# Finding the maximum increase in an random array

• leon1127
In summary, the conversation discusses finding the indices pair (i, j) in an array with random real elements where j>i and a[j] - a[i] is maximized in O(n ln n) time. The suggested approach involves sorting the array by (value, index) pairs and inspecting the index array, but it is not a fast algorithm. Recursion is also suggested, but it is not clear how to divide the problem space due to the dependence on all permutations of pairs. Suggestions for a solution are welcomed.
leon1127

## Homework Statement

Given an array with random real elements, find the indices pair (i, j) where j>i s.t

a[j] - a is maximised in O(n ln n) time

I tried sorting the array of (value, index) pair with O(n ln n) sort, and then inspect the index array. However it does not suggest me any fast alsogorithm to find the (i, j) pair fast from here.

O(n ln n) suggest that recursion is necessary. However the difference a[j] - a depends on all the permutation of pairs, I do not see an obvious way to divide the problem space. Any suggestion is appriciated.

Homework Equations N/AThe Attempt at a Solution I tried sorting the array of (value, index) pair with O(n ln n) sort, and then inspect the index array. However it does not suggest me any fast alsogorithm to find the (i, j) pair fast from here.O(n ln n) suggest that recursion is necessary. However the difference a[j] - a depends on all the permutation of pairs, I do not see an obvious way to divide the problem space. Any suggestion is appriciated.

## 1. What is the concept of finding the maximum increase in a random array?

The concept of finding the maximum increase in a random array involves finding the largest difference between two consecutive elements in the array. This represents the maximum increase in the array.

## 2. How can I find the maximum increase in a random array?

To find the maximum increase in a random array, you can iterate through the array and keep track of the largest difference between two consecutive elements. This can be done using a loop or built-in functions in certain programming languages.

## 3. What is the significance of finding the maximum increase in a random array?

Finding the maximum increase in a random array can provide valuable insights into the data. It can help identify trends and patterns, and can also be used for data analysis and prediction.

## 4. Can the maximum increase in a random array be negative?

Yes, the maximum increase in a random array can be negative. This means that there is a decrease in value between two consecutive elements in the array, but it is the largest decrease in the array.

## 5. Are there any efficient algorithms for finding the maximum increase in a random array?

Yes, there are efficient algorithms for finding the maximum increase in a random array such as Kadane's algorithm and Divide and Conquer algorithm. These algorithms have a time complexity of O(n) which makes them efficient for large arrays.

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