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+---
+title: Divide and Conquer
+created_date: 2024-10-22
+updated_date: 2024-10-22
+aliases:
+tags:
+---
+# Divide and Conquer
+
+This is an algorithm design paradigm, where the main problem is split into sub problems, which then are split into further sub problems to be finally solved on a smaller level and if needed stitched back together to the overall solution. This recursive approach is often used in [[computer science]].
+Mathematically, the algorithms are often proved to be true by [[mathematical induction]].
+## Example Algorithms
+- [[Sorting Algorithms]] such as quicksort or merge sort
+- Multiplying large numbers: [[Karatsuba Algorithm]]
+- Find the closest pair of points
+- Computing the discrete Fourier Transform ([[Fast Fourier Transform |FFT]])
+
+It can also be used in [[Computer Vision]] by first defining interesting [[Region of Interests |ROI]]s and only running the heavy algorithm on the subpart of the image.
+
+## Advantages
+- [[GPU]]s can be used to parallelize those subtasks and thus run the process much faster
+- simplification: the problems become simpler to solve
+- Algorithmic efficiency: reduce the [[big-O notation]]
+- Memory Access: If the problem is small enough one can use only the computer [[cache]] to solve the subproblem, which makes it way faster