SDE - 1

You are given an integer ‘N’, your task is to find and return the N’th Fibonacci number using matrix exponentiation.

Since the answer can be very large, return the answer modulo 10^9 +7.

Fibonacci number is calculated using the following formula:

F(n) = F(n-1) + F(n-2), 
Where, F(1) = F(2) = 1.

For Example:

For ‘N’ = 5, the output will be 5.

You have given a sorted array 'A' of 'N' integers.

Now, you are given 'Q' queries, and each query consists of a single integer 'X'. Your task is to check whether 'X' is present in array 'A' or not for each query. If 'X' exists in array 'A', you need to print 1 else print 0.

Note :

The given array is sorted in non-decreasing order. 

Stack is a data structure that follows the LIFO (Last in First out) principle. Design and implement a stack to implement the following functions:

1. Push(num): Push the given number in the stack if the stack is not full.

2. Pop: Remove and print the top element from the stack if present, else print -1.

3. Top: Print the top element of the stack if present, else print -1.

4. isEmpty: Print 1 if the stack is empty, else print 0.

5. isFull: Print 1 if the stack is full, else print 0.

You have been given ‘m’ operations which you need to perform in the stack. Your task is to implement all the functions of the stack.

Example:

We perform the following operations on an empty stack which has capacity 2:

When operation 1 1 is performed, we insert 1 in the stack.

When operation 1 2  is performed, we insert 2 in the stack. 

When operation 2 is performed, we remove the top element from the stack and print 2.

When operation 3 is performed, we print the top element of the stack, i.e., 3.

When operation 4 is performed, we print 0 because the stack is not empty.

When operation 5 is performed, we print 0 because the stack is size 1, which is not equal to its capacity.

Chess tournament is going to be organized in Ninjaland. There will be C chess players going to attend the tournament. All the players will be staying in a hotel. The hotel has N free rooms available for the players, where one player will choose one room to live in. The ith room is at position[i] in the hotel. All rooms are in distinct positions.

Focus level of a chess player is defined as the minimum distance between his room and the room of another player. The overall focus of a tournament is defined as the minimum focus level among all players. You as an organizer obviously want the overall focus as high as possible so you assign the rooms to players such that the overall focus is as high as possible.

For example,

let say we have 3 players and 5 rooms available and the rooms are at positions:  1 2 3 4 6
Here the optimal allocation is in rooms 1 3 6 and the overall focus level is 2.