Leetcode #2036: Maximum Alternating Subarray Sum
In this guide, we solve Leetcode #2036 Maximum Alternating Subarray Sum 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
A subarray of a 0-indexed integer array is a contiguous non-empty sequence of elements within an array. The alternating subarray sum of a subarray that ranges from index i to j (inclusive, 0 <= i <= j < nums.length) is nums[i] - nums[i+1] + nums[i+2] - ...
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: 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 = [3,-1,1,2]
Output: 5
Explanation:
The subarray [3,-1,1] has the largest alternating subarray sum.
The alternating subarray sum is 3 - (-1) + 1 = 5.
Python Solution
class Solution:
def maximumAlternatingSubarraySum(self, nums: List[int]) -> int:
ans = f = g = -inf
for x in nums:
f, g = max(g, 0) + x, f - x
ans = max(ans, f, g)
return ans
Complexity
The time complexity is , where is the length of the array . 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.