mediumBacktrackingPattern: Mixed
Combination Sum with Restrictions Solution
Problem Statement
You are given an array of integers `asteroids` representing the number of gems in each asteroid and a target total of gems `targetGems`. Using backtracking, find all unique combinations of asteroids that sum up to `targetGems`, with the restriction that no asteroid can be used more than once and each asteroid type can only be used as many times as it appears in the array.
Constraints
- The number of asteroids will not exceed 10.
- The target number of gems will be between 1 and 100.
- Each asteroid contains between 1 and 50 gems.
Time: O(N*2^N) Space: O(N)
The optimal approach involves using a recursive backtracking function with pruning to efficiently explore the search space and find all valid combinations of asteroids, achieving an improved time complexity of O(N*2^N) in the worst case. It utilizes a sorted array to prioritize larger gems and minimize the search space.
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