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Thinking of using advanced data structures? You are thinking it too complicated.
For each update operation, do you really need to update all elements between i and j?
Update only the first and end element is sufficient.
The optimal time complexity is O(<b><i>k</i></b> + <b><i>n</i></b>) and uses O(1) extra space.
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Yes, problems involving range updates and prefix sums are common in technical interviews at companies like Google, Amazon, and Meta. They test your understanding of array optimization techniques and algorithmic thinking.
The optimal approach uses a difference array with a prefix sum technique. Instead of updating every element in a range, you mark the start and end boundaries of the update and reconstruct the final values with a prefix sum pass.
An array-based difference array works best for this problem. It allows constant-time updates for each range operation and then uses a prefix sum to build the final array efficiently.
Prefix sums help convert boundary updates into actual values across the array. After marking increments and decrements at range boundaries, a single prefix sum traversal propagates the updates to all affected indices.
