How to Solve Maximum Subarray Sum on LeetCode
The Maximum Subarray Sum problem (Kadane's Algorithm) is a classic LeetCode challenge that tests your understanding of dynamic programming and array traversal.
Problem Statement
Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
Example:
Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.
Why This Problem Matters for Interviews
This problem:
- Demonstrates dynamic programming intuition
- Requires optimal state tracking
- Is foundational for many real-world optimizations
Kadane's Algorithm Approach (Optimal)
Track current max subarray sum at each index, update global max.
Time Complexity: O(n)
Space Complexity: O(1)
def maxSubArray(nums: list[int]) -> int:
max_sum = curr_sum = nums[0]
for n in nums[1:]:
curr_sum = max(n, curr_sum + n)
max_sum = max(max_sum, curr_sum)
return max_sum
Key Interview Talking Points
- Intuition for when to restart the subarray
- Why greedy/DP merge works
- Edge cases: all negative numbers, single-element arrays
- Relation to other subarray problems
Big O Complexity Recap
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Kadane's Algo | O(n) | O(1) |
Pro Interview Tips
- Walk through Kadane’s on sample input.
- Clarify restart condition for current sum.
- Practice with test cases