SDE - Intern

You have been given a permutation of ‘N’ integers. A sequence of ‘N’ integers is called a permutation if it contains all integers from 1 to ‘N’ exactly once. Your task is to rearrange the numbers and generate the lexicographically next greater permutation.

To determine which of the two permutations is lexicographically smaller, we compare their first elements of both permutations. If they are equal — compare the second, and so on. If we have two permutations X and Y, then X is lexicographically smaller if X[i] < Y[i], where ‘i’ is the first index in which the permutations X and Y differ.

For example, [2, 1, 3, 4] is lexicographically smaller than [2, 1, 4, 3].

You are given an 'N' * 'M' sized binary-valued matrix 'MAT, where 'N' is the number of rows and 'M' is the number of columns. You need to return the maximum size (area) of the submatrix which consists of all 1’s i.e. the maximum area of a submatrix in which each cell has only the value ‘1’.

In the above image, areas in green, red, and violet color are all submatrices of the original 4x4 matrix.

Note:

1. Binary valued matrix has only two values in each cell : 0 and 1.
2. A submatrix is a matrix formed by selecting certain rows and columns from a larger matrix.
3. The area of a matrix with 'h' rows and 'w' columns is equal to 'h' * 'w'. 

Design a Parking System that returns the number of cars that are parked in the area, given maximum n cars can be parked at one time.

Explain how Semaphores Work. What are the conditions for a system to be in deadlock?