Leetcode #1567: Maximum Length of Subarray With Positive Product
In this guide, we solve Leetcode #1567 Maximum Length of Subarray With Positive Product in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of integers nums, find the maximum length of a subarray where the product of all its elements is positive. A subarray of an array is a consecutive sequence of zero or more values taken out of that array.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nums = [1,-2,-3,4]
Output: 4
Explanation: The array nums already has a positive product of 24.
Python Solution
class Solution:
def getMaxLen(self, nums: List[int]) -> int:
n = len(nums)
f = [0] * n
g = [0] * n
f[0] = int(nums[0] > 0)
g[0] = int(nums[0] < 0)
ans = f[0]
for i in range(1, n):
if nums[i] > 0:
f[i] = f[i - 1] + 1
g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
elif nums[i] < 0:
f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
g[i] = f[i - 1] + 1
ans = max(ans, f[i])
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.