As in mathematical induction, it is often necessary to generalize the problem to make it amenable to a recursive solution. ĭesigning efficient divide-and-conquer algorithms can be difficult. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform ( FFT). The solutions to the sub-problems are then combined to give a solution to the original problem. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. In computer science, divide and conquer is an algorithm design paradigm. Algorithms which recursively solve subproblems
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