Maximum Alternating Subarray Sum - Problem
Maximum Alternating Subarray Sum
You're given an array of integers and need to find the maximum alternating sum of any contiguous subarray. An alternating sum starts with a positive sign and alternates between positive and negative:
For example, given array
• Subarray
• Subarray
• Single element
Your goal: Return the maximum possible alternating sum from any subarray.
You're given an array of integers and need to find the maximum alternating sum of any contiguous subarray. An alternating sum starts with a positive sign and alternates between positive and negative:
nums[i] - nums[i+1] + nums[i+2] - nums[i+3] + ...For example, given array
[4,2,5,3]:• Subarray
[4,2,5] has alternating sum: 4 - 2 + 5 = 7• Subarray
[2,5,3] has alternating sum: 2 - 5 + 3 = 0• Single element
[5] has alternating sum: 5Your goal: Return the maximum possible alternating sum from any subarray.
Input & Output
example_1.py — Basic Case
$
Input:
nums = [4,2,5,3]
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Output:
7
💡 Note:
The optimal subarray is [4,2,5] with alternating sum 4 - 2 + 5 = 7. This gives the maximum possible alternating sum.
example_2.py — All Negative
$
Input:
nums = [5,6,7,8]
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Output:
8
💡 Note:
When all elements form a non-decreasing sequence, the best strategy is to take just the largest single element. Subarray [8] gives sum = 8.
example_3.py — Single Element
$
Input:
nums = [6]
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Output:
6
💡 Note:
With only one element, the alternating sum is just that element itself. The subarray [6] gives sum = 6.
Constraints
- 1 ≤ nums.length ≤ 105
- 1 ≤ nums[i] ≤ 105
- All array elements are positive integers
Visualization
Tap to expand
Understanding the Visualization
1
Start with no position
buy=0, sell=0 - we haven't made any trades yet
2
See stock price 4
We can buy it (buy=4) or stay neutral. Selling would lose money.
3
See stock price 2
If we bought at 4, selling at 2 loses money. Better to stay at buy=4.
4
See stock price 5
Now we can sell at 5 after buying sequence, giving us profit of 7!
Key Takeaway
🎯 Key Insight: By maintaining two states (buy/sell), we can make optimal local decisions that lead to the global maximum without exploring all possible subarrays.
💡
Explanation
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// Output will appear here after running code