'''
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.
Given an array nums, return the maximum alternating sum of any subsequence of nums (after reindexing the elements of the subsequence).

A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements' relative order. For example, [2,7,4] is a subsequence of [4,2,3,7,2,1,4] (the underlined elements), while [2,4,2] is not.

 

Example 1:

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.
Example 2:

Input: nums = [5,6,7,8]
Output: 8
Explanation: It is optimal to choose the subsequence [8] with alternating sum 8.
Example 3:

Input: nums = [6,2,1,2,4,5]
Output: 10
Explanation: It is optimal to choose the subsequence [6,1,5] with alternating sum (6 + 5) - 1 = 10.
 

Constraints:

1 <= nums.length <= 105
1 <= nums[i] <= 105
'''
import unittest
from typing import *


class Solution:
    def maxAlternatingSum(self, nums: List[int]) -> int:
        max_even = 0
        max_odd = nums[0]
        
        for i in range(1, len(nums)):
            even = max_odd - nums[i]
            odd = max_even + nums[i]
            
            max_even = max(max_even, even)
            max_odd = max(max_odd, odd)
        return max(max_even, max_odd)

class TestSolution(unittest.TestCase):

    def test_case(self):
        examples = (
            (([6,2,1,2,4,5],),10),
        )
        for first, second in examples:
            self.assert_function(first, second)

    def assert_function(self, first, second):
        self.assertEqual(Solution().maxAlternatingSum(*first), second,
                         msg="first: {}; second: {}".format(first, second))


unittest.main()