Question

a company has a list of expected revenues and payments for the upcoming year in chronological order. the problem is that at some moments in time the sum of previous payments can be larger than the total previous revenue, which would put the company in debt. to avoid this problem the company takes a very simple approach: it reschedules some expenses to the end of the year. you are given an array of integers, where positive numbers represent revenues and negative numbers represent expenses, all in chronological order. in one move you can relocate any expense (negative number) to the end of the array. what is the minimum number of such relocations to make sure that the company never falls into debt (in other words: you need to ensure that there is no consecutive sequence of elements starting from the beginning of the array, that sums up to a negative number)?

Answer 1

To avoid company debt by rearranging expenses, calculate the cumulative sum of finances and strategically relocate the largest expenses from where the sum dips negative until it remains non-negative throughout.

Step-by-step explanation:

To determine the minimum number of relocations of expenses to the end of the array to ensure that the company does not go into debt, we need to approach this problem algorithmically. Starting from the beginning of the array, calculate the cumulative sum of the revenues and expenses. If at any point the cumulative sum becomes negative, this indicates that the company would go into debt without rearranging some expenses. The process involves identifying the largest expense that has occurred before or at the point where the cumulative sum is negative and moving that expense to the end of the array. Repeat this process until the cumulative sum is non-negative at all points in the array.

The minimum number of relocations is equal to the number of negative dips in the cumulative sum graph that you encounter. By always moving the largest preceding negative number, you are guaranteed to have the largest positive impact on the cumulative sum with the fewest moves.

This can be visualized by plotting a graph of the cumulative sum versus time and seeing how many times the graph dips below zero. Each of these dips might require one or more relocations, but strategic relocations will minimize the total number needed.

Answer 2

This Mathematics question requires the minimization of expense relocations in an array to avoid cumulative debt, using cumulative sums and array manipulation.

Step-by-step explanation:

The subject of this question is Mathematics, and it involves finding the minimum number of relocations of expenses to ensure that the cumulative total of revenues and expenses never becomes negative. To solve this, one needs to track the cumulative sum of the array and whenever the sum becomes negative, relocate the most recent expense to the end of the array. This is repeated until no negative cumulative sum exists from the start of the array. It requires understanding of array manipulation, cumulative sums, and optimization strategies.