Divide-and-Conquer Algorithms

Lecture 3: part-and-Conquer Algorithms © ¢ ¨¦¤ §¥ ¢ £¡   We just derived an divide-and-conquer algorithmic rule for settlement the level best Contiguous Subarray problem. © ¢ ¦¤ §¥ ¢ £¡   In COMP171 you already see Mergesort, an time divide-and-conquer form algorithm. Divide-and-Conquer is not a trick. It is a very(prenominal) useful everyday purpose tool for designing ef?cient algorithms. 1 The Basic Divide-and-Conquer Approach Divide: Divide a habituated problem into both subproblems (ideally of approximately be size). Conquer: assoil distributively subproblem (directly or recursively), and Combine: Combine the solutions of the two subproblems into a global solution. Note: the hard work and briskness is commonly in the Combine step. 2 MERGESORT   ¨ © §¥¤¢ ¡¡ ¦¢£   Sort  ¦ £ © Mergesort If Mergesort ©¦ © £ @ §¡ ¦ 20! $76( 5 0! $5 76( 2 ! 2 10 & ¦§¢ ()$ 9 6¢   8 ! 2 31 0 ( &$ ¢£ )%#¥¤¢   4 4   E ¦ §¢ 1   ¤¡ £ Mergesort Merge the two sort lists and and pop off complete sorted list 0 ( &$ )% 9 FA 8   0 ( &$    £ )DCBA E 1   G The algorithm sorts an array of size by splitting it into two parts of (almost) equal size, recursively sorting all(prenominal) of them, and then integrate the two sorted subarrays back together into a amply sorted list in time (how?).

¡   © H ¡   9 U© S  V© 3 H T H ¡ S 4 R© H ¡ ¢ Q8 4 ! P H I which we previously saw implies © H The running time of the algorithm satis?es H §¥ ¦¤ H ¡   © H ¡ 4 Mergesort Example 3 13 8 4 11 24 ¢ 12 23   ¢     13 8 £ ¤¢   ¡  3 ¢ 12 23 ¢ split 4 11 24 sort each sublist ¥ ¥ 12 13 23 4 8 ¦ ¦ Merge     ¦ § ¨¦ ¡  ¦ 4   3 11 24   3 8 11 12 13 23 24 4...If you want to get a full essay, do it on our website: OrderCustomPaper.com

If you want to get a full essay, visit our page: write my paper