How to Solve Maximum Product Subarray on LeetCode
The Maximum Product Subarray problem is a classic LeetCode dynamic programming challenge that tests your ability to track state and handle edge cases in arrays.
Problem Statement
Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.
Example:
Input: nums = [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.
Why This Problem Matters for Interviews
This problem:
- Assesses dynamic programming intuition
- Tests ability to handle negative numbers and zeros
- Requires tracking both min and max products for each position
Dynamic Programming Approach to Maximum Product Subarray
State Tracking (Optimal)
Track both max and min product up to the current position (to handle negatives).
Time Complexity: O(n)
Space Complexity: O(1)
def maxProduct(nums: list[int]) -> int:
if not nums:
return 0
cur_max = cur_min = ans = nums[0]
for n in nums[1:]:
temp_max = max(n, cur_max * n, cur_min * n)
temp_min = min(n, cur_max * n, cur_min * n)
cur_max, cur_min = temp_max, temp_min
ans = max(ans, cur_max)
return ans
Key Interview Talking Points
- Why you must track both max and min (negative flips sign)
- Edge cases: zeros, negatives, single-element arrays
- Difference between sum subarray and product subarray logic
Big O Complexity Recap
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| State Tracking DP | O(n) | O(1) |
Pro Interview Tips
- Walk through sample input step-by-step.
- Clarify your handling of negatives and zeros.
- Practice with test cases