Let6-uick Sort.ppt

1 Simple Review Heap Sort Heaps MAX-HEAPIFY BUILD-MAX-HEAP HEAPSORT Priority Queues MAXIMUM(S) EXTRACT-MAX(S) INCREASE-KEY(S,x,k) INSERT(S, x) Applications Design and Analysis of Algorithms Quicksort (Ch7) Quicksort VS. Mergesort Which is better? Test environment: IBM370/158 Programming in PL/1 Input consists of random integers range in (0, 10000) Homework 7.2-2 *Software School of XiDian University *Software School of XiDian University 怯遂因逛吏难蕾驮檀沟澎记簧匿肿氏渊赡叼膳翟羹贞拍饱绩俊宏腹攀疽勿Let6-uick SortLet6-uick Sort 闺龙峻错洽脱扛界孩掩始修玖涛庆脸炎课脑曲串业皂裳耗很由机祖洽慧鸽Let6-uick SortLet6-uick Sort 遂磕织疾膨姐止佯过三税购做而镐担馆继悍去梯猩呛沙郸缄麻茄谦傀茁组Let6-uick SortLet6-uick Sort Design and Analysis of Algorithms Quicksort Topics: Quicksort Randomized quicksort algorithms 闽苛成轧苔诗锗找瑟桶咋巷攘抨搏功掂磊殿塔吾谎都捆插钠恕猩涤玩赢召Let6-uick SortLet6-uick Sort Randomized algorithm Randomized algorithms: algorithms that flip coins --Applications Quicksort Discovering common motif in DNA sequence in computational biology Algorithms that make random decisions That is: --Can generate a random number x from some range {1,r} --Make decisions based on the value of x Why would it make sense? 叹驴漳恰菊亥诫虽键挟烂铺察盈眼猜省毯峡虹眉栗囊蛾类恕祁烂汀寒萌舵Let6-uick SortLet6-uick Sort Two cups, one coin If you always choose a fixed cup, the adversary will put the coin in the other one, so the expected payoff=$0 If you choose a random cup, the expected payoff=$0.5 匈赘毫宽梨栏魏司胀汤瑞经育觅产弛吾陶集袖结柞窃蜀疑腥镭做柜亢谊吞Let6-uick SortLet6-uick Sort Randomized algorithm Two basic types: --Typically fast (but sometimes slow): Las Vegas --Typically correct (but sometimes output garbage): Monte Carlo The probabilities are defined by the random numbers of the algorithm! (not by random choices of the problem instances) 呻猫片伴省左胰趴价洼颠钒随妓我抑沼茧沧荤沥吻颧错鸡址豹键蔷款险爱Let6-uick SortLet6-uick Sort Quicksort Efficient sorting algorithm --Proposed by C.A.R. Hoare in 1962 --Divide-and-Conquer algorithm --Sorts “in place” (like insertion sort, but not like merge sort) --Very practi