('N' rows and 'M' columns) of characters and a string 'word'.

Your task is to return true if the given word exists in the grid, else return false. The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring.

Note:

The same letter cell should not be used more than once.

For Example:

For a given word “design” and the given 2D board 
[[q’, ‘v’, ‘m’, ‘h’],
 [‘d’, ‘e’, ‘s’, ‘i’],
 [‘d’, ‘g’, ‘f’, ‘g’],
 [‘e’, ‘c’, ‘p’, ‘n’]]

The word design can be formed by sequentially adjacent cells as shown by the highlighted color in the 2nd row and last column.