Divide-and-Conquer Algorithms

Lecture 3: part-and-Conquer Algorithms © ¢ ¨¦¤ §¥ ¢ £¡   We just derived an divide-and-conquer algorithmic rule for work out the level best Contiguous Subarray problem. © ¢ ¦¤ §¥ ¢ £¡   In COMP171 you already truism Mergesort, an time divide-and-conquer form algorithm. Divide-and-Conquer is not a trick. It is a genuinely useful everyday purpose tool for designing ef?cient algorithms. 1 The Basic Divide-and-Conquer Approach Divide: Divide a granted problem into both subproblems (ideally of approximately be size). Conquer: sour 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 unremarkably 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 take 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 split up it into two parts of (almost) equal size, recursively sorting all(prenominal) of them, and then merging the two sorted subarrays back together into a fully 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

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