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详细说明： Practice 1 Date: Monday, March 18th, 2013 We highly encourage being environment friendly and trying all problems on your own. Implement exercise 2.3-7. Implement priority queue. Implement Quicksort and answer the following questions. (1) How many comparisons will Quicksort do on a list of n elements that all have the same value? (2) What are the maximum and minimum number of comparisons will Quicksort do on a list of n elements, give an instance for maximum and minimum case respectively. Give a divide and conquer algorithm for the following problem: you are given two sorted lists of size m and n, and are allowed unit time access to the ith element of each list. Give an O(lg m + lgn) time algorithm for computing the kth largest element in the union of the two lists. (For simplicity, you can assume that the elements of the two lists are distinct). Practice 2 Date: Monday, April 1st, 2013 We highly encourage being environment friendly and trying all problems on your own. Matrix-chain product. The following are some instances. <3, 5, 2, 1,10> <2, 7, 3, 6, 10> <10, 3, 15, 12, 7, 2> <7, 2, 4, 15, 20, 5> Longest Common Subsequence (LCS). The following are some instances. X: xzyzzyx Y: zxyyzxz X:MAEEEVAKLEKHLMLLRQEYVKLQKKLAETEKRCALLAAQANKESSSESFISRLLAIVAD Y:MAEEEVAKLEKHLMLLRQEYVKLQKKLAETEKRCTLLAAQANKENSNESFISRLLAIVAG Longest Common Substring. The following are some instances. X: xzyzzyx Y: zxyyzxz X:MAEEEVAKLEKHLMLLRQEYVKLQKKLAETEKRCALLAAQANKESSSESFISRLLAIVAD Y:MAEEEVAKLEKHLMLLRQEYVKLQKKLAETEKRCTLLAAQANKENSNESFISRLLAIVAG Max Sum. The following is an instance. (-2，11，-4，13，-5，-2) Shortest path in multistage graphs. Find the shortest path from 0 to 15 for the following graph. A multistage graph is a graph (1) G=(V,E) with V partitioned into K >= 2 disjoint subsets such that if (a,b) is in E, then a is in Vi , and b is in Vi+1 for some subsets in the partition; and (2) | V1 | = | VK | = 1. Practice 3 Date: Monday, April 15th, 2013 We highly encourage being environment friendly and trying all problems on your own. Knapsack Problem. There are 5 items that have a value and weight list below, the knapsack can contain at most 100 Lbs. Solve the problem both as fractional knapsack and 0/1 knapsack. A simple scheduling problem. We are given jobs j1, j2… jn, all with known running times t1, t2… tn, respectively. We have a single processor. What is the best way to schedule these jobs in order to minimize the average completion time. Assume that it is a nonpreemptive scheduling: once a job is started, it must run to completion. The following is an instance. (j1, j2, j3, j4) : (15，8，3，10) Single-source shortest paths. The following is the adjacency matrix, vertex A is the source. A B C D E A -1 3 B 3 2 2 C D 1 5 E -3 All-pairs shortest paths. The adjacency matrix is as same as that of problem 3.(Use Floyd or Johnson’s algorithm) Practice 4 Date: Monday, May 8th, 2013 We highly encourage being environment friendly and trying all problems on your own. 0/1 Knapsack Problem. There are 5 items that have a value and weight list below, the knapsack can contain at most 100 Lbs. Solve the problem using back-tracking algorithm and try to draw the tree generated. Solve the 8-Queen problem using back-tracking algorithm. ...展开收缩
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