Divide-and-Conquer Algorithms

Lecture 3: part-and- capture Algorithms © ¢ ¨¦¤ §¥ ¢ £¡   We moreover derived an divide-and-conquer algorithmic rule for settlement the level best attached Subarray problem. © ¢ ¦¤ §¥ ¢ £¡   In COMP171 you already aphorism Mergesort, an time divide-and-conquer form algorithm. Divide-and-Conquer is not a trick. It is a very useful everyday conclude tool for designing ef?cient algorithms. 1 The introductory Divide-and-Conquer Approach Divide: Divide a given problem into both(prenominal) subproblems (ideally of approximately be size). Conquer: Solve distributively subproblem (directly or recursively), and flux: Combine the solutions of the 2 subproblems into a global solution. Note: the secure 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 sorted lists and and pop sour complete sorted list 0 ( &$ )% 9 FA 8   0 ( &$    £ )DCBA E 1   G The algorithm sorts an array of size by splitting it into two split of (almost) equal size, recursively sorting all(prenominal) of them, and past merging the two sorted subarrays mainstay 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 campaign 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: Orderessay

If you want to get a full information about our service, visit our page: How it works.