Problem Description
Given an integer length and an array updates where each update is of the form [startIdx, endIdx, inc], start with an array of zeros of that length. For each update, increment all elements from startIdx to endIdx by the value inc. Return the modified array after all updates are applied.
Key Insights
- Use a difference array (prefix sum technique) to update ranges efficiently.
- Instead of updating every element for each range (which could be slow), update the start index and subtract after the end index.
- Compute the final array by taking the cumulative sum of the difference array.
- This approach reduces the time complexity from potentially O(n * number_of_updates) to O(n + number_of_updates).
Space and Time Complexity
Time Complexity: O(n + k), where n is the length of the array and k is the number of updates.
Space Complexity: O(n) for the difference array (and output array).
Solution
We use a difference array to efficiently perform range updates. The idea is to add the increment at the start index and subtract the increment just after the end index. After processing all updates, a single pass of cumulative sum across the array gives the final result. This method avoids updating every element within the range for each query, making it efficient for large inputs.