Maximum Alternating Subsequence Sum — LeetCode 1911 Python Solution

The problem

The alternating sum of a 0-indexed array is defined as the sum of the elements at even indices minus the sum of the elements at odd indices. For example, the alternating sum of [4,2,5,3] is (4 + 5) - (2 + 3) = 4.

Example

Input

nums = [4,2,5,3]

Output

7

Explanation

It is optimal to choose the subsequence [4,2,5] with alternating sum (4 + 5) - 2 = 7.

Python solution

class Solution:
    def maxAlternatingSum(self, nums: List[int]) -> int:
        n = len(nums)
        f = [0] * (n + 1)
        g = [0] * (n + 1)
        for i, x in enumerate(nums, 1):
            f[i] = max(g[i - 1] - x, f[i - 1])
            g[i] = max(f[i - 1] + x, g[i - 1])
        return max(f[n], g[n])

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1911. Maximum Alternating Subsequence Sum is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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