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This approach leverages dynamic programming techniques to break down the problem into overlapping subproblems and solve them using a bottom-up manner. The core idea is to store the results of subproblems to avoid redundant computations, therefore optimizing the solution.
Time Complexity: O(n)
Space Complexity: O(n)
1/* C++ code for dynamic programming approach */This C++ solution employs a vector for the same purpose as the C solution, providing an STL-based simple syntax for array handling. The use of the 'vector' STL simplifies memory management and provides dynamic resizing capabilities.
The greedy approach aims to find a solution by making the most favorable choice at every stage, intending to reach an overall optimal solution. This approach might not always work for all types of problems but can provide simpler solutions where applicable.
Time Complexity: O(n)
Space Complexity: O(1)
1Python's inherent capabilities allow concise expression of greedy algorithms, where decision points are processed sequentially within a loop structure.