四川大学期末考试试题（2007-2008学年第1学期）课程号：课程名称：数据结构与算法分析（B卷）任课教师：适用专业年级：06级软件工程学号：姓名：（1）The primary purpose of most computer programs isa) to perform a mathematical calculation.b) to store and retrieve information.c) to sort a collection of records.d) all of the above.（2）Assume that P contains n elements. The number of sets in the powerset of P isa) n b) n^2c) 2^n d) 2^n - 1e) 2^n + 1（3）Pick the growth rate that corresponds to the most efficientalgorithm as n gets large:a) 5n b) 20 log nc) 2n^2 d) 2^n（4）A sequence has the following properties:a) May have duplicates, element have a position.b) May have duplicates, elements do not have a position.c) May not have duplicates, elements have a position.d) May not have duplicates, elements do not have a position.（5）The correct traversal to use on a BST to visit the nodes in sorted order is:a) Preorder traversal. b) Inorder traversal.c) Postorder traversal.（6）When sorting n records, Insertion sort has best-case cost:a) O(log n). b) O(n).c) O(n log n). d) O(n^2)e) O(n!) f) None of the above.（7）For a list of length n, the linked-list implementation's prevfunction requires worst-case time:a) O(1).b) O(log n).c) O(n).d) O(n^2).（8）The easiest way to represent a general tree is to:a) convert to a list. b) convert to a binary tree.c) convert to a graph.（9）Depth-first search is best implemented using:a) A stack or recursion. b) A queue.c) A tree.（10）For set P, the notation |P| indicatesa) The number of elements in P. b) The inverse of P.c) The powerset of P. d) None of the above.2．（10 scores）Write a series of C++ statements that uses the List ADT as follows to create a list capable of holding twenty elements and which actually stores the list with following configuration:<6, 28 | 18, 8, 19>// List abstract classtemplate <class Elem> class List {public:// Reinitialize the list. The client is responsible for// reclaiming the storage used by the list elements. virtual void clear() = 0;// Insert an element at the front of the right partition.// Return true if successful, false if the list is full. virtual bool insert(const Elem&) = 0;// Append an element at the end of the right partition.// Return true if successful, false if the list is full. virtual bool append(const Elem&) = 0;// Remove the first element of right partition. Return// true if successful, false if right partition is empty.// The element removed is returned in the parameter. virtual bool remove(Elem&) = 0;// Place fence at list start, making left partition empty virtual void setStart() = 0;// Place fence at list end, making right partition empty virtual void setEnd() = 0;// Move fence one step left; no change if already at start virtual void prev() = 0;// Move fence one step right; no change if already at end virtual void next() = 0;// Return length of left partitionvirtual int leftLength() const = 0;// Return length of right partitionvirtual int rightLength() const = 0;// If pos or more elements are in the list, set the size// of left partition to pos and return true. Otherwise,// do nothing and return false.virtual bool setPos(int pos) = 0;// Return in first parameter the first element of the// right partition. Return true if successful, false// if the right partition is empty.virtual bool getV alue(Elem&) const = 0;// Print the contents of the listvirtual void print() const = 0;};3．（10 scores）Build the Huffman coding tree and determine the codes for the following set of letters and weights:a b c d e.1 3 5 7 114．（15 scores）What are the minimum and maximum number of elememts in a heap of height h ?5．（15 scores）The Bubble Sort implentation has the following inner for loop:for (int j = n – 1; j > i; j--)Consider the effect of replacing this with the following staement:for (int j = n – 1; j > 0; j--)W ould the new implementation work correctly? W ould the change affect the asymptotic complexity of the algorithm? How would the change affect the running time of the algorithm?6．（15 scores）// Binary tree node abstract classtemplate <class Elem> class BinNode {public:// Return the node's elementvirtual Elem& val() = 0;// Set the node's elementvirtual void setV al(const Elem&) = 0;// Return the node's left childvirtual BinNode* left() const = 0;// Set the node's left childvirtual void setLeft(BinNode*) = 0;// Return the node's right childvirtual BinNode* right() const = 0;// Set the node's right childvirtual void setRight(BinNode*) = 0;// Return true iff the node is a leafvirtual bool isLeaf() = 0;};Write a recursive function that returns a count of the number of leaf nodes in a binary true..7．（15 scores）List the order in which the edges of the following graph are visited when running Kruskal’s MST algorithm. Show the final MST.。