maximum subarray

LeetCode 53: Maximum Subarray

i recently solved the maximum subarray problem on leetcode, and it's a great example of array, dynamic programming techniques. this medium problem tests your understanding of array, dynamic programming.

Problem Statement

[problem description would go here - you can add the actual problem statement]

My Approach

when i first saw this problem, i immediately thought about using kadane's algorithm. the key insight is [to be filled based on the specific problem].

Initial Thoughts

i started by thinking about different approaches:

• **brute force** - [brute force approach description]
• **optimized approach** - Kadane's Algorithm
• **alternative approach** - [alternative approach if applicable]

Solution Strategy

i decided to use a Kadane's Algorithm with the following strategy:

• **[step 1]** - [description]
• **[step 2]** - [description]
• **[step 3]** - [description]

My Solution

def solution(self, params):
# implementation would go here
pass

Code Breakdown

let me walk through how this solution works:

1. [Section 1]

# code snippet

[explanation]

2. [Section 2]

# code snippet

[explanation]

Example Walkthrough

let's trace through an example:

[step-by-step walkthrough]

Time and Space Complexity

• **time complexity:** [complexity analysis]
• **space complexity:** [complexity analysis]

Key Insights

• **[insight 1]** - [explanation]
• **[insight 2]** - [explanation]
• **[insight 3]** - [explanation]

Alternative Approaches

i also considered:

• **[alternative 1]** - [description]
• **[alternative 2]** - [description]

Edge Cases to Consider

• **[edge case 1]** - [description]
• **[edge case 2]** - [description]
• **[edge case 3]** - [description]

Lessons Learned

this problem taught me:

• [lesson 1]
• [lesson 2]
• [lesson 3]

Conclusion

the maximum subarray problem is a great exercise in array, dynamic programming. the key insight is [key takeaway].

you can find my complete solution on [leetcode](https://leetcode.com/problems/maximum-subarray/solutions/1234569/maximum-subarray-solution-by-1cbyc).

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*this is part of my leetcode problem-solving series. i'm documenting my solutions to help others learn and to track my own progress.*