Implement two array-cost minimization algorithms

Q: Implement two array-cost minimization algorithms

This question evaluates algorithm design, data structure selection, and complexity analysis by requiring implementations for minimizing total merge cost and for removing a contiguous block to minimize the sum of adjacent absolute differences.

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Question

Implement two array-cost minimization algorithms.

Minimize merge cost: Given a list of positive integers workloads representing task sizes, you may repeatedly merge any two items a and b into a single item of size a+b, incurring cost a+b for that merge. Implement minimizeSystemCost(workloads: int[]) -> long that returns the minimal total cost to end with one item. State the algorithm and its time/space complexity.
Remove a contiguous block: Given an integer array machines representing machine strengths and an integer k (1 <= k < machines.length), remove exactly k consecutive elements so that, for the remaining sequence in original order, the sum over all adjacent pairs of |strength[i] - strength[i+1]| is minimized. Implement minimizeRemainingAdjDiff(machines: int[], k: int) -> (long minCost, int startIndex), returning the minimal cost and a valid starting index of the removed block. Target O(n) or O(n log n).

Implement two array-cost minimization algorithms

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