hardArraysPattern: Dynamic
Optimizing Space Station Oxygen Levels Solution
Problem Statement
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
Example 1:
Input:{"oxygenLevels":[10,20,30,40,50],"adjustments":[[1,2,5],[2,3,10],[3,1,8]]}
Output:173
Explanation: Apply adjustment [3, 1, 8] to modules 1, 2, 3, then apply adjustment [1, 2, 5] to modules 1, 2, resulting in oxygen levels [18, 28, 38, 40, 50] and total oxygen level 174, but the maximum achievable is 173 by applying [2, 3, 10] to modules 2, 3, 4, 5, then [1, 2, 5] to modules 1, 2.
Example 2:
Input:{"oxygenLevels":[5,10,15,20],"adjustments":[[1,1,3],[2,2,5]]}
Output:48
Explanation: Apply adjustment [2, 2, 5] to modules 1, 2, resulting in oxygen levels [10, 15, 15, 20] and total oxygen level 60, but the maximum achievable is 48 by not applying any adjustments due to negative outcomes from other sequences.
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
Time: O(n * 2^n) Space: O(n * 2^n)
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).
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