(完整word版)哈工大深圳算法设计与分析试卷-师兄只能帮你到这啦(额外再加8道保命题)-何震宇

1、Using figure to illustrate the operation of RADIX-SORT on the following list of English words: COW, DOG , SEA, RUG , ROW, MOB, BOX, TAB.

2、Please write inorder, preorder and postorder tree walks of the following binary search tree.

3、Please write down the elements of dynamic programming.

4、Using a recursion tree to give an asymptotically tight solution to the recurrence T(n) = T(n/3)+T(2n/3)+cn.

5、Please give an optimal Huffman code for the following set of frequencies. a b c d e f Frequency 5 9 16 12 13 45

6、Converting the following linear program into standard form:

Minimize 2172x x +

Subject to 71=x

24321≥+x x

02≥x

03≤x

7、Solve the following linear program using SIMPLEX:

maximize 215.1218x x +

Subject to 2021≤+x x

121≤x

162≤x

0,21≥x x

8、Suppose A1 a 105⨯ matrix, A2 a 310⨯ matrix, A3 a 123⨯ matrix, A4 a 512⨯ matrix, A5 a 505⨯ matrix, A6 a 650⨯ matrix. Please give an optimal parenthesization of a matrix-chain A1A2A3A4A5A6.

9、Using a recursion tree to give an asymptotically tight solution to the recurrence T (n ) = T(n/4)+T(n/2)+ n 2.

10、Using figure to illustrate the operation of COUNTING-SORT on the array A=<6,0,2,0,1,3,4,6,1,3,2>

11、Using figure to illustrate the operation of RADIX-SORT on the following list of English words: COW, DOG , SEA, RUG , ROW, MOB, BOX, TAB.

12、Please write inorder, preorder and postorder tree walks of the following binary search tree.

13、X=, Y=. Please illustrate the whole procedure for finding the longest common sequence of X and Y using dynamic programming.

14、Please give an optimal Huffman code for the following set of frequencies.

15、Please draw the result after the operation Left-Rotate(9)

.

16、X=, Y=. Please illustrate the whole procedure for finding the longest common sequence of X and Y using dynamic programming. 17、Please give an optimal Huffman code for the following set of frequencies. a b c d e f Frequency 15 19 6 12 13 35

18、A red-black tree (RB tree) is a binary search tree with one extra bit of storage per node: its color, which can be either RED or BLACK, and the red-black is a nearly balanced tree. Please prove n-node RB tree has height )(lg n O h =

19、Solve the following linear program using SIMPLEX:

maximize 215.1218x x +

Subject to 2021≤+x x

121≤x

162≤x

0,21≥x x

20、In the activity-selection problem,

}:{j k k i k ij s f s f S a S ≤≤≤∈= represents the activities that start after an activity

i a finishes and finish before one activity j a starts. Here, an activity i a occurs during period ),[i i f s , and activities are sorted by

monotonically increasing finish time. Let

Φ≠ij S , and let m a be the activity in ij S with the earliest finish time: }:min{ij k k m S a f f ∈=. Then prove m a is used in some maximum-size subset of mutually compatible activities of ij S