SDE - Intern

You will be given a stream of numbers, and you need to find the 'kth' largest number in the stream at any given time.

As the stream of numbers can not be given during compile time, so you need to design a data structure which can accept infinite numbers and can return the 'kth' largest number at any given time.

The stream of numbers is nothing but a large collection of numbers from which integers are read at runtime, such as the user will never know the upper limit on the number of integers that will be read.

The implemented data structure must support the following operations:

1. add(DATA) :
   This function should take one argument of type and store it in its pool and returns the 'kth' largest number from the current pool of integers.

You will be given 'q' queries:

val - For this query, insert the integer into your current pool of integers and return the 'kth' largest integer from the existing pool of integers.

Note

 1. The maximum number of integers that will be given will always be under memory limits.

 2. You will also be given an initial pool of integers whose size equals k.

 3. The maximum number of queries will be less than 10^5.

 4. The 'kth' largest element is not the 'kth' distinct element but the 'kth' largest element in the sorted order.

 5. There will be at least one query of type 2.

You are given a starting position for a rat which is stuck in a maze at an initial point (0, 0) (the maze can be thought of as a 2-dimensional plane). The maze would be given in the form of a square matrix of order 'N' * 'N' where the cells with value 0 represent the maze’s blocked locations while value 1 is the open/available path that the rat can take to reach its destination. The rat's destination is at ('N' - 1, 'N' - 1). Your task is to find all the possible paths that the rat can take to reach from source to destination in the maze. The possible directions that it can take to move in the maze are 'U'(up) i.e. (x, y - 1) , 'D'(down) i.e. (x, y + 1) , 'L' (left) i.e. (x - 1, y), 'R' (right) i.e. (x + 1, y).

Note:

Here, sorted paths mean that the expected output should be in alphabetical order.

For Example:

Given a square matrix of size 4*4 (i.e. here 'N' = 4):
1 0 0 0
1 1 0 0
1 1 0 0
0 1 1 1 
Expected Output:
DDRDRR DRDDRR 
i.e. Path-1: DDRDRR and Path-2: DRDDRR

The rat can reach the destination at (3, 3) from (0, 0) by two paths, i.e. DRDDRR and DDRDRR when printed in sorted order, we get DDRDRR DRDDRR.

If was to conduct a rubrics cube solving contest in some college. So I had to design a system that when given a shuffeed rubric cube is able to judge weather its on some predefined difficulty[state] or not.

Give idea as to a to a non-tech guy as to why he needs that system and what benefits give over some human volunteers
Give an idea as to a tech guy about working and all.

Some follow up questions in my idea