Specialist Programmer

In Ninja Land, there is a famous restaurant named ‘CookingNinjas’. There are ‘N’ cooks in ‘CookingNinjas’ numbered from 0 to N-1. Each cook has rank ‘R’ (1 <= R <= 10).

A cook with a rank ‘R’ can prepare 1 dish in the first ‘R’ minutes, 1 more dish in the next ‘2R’ minutes, 1 more dish in next ‘3R’ minutes, and so on (A cook can only make complete dishes) For example if a cook is ranked 2. He will prepare one dish in 2 minutes, one more dish in the next 4 mins and one more in the next 6 minutes hence in a total of 12 minutes he can make 3 dishes, Note, In 13 minutes also he can make only 3 dishes as he does not have enough time for the 4th dish).

One day ‘CookingNinjas’ receive an order of ‘M’ dishes that they need to complete as early as possible. You are given an integer array ‘rank’ of size ‘N’ in which ‘rank[i]’ gives ‘rank’ of ith cook and an integer ‘M’, You need to find out the minimum times required to complete this order of ’M’ dishes.

Note

One dish can be prepared by only one cook, however, two or more cooks can simultaneously prepare different dishes.

For Example

Let ‘N’ = 4,  ‘ranks’ = [1, 2, 3, 4] and ‘M’ = 11.  Then the minimum time required to cook 11 dishes will be 12 minutes.  The cooks should prepare dishes in the following manner -:
Cook-0 prepare 4 dishes in 10 minutes i.e (1 dish in 1 minute, 1 more dish in next 2 minutes, 1 more dish in next 3 minutes, 1 more dish in next 4 minutes).
Cook-1 prepare 3 dishes in 12 minutes i.e (1 dish in 2 minutes, 1 more dish in 4 minutes, 1 more dish in 6 minutes).
Cook-2 prepare 2 dishes in 9 minutes i.e (1 dish in 3 minutes, 1 more dish in the next 6 minutes).
Cook-3 prepare 2 dishes in 12 minutes i.e (1 dish in 4 minutes, 1 more dish in the next 8 minutes).
If all four cooks work simultaneously then they can prepare(4 + 3 + 2 + 2 = 11) dishes in 12 minutes. And it is the minimum possible time.

Ninja has built his team of ninjas to fight with the enemies in his city. Ninja made a plan of attacking all his enemies. In his team, every ninja has his own range of hitting and they had secretly got the hitting range of their enemies as well. So Ninja allowed some swaps between his ninjas so that they can minimize the hamming distance that is the number of positions where the hitting range of enemies and ninjas are different.

Your task is to write a code that can minimize the hamming distance. You are being provided with two arrays ‘ninja’ and ‘enemies’ both of the same size and an array ‘allowedSwaps’ where each allowedSwaps[i] = [ ai, bi ] indicates that you are allowed to swap the elements at index ai and index bi.

The Hamming distance of two arrays of the same length, ninja, and enemies, is the number of positions where the elements are different.

Example :

Consider the case ‘ninja’array is [ 1, 2, 3, 4 ], ‘enemies’array is [ 2, 1, 4, 5 ] and ‘allowedSwaps’ are  = [ [ 0, 1 ], [ 2, 3 ] ] so after swapping in best manner according to ‘allowedSwaps’ our ‘ninja’ array becomes [ 2, 1, 4, 3 ]. So minimum Hamming distance is ‘1’ as now there is only one different element as compared to ‘ninja’ and ‘enemies’ array index.

Note :

1. You are allowed to do as many swap operations on the ‘ninja’ array as you want but according to the ‘allowedSwap’ array.
2. You are not required to print anything explicitly. It has already been taken care of. Just implement the function.

In Ninja land, there are N cities that are connected to each other by undirected roads. The cities along with all the roads form a tree-like structure. Each city has an initial height associated with it. The heights of the cities can change also. Now Ninja got bored at home and decided to visit different cities. But Ninja only wants to visit two cities if the path between them forms an alternate series of ups and downs. Since Ninja doesn’t know whether the path between the two cities is alternating or not, he asked you to help him.

For Example:

Suppose Ninja is currently standing at X city and want to visit Y city. Let the heights of all the cities in the path from X to Y(including X and Y) are 10 20 5 30. Now these series of heights forms and alternate series. So Ninja will visit the city Y.

Some examples of alternate series are 15 4 11 8 25, 100 120 50 70 60 but the series like 3 5 4 1, 6 3 10 12 are not alternating.

Now you will be asked q queries, and there are two types of queries:

1 X Y: change the height of city X to Y.

2 X Y: Check whether the path between city X to Y is alternating or not.

Given an array 'arr' with 'n' elements, the task is to rotate the array to the left by 'k' steps, where 'k' is non-negative.

Example:

'arr '= [1,2,3,4,5]
'k' = 1  rotated array = [2,3,4,5,1]
'k' = 2  rotated array = [3,4,5,1,2]
'k' = 3  rotated array = [4,5,1,2,3] and so on.

Different states of a process.

Polymorphism, semaphores, Normalization and its types.

You are given a binary tree having 'n' nodes. Each node of the tree has an integer value.

Your task is to find the maximum possible sum of a simple path between any two nodes (possibly the same) of the given tree.

A simple path is a path between any two nodes of a tree, such that no edge in the path is repeated twice. The sum of a simple path is defined as the summation of all node values in a path.