銘傳大學九十學年度轉學生招生考試 七月二十九日 第三節
資管 轉三 資料結構 試題
一、 ( 16 points)
(a) Draw a tree that is both a heap and a binary search tree.
(b) A binary tree has eight nodes. The inorder and postorder traversal of the tree are given below.
Draw the tree.
Postorder: FECHGDBA Inorder: FCEABHDG
(c) Given the following postfix expression, write the minimally parenthesized infix expression:
AB + C – BAD – D/**
(d) Draw the corresponding expression tree in part c.
二、 ( 15 points)
(a) Build a binary search tree, given the keys added in the following order:
17 18 5 20 27 29 9 33 11 10 (b) Is this an AVL tree? Why or why not?
(c) Draw threaded links in place of the null links in this binary tree, where a left null link points to the previous inorder node, and a right null link points to the next inorder node.
(d) Using this threaded tree, can the threaded links be used to find the parent of each node? If not, give an example; if so, explain how to find the parent with key 29 using the threaded links. The generalized your algorithm.
三、 ( 8 points)
(a) Draw a Fibonacci tree with 20 nodes and height 5.
(b) Color this as a red-black tree.
四、 ( 15 points)
(a) After two passes of a sorting algorithm, the following array:
47 3 21 32 56 92
has been rearranged as shown below.
3 21 47 32 56 92
Which sorting algorithm is being used?
(b) In what way(s) is a circular queue better than a linear queue?
(c) What is the minimum number of keys that can be placed in a B-tree of order 17 and of height 3(four levels)?
五、 ( 10 points)
Insert the keys k: [25, 76, 18, 9, 41, 56] into an initially empty hash table of size 7 using the hash
function h1(k) = k mod 7, giving the total number of collisions for each of the following two cases:
Quadratic collision resolution, using i(i+1)/2 as the total displacement from the initial address for step i.
Double hashing with h2(k) = 1 + [k mod 3] representing the incremental displacement from the previous address.
六、 ( 18 points)
(a) How long does it take to insert a new element into a heap? To return the smallest thing in a min-heap? To delete the smallest thing in a min-heaps? To find the largest thing in a min-heap?
8%
(b) What I sthe maximum and minimum number of elements in a heap of height h? 4%
(c) Where in a max-heap might the smallest element reside? 3%
(d) Which of the following sequences are heaps? 3%
(i) 42 35 37 20 14 18 7 10 (ii) 42 35 18 20 14 30 10 (iii) 20 20 20 20 20 20 20
七、 ( 8 points) State whether true or false.
(a) All AVL-trees are binary search trees.
(b) Inserting an element in an AVL-tree may require up to log(n)rotations, where n is the number of nodes in the tree.
(c) Hash tables are attractive because the operations insert and delete have O(1) worst case running time.
(d) With AVL-trees we can find the maximum element and the minimum element in O(log n) time.
八、 ( 10 points) Multiple choice: only one answer for each question (1) What is wrong with the following?
if sum == SIZE {
result = total / SIZE;
cout << result << endl;
}
(a) cout not allowed in if block (b) expression not in parentheses
(c) expression should have been sum = SIZE (d) no semi-colon after
(2) Suppose size == MEDIUM. What value will x be after the switch statement?
swith (size) {
case SMALL;
x = 100;
case MEDIUM;
x = 200;
case LARGE;
x += 300;
break;
} (a) 100 (b) 200 (c) 300 (d) 500
(3) The program containing the if statement below is not working. What is MOST LIKELY wrong?
float speed;
float rate;
…
if ( speed == rate )
…
(a) Float values should not be tested for equality (b) There should be no parentheses
(c) The == should most likely be just = (d) The “if” should most likely be “while”
(4) What is the difference between lines (2) and (3) below?
(1) char name[30];
(2) cin>> name[i];
(3) cin>>name;
(a) (2) and (3) do exactly the same thing.
(b) (2) reads a character string. (3) reads a single character.
(c) (2) reads a character string that includes blanks. (3) reads a character string up to but not includes blanks. (3) reads a character string up to but not including a blank.
(d) (2) reads a single character. (3) reads a character string.
(5) Which statement below correctly outputs x, y, and z followed by an end-of line?
(a) cout >> x >> y >> z >> endl;
(b) cout << x, y, z << endl;
(c) cout << x << y << z;
(d) cout << x << y << z << endl;
〈試題完〉
