Apply Operations To An Array - Leetcode Solution

The Apply Operations To An Array problem on Leetcode is a medium-level problem that involves performing multiple operations on an array. The problem statement is as follows:

Given an integer array nums and two integers start and goal, you have to perform the following operation n times:

1. Pick an index i where 0 <= i < nums.length.
2. Replace nums[i] with nums[i] + x where x = start + i * step.
3. You can apply the above operation on the same index i more than once.
4. After applying the operation n times, find the maximum value in the array.

You have to return the maximum value that can be obtained after applying the above operation n times.

To solve this problem, we will first initialize a variable 'max_value' to the minimum integer value. We will then iterate over the array nums, and for each index i, we will perform the following operations:

1. Initialize a variable 'current_value' to the value of nums[i].
2. For each of the n operations, we will increment 'current_value' by the value of start + i * step.
3. If 'current_value' is greater than 'max_value', we will update 'max_value' to 'current_value'.

After iterating over all indices i, we will return 'max_value'.

The time complexity of this solution is O(n), where n is the length of the array nums. The space complexity is O(1) as we are not using any additional space.

Here is the Python code for the solution:

class Solution:
    def max_value(self, nums: List[int], start: int, step: int, n: int) -> int:
        max_value = -sys.maxsize - 1
        
        for i in range(len(nums)):
            current_value = nums[i]
            for j in range(n):
                current_value += start + i * step
                max_value = max(max_value, current_value)
                
        return max_value

In this code, we have defined a class Solution with a method max_value that takes in an integer array nums, and three integers start, step, and n. The method returns the maximum value that can be obtained after applying the above operations n times.

We have used the inbuilt module sys to set the maximum integer value as a starting point for 'max_value'. We have then iterated over the array nums using a for loop, and for each index i, we have defined a nested for loop that performs the operations described above.

We have then used the inbuilt function max to update 'max_value' to the maximum value between the current value and the previous maximum value. Finally, we have returned 'max_value' as the solution to the problem.

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