SDE - 1

You are given a 2-dimensional array/list having N rows and M columns, which is filled with ones(1) and zeroes(0). 1 signifies land, and 0 signifies water.

A cell is said to be connected to another cell, if one cell lies immediately next to the other cell, in any of the eight directions (two vertical, two horizontal, and four diagonals).

A group of connected cells having value 1 is called an island. Your task is to find the number of such islands present in the matrix.

A girl found that she had a 56 cms strip of ribbon. She could cut a cm off every second. How long would it take for her to cut 56 pieces? She can not fold the strip and also, can not stack two or more strips and cut them together.

The Ultimate Ninja Ankush, has prepared a test for all of his fellow Ninja students, but since he is the Ultimate Ninja, he does not like cheating, and since his students are also ninjas, they broke some chairs in the dojo while practicing their moves.

The class consists of ‘M’ * ‘N’ seats, represented in a matrix ‘SEATS’. Among the seats, some of the seats are broken. If a seat is broken, it is denoted by '#' character otherwise it is denoted by a '.' character, denoting that the seat can be occupied. A Ninja can’t sit in a broken seat.

Ankush wants to avoid cheating at any cost. According to his observations, a student can see the answers of four neighboring students sitting next to the left, right, upper left, and upper right, but they cannot see the answers of the student sitting directly in front or behind him. Ankush is very busy so he wants to use the dojo to the fullest. More formally he wants to know the maximum number of ninja students that can be placed in the dojo.

For example

Given:
‘M’ = 3, ‘N’ = 3.
‘SEATS’ = {
   {‘.’, ‘.’, ‘.’},
   {‘#’,’#’, ‘#’},
   {‘.’,’.’,’.’} 
   }
The answer will be 4, since 4 students can be placed at the four corners, i.e. (0,0), (2,2), (2,0), and (0,2) such that no cheating is possible.

Given an array of integers of size ‘N’ and a positive integer ‘K’. Return the number of non-empty subarrays whose sum is divisible by K.

A subarray is a contiguous subset of an array.

For Example :

Consider an array of size four. The elements of the array are { -4, 5, 6, 1}. 
The value of K is 4. 
The subarrays whose sum is divisible by 4 are as  follows:
[ -4 ] 
[-4, 5, 6, 1] 
[ 5, 6, 1] 
Hence, there are three subarrays whose sum is divisible by 4. 

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