Senior Software Engineer

Print the following pattern for the given number of rows.

Pattern for N = 4

The dots represent spaces.

You are given an integer array ‘ARR’ of size ‘N’, where ‘ARR[i]’ denotes the number of balls in the ‘i-th’ bag. You are also given an integer ‘M’, denoting the maximum number of operations you can perform on ‘ARR’ (the given collection of bags).

In each operation, you can do the following:

• Choose a bag from the collection and divide it into two new bags such that each bag contains a positive (non-zero) number of balls. Remove the chosen bag from the collection and add the new bags into the collection.

After performing the operations, let ‘X’ be the maximum number of balls in a bag. The task is to find the minimum possible value of ‘X’ and return it.

Example:

ARR = [5, 7], N = 2, M = 2

Perform the following two operations on ‘ARR’: 
1. Divide the bag with 7 balls into 3 and 4. New ARR = [3, 4, 5].
2. Divide the bag with 5 balls into 1 and 4. New ARR = [1, 3, 4, 4].

The bag with the maximum number of balls has 4 balls. Hence, the minimum possible value of ‘X’ is 4. Return 4 as the answer.

Note:

1. You can perform any number of operations between [0, M], both included.
2. Avoid using the 'Modulo' operator as it can cause Time Limit Exceeded.

In a city, there are N houses in a line. Each house is 1 unit apart from the other i.e. distance between any two adjacent houses is 1 unit. The city has both corrupt and honest inhabitants. As a result, some houses contain black money while some contain white money.

The government of India decided to raid this city. Now people having black money want to convert it into white money as soon as possible. The only possible way to do this conversion is to take the black money to the houses with white money. But there is the following restriction: The maximum amount of black money that a white money house can convert is equal to the amount of money that the white house contains.

Note:

We are representing white money as positive integers and black money as negative integers. 

For example:

Let‘s assume ‘HOUSES’ =   [2, -2, -1, 2, -1]. In this example ‘HOUSES[0]’ and ‘HOUSES[3]’ ( 0-based indexing) contain white money while ‘HOUSES[1]’, ‘HOUSES[2]’ and ‘HOUSES[4]’ and  (0-based indexing) contain black money.

The cost of transferring money from one house to another house is the distance between these houses * amount of money transferred.

For example:

Let‘s assume ‘HOUSES’ =   [2, -2, -1, 2, -1]. If we want to transfer all black money from ‘HOUSE[1]’ to ‘HOUSE[3], then the cost of transferring the money is (abs(1 - 3) * (2)) => 4.

Your task is to find the minimum cost of converting all the black money into white.

Note:

The sum of the amount of black money in all houses is exactly equal to the sum of the amount of white money in all houses.

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