Optimizing Space Station Oxygen Levels — Problem Statement & Solution Guide
Problem Description
Given an array of oxygen levels in different modules of a space station and a list of possible adjustments, where each adjustment is represented as [duration, module_start_index, adjustment_amount], find the maximum total oxygen level achievable by applying a sequence of adjustments. Each adjustment modifies the oxygen level of a contiguous subset of modules starting from module_start_index.
Examples
Input
[10, 20, 30, 40, 50], [[3, 1, 8], [1, 2, 5]]
Output
188
Explanation: Step-by-step: Given oxygen levels [10, 20, 30, 40, 50] and adjustments [[3, 1, 8], [1, 2, 5]], we first apply the first adjustment [3, 1, 8] to modules 1-3 (10, 20, 30), resulting in oxygen levels [18, 28, 38, 40, 50]. Then, we apply the second adjustment [1, 2, 5] to modules 2-3 (28, 38), resulting in oxygen levels [18, 33, 38, 40, 50]. Finally, we increase the oxygen level of module 4 by 5 because the adjustment is applied to a contiguous subset of modules starting from module_start_index 2, so the correct oxygen levels are [18, 33, 38, 45, 50]. The maximum total oxygen level achievable is 188.
Input
[10, 20, 30, 40, 50], [[2, 2, 5], [1, 3, 10]]
Output
70
Explanation: Step-by-step: Given oxygen levels [10, 20, 30, 40, 50] and adjustments [[2, 2, 5], [1, 3, 10]], we first apply the first adjustment [2, 2, 5] to modules 2-3 (20, 30), resulting in oxygen levels [10, 25, 35, 40, 50]. Then, we apply the second adjustment [1, 3, 10] to modules 3 (35), resulting in oxygen levels [10, 25, 45, 40, 50]. The maximum total oxygen level achievable is 70.
Constraints
- 1 <= length of oxygenLevels <= 20
- 1 <= number of adjustments <= 10
- 1 <= duration <= 5
- 1 <= module_start_index <= length of oxygenLevels
- -10 <= adjustment_amount <= 10
Optimal Approach & Strategy
The optimized approach uses dynamic programming to store the maximum oxygen levels achievable at each step, reducing the time complexity to O(n * 2^n).
Brute Force Approach
The brute-force approach involves trying all possible sequences of adjustments and calculating the total oxygen level for each sequence, resulting in a time complexity of O(n^2 * 2^n).
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