How do you solve Maximum Subarray on LeetCode?

Maximum Subarray (LeetCode #53) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Kadane's algorithm is a powerful technique for solving maximum subarray problems efficiently.

What is the brute force solution for Maximum Subarray?

The brute force approach for Maximum Subarray is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks all possible subarrays to find the one with the maximum sum. This is simple to understand but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Subarray?

Maximum Subarray uses the following concepts: Array, Divide and Conquer, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Sliding Window.

What are the interview tips for Maximum Subarray?

Always explain your thought process while coding; it helps the interviewer understand your approach. Consider edge cases, such as arrays with all negative numbers or a single element. Practice writing both brute-force and optimal solutions to strengthen your understanding of the problem.

What are common mistakes when solving Maximum Subarray?

Not initializing the maximum sum correctly, which can lead to incorrect results. Forgetting to handle negative numbers properly, which can affect the current sum calculation.

#53

Maximum Subarray

Medium

ArrayDivide and ConquerDynamic ProgrammingDynamic ProgrammingSliding Window

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution uses Kadane's algorithm, which efficiently finds the maximum subarray sum in a single pass through the array. It keeps track of the current subarray sum and updates the maximum sum found so far.

⚙️

Algorithm

4 steps

1Step 1: Initialize two variables: max_sum to the first element and current_sum to the first element.
2Step 2: Iterate through the array starting from the second element.
3Step 3: For each element, update current_sum to be the maximum of the current element or current_sum plus the current element.
4Step 4: Update max_sum if current_sum is greater than max_sum.

solution.py6 lines

1def maxSubArray(nums):
2    max_sum = current_sum = nums[0]
3    for num in nums[1:]:
4        current_sum = max(num, current_sum + num)
5        max_sum = max(max_sum, current_sum)
6    return max_sum

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the array. The space complexity is O(1) since we are using a constant amount of space.

1Kadane's algorithm is a powerful technique for solving maximum subarray problems efficiently.
2Understanding how to maintain a running sum can greatly simplify many problems involving arrays.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.