algoadvance

You are given an integer array nums. A subarray of nums is called an ascending subarray if it is a contiguous non-empty sequence of elements such that for all i, nums[i] < nums[i + 1]. The sum of an ascending subarray is the sum of its elements.

Return the maximum sum of any ascending subarray.

Example:

Input: nums = [10, 20, 30, 5, 10, 50]
Output: 65
Explanation: [10, 20, 30] and [5, 10, 50] are the two ascending subarrays with the maximum sum of 60 and 65 respectively. Thus, we return 65.

Clarifying Questions

  1. Can nums contain negative numbers?
    • Yes, the array can contain negative numbers.
  2. What should be returned if nums is empty?
    • If nums is empty, the function should return 0.

Strategy

To solve this problem, we will use the following approach:

  1. Initialize two variables:
    • max_sum to store the maximum sum found so far, initialized to 0 (or to the first element if nums is not empty).
    • current_sum to store the sum of the current ascending subarray, initialized to 0.
  2. Iterate through each element in the array:
    • If the current element is greater than the previous element, add it to current_sum.
    • If it is not, compare current_sum with max_sum to keep track of the maximum sum found so far, then reset current_sum to the current element.

  3. After finishing the loop, there might still be an unsaved current_sum since the last subarray might be the maximum ascending one. Compare and save it if necessary.

  4. Return the max_sum.

Code

Here is the Python code implementing the above strategy:

def maxAscendingSum(nums):
    if not nums:
        return 0

    max_sum = 0
    current_sum = nums[0]

    for i in range(1, nums.length):
        if nums[i] > nums[i - 1]:
            current_sum += nums[i]
        else:
            max_sum = max(max_sum, current_sum)
            current_sum = nums[i]

    max_sum = max(max_sum, current_sum)
    return max_sum

# Example usage
nums = [10, 20, 30, 5, 10, 50]
print(maxAscendingSum(nums)) # Output: 65

Time Complexity

The time complexity of this solution is (O(n)), where (n) is the length of the input array nums. This is because we iterate through the array exactly once. The space complexity is (O(1)) because we use a constant amount of extra space regardless of the input size.

Feel free to ask any more questions or provide input for additional modifications.

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