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This approach involves breaking down the problem into smaller subproblems. Each subproblem is solved independently, and the solutions to these subproblems are combined to solve the original problem. This is typically implemented through recursive functions.
Time Complexity: O(n log n) due to the divide and conquer methodology where the problem is divided into two halves.
Space Complexity: O(log n) due to the recursive stack depth.
1def solve_sub_problem(data, start, end):
2 if start >= end:
3 return
4 mid = (start + end) // 2
5 solve_sub_problem(data, start, mid)
6 solve_sub_problem(data, mid + 1, end)
7 # Combine results
8 ...
9
10
11def divide_and_conquer(data):
12 solve_sub_problem(data, 0, len(data) - 1)
13
14
15data = [ # Your data here ]
16divide_and_conquer(data)This Python script uses recursion through the function solve_sub_problem to apply the divide and conquer technique, splitting the array and processing subproblems until they are solved individually and then merging them as needed.
This approach avoids recursion by iteratively solving subproblems. It may use data structures as stacks or queues to keep track of subproblems, or directly manipulate indices to iterate over sections of the data.
Time Complexity: O(n), if the problem can be iteratively solved in linear time.
Space Complexity: O(1), if no extra storage apart from input data is used.
1
Python's solve_iteratively function embodies the iteration process to systematically handle each segment of the data, suitable for contexts where recursion might be too memory-intensive.