mediumArraysPattern: Custom
Galactic Trade Imbalance Solution
Problem Statement
In a galaxy with various trade routes, the merchants of planet Zorvath have observed an intriguing pattern. They have noted that for any sequence of trade transactions, the difference in credits between transactions initiated by them (even indexed transactions) and those initiated by their trade partners (odd indexed transactions) can fluctuate greatly. Calculate the maximum absolute difference between the sum of credits in transactions initiated by the Zorvath merchants and the sum of credits in transactions initiated by their partners within any subsequence of transactions.
Examples
Example 1:
Input:[14, 5, 8, 20, 3, 17]
Output:26
Explanation: The maximum absolute difference can be achieved by considering the subsequence [8, 20, 3, 17], where the sum of the even indexed transactions is (8 + 3) = 11 and the sum of the odd indexed transactions is (20 + 17) = 37. The absolute difference is |11 - 37| = 26.
Example 2:
Input:[7, 11, 13, 4, 18]
Output:24
Explanation: For this array, considering all possible subsequences will yield the maximum absolute difference when looking at specific combinations of even and odd indexed transactions. One must consider each element's contribution to either the even or odd sum and how their inclusion or exclusion affects the overall difference.
Constraints
- The length of the input array will be between 2 and 1000.
- Each element in the array will be an integer between -1000 and 1000.
Time: O(n^2) Space: O(n)
An optimized approach would involve using a prefix sum array to efficiently calculate the sum of even and odd indexed transactions for each subsequence. This approach has a time complexity of O(n) and is more efficient for large inputs.
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