mediumArraysPattern: prefix sum and sign tracking
Maximum Alternating Profit Solution
Problem Statement
In a galaxy with fluctuating resource prices, find the maximum profit that can be achieved by trading resources along a route where the price difference between each pair of consecutive resources alternates between positive and negative. If no such route exists, return 0.
Examples
Example 1:
Input:[7,1,5,3,6,4]
Output:7
Explanation: Maximum profit achieved by buying at index 1 and selling at index 5, then buying at index 2 and selling at index 4, but since the problem states the price difference alternates between positive and negative this example does not satisfy the given condition, hence it is 0 for this example
Example 2:
Input:[7,6,4,3,1]
Output:0
Explanation: No route exists where the price difference alternates between positive and negative
Constraints
- The input array contains at least 2 and no more than 1000 elements.
- Each element in the array is between -1000 and 1000.
Time: O(n) Space: O(n)
The optimized approach uses prefix sums and sign tracking to find the maximum subarray sum with alternating signs in linear time, O(n), by iterating through the array and maintaining variables to track the maximum sum and the sign of the previous difference.
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