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Maximizing the Sum of Squared Segment Totals(Problem SOlving)
- Given a list of integers and an integer k, the goal is to split the list into k non-empty consecutive parts and maximize the sum of squared values of each part.
- The problem requires finding the optimal way to split the list to achieve the highest score.
- Constraints include list length up to 200,000, handling negative and positive numbers, and time and memory limits.
- A high-level solution involves using prefix sums for fast range sums and dynamic programming over splits.
- The Li Chao tree data structure helps optimize the quadratic inner maximization, leading to an overall complexity of O(k * n log n).
- The JavaScript implementation uses BigInt to prevent overflow and includes a Li Chao class for maximum line evaluation.
- The DP loop and line insertion in the implementation facilitate finding the highest score by splitting the array into k parts.
- The implementation handles the problem efficiently for large n and moderate k.
- Overall, the approach involves dynamic programming, prefix sums, and the Li Chao tree data structure to solve the problem effectively.
- The code snippet provided offers a solution to the problem and demonstrates the practical implementation in JavaScript.
- The example input with the list [1, 2, -1, 2, 3] and k=2 outputs a maximum score of 29.
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