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In this approach, we solve the problem by checking all possible combinations or configurations naively. Although not efficient for large inputs, this approach is often straightforward and can provide insights into the problem structure.
Time Complexity: O(n).
Space Complexity: O(1), as no extra space is used other than loop variables.
1def solve(n):
2 # Brute force in Python
3 for i in range(n):
4 print(i, end=' ')
5 print()
6
7solve(10)In Python, this solution uses a range-based loop to iterate and print each number from 0 to n-1, showing a basic brute force solution.
This approach utilizes dynamic programming to optimize the solution by storing interim results and eliminating redundant calculations seen in a brute force approach. This method can significantly improve efficiency when dealing with complex recursive problems.
Time Complexity: O(n).
Space Complexity: O(n) due to the storage array.
1
This JavaScript solution demonstrates the use of dynamic programming for Fibonacci numbers, optimizing by storing results in an array.