Specialist Programmer

You just bought a game of monsters which consists of various levels consisting of monsters. Each monster has power ‘P’ associated with it. Each monster follows (‘P’ * ‘P’ + 1) % ‘M’ distinct monsters in the next level having values from 0 to [(‘P’ * ‘P’ + 1) % ‘M’] - 1 where ‘M’ is a modulo integer given to you. Find the total number of monsters in all levels you need to finish to clear the game.

Note :

In the first level, there is only one monster with power, ‘P’ = 2.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. A string of length 'N' has 'N'! permutations.

Given an array of distinct integers, return all the possible permutations of the array.

Example:

'ARR[]' = [1, 2]

The size of the array is 2. So, the total number of permutations is 2! = 2. The possible permutations are [1, 2] (the array itself) and [2,1] where the position of element 1 in the original array is swapped with element 2 and vice-versa.   

Note:

1. All the numbers in the array are unique.

2. You can return the answer in any order.

3. The original array is also a permutation of the given array.

For a given array with N elements, you need to find the length of the longest subsequence from the array such that all the elements of the subsequence are sorted in strictly increasing order.

Strictly Increasing Sequence is when each term in the sequence is larger than the preceding term.

For example:

[1, 2, 3, 4] is a strictly increasing array, while [2, 1, 4, 3] is not.

You are given an array consisting of 'N' distinct positive integers and a number 'K'. Your task is to find the kth largest element in the array.

Example:

Consider the array {2,1,5,6,3,8} and 'K' = 3, the sorted array will be {8, 6, 5, 3, 2, 1}, and the 3rd largest element will be 5.

Note:

1) Kth largest element in an array is the kth element of the array when sorted in non-increasing order. 

2) All the elements of the array are pairwise distinct.

You are given an integer ‘NUM’ . Your task is to find out whether this number is an Armstrong number or not.

A k-digit number ‘NUM’ is an Armstrong number if and only if the k-th power of each digit sums to ‘NUM’.

Example

153 = 1^3 + 5^3 + 3^3.

Therefore 153 is an Armstrong number.

Given a sequence of numbers ‘ARR’. Your task is to return a sorted sequence of ‘ARR’ in non-descending order with help of the merge sort algorithm.

Example :

Merge Sort Algorithm -

Merge sort is a Divide and Conquer based Algorithm. It divides the input array into two-parts, until the size of the input array is not ‘1’. In the return part, it will merge two sorted arrays a return a whole merged sorted array.

The above illustrates shows how merge sort works.

Note :

It is compulsory to use the ‘Merge Sort’ algorithm.