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Ho Chi Minh City University of Technology

Department of Electrical and Electronics Engineering

FINAL EXAMINATION (K2010)

Grading: 50%

CS225 Data Structures and Programming Principles

(Equivalent course: Computer System Engineering)

Course ID: 407406

Date: 20 Dec, 2012 Duration: 120 minutes

Student name: Student ID:

Students are allowed to use one A4 page with two sides for reference.

Books and other documents are not allowed to use.

This examination consists of 6 pages

Problem 1: Answer the following questions for the binary tree :1. The height of the tree is2. The depth of the node B is3. Descendants of the node B are4. External nodes of the tree are5. Pre-order traversal of the tree is6. Post-order traversal of the tree is

Problem 2: Give the following code for Node class#include using namespace std;class Node {

private:char element;

Node* parent; Node* left; Node* right;

public: Node() {

element = 0; parent = NULL;left = NULL; right = NULL; }

Node(char value) {element = value; parent = NULL;left = NULL; right = NULL; }

void insert_left(Node* L) {left = L; }

void insert_right(Node* R) {left = R; }

void node_print() {cout

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int main(){

Node* A = new Node('A'); Node* B = new Node('B');

2. Write a function that print out preorder traversal of the binary treevoid preorder_traversal(BinaryTree BT){

Problem 3: Balance the binary search tree below15

10

2

5

7

8

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Describe step by step the balance process; note the steps that use single rotation or double rotation Step 1 Step 2 Step 3

Step 4 Step 5 Step 6

Problem 4: Insert into an initially empty binary search tree, items with the following key (in this order):50, 45, 18, 55, 20, 60, 46, and 58. Draw the tree after each insertion.Insert 50 Insert 45 Insert 18 Insert 55

50

Insert 20 Insert 60 Insert 46 Insert 58

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Problem 5: Give the C++ code for Quick-sort using List STLvoid quick_sort(list *L){ list *L1 = new list ;

list *L2 = new list ;int pivot_num;int N = L->size();if (N>1){ pivot_num = pivot(L);

partition(L, L1, L2, pivot_num);quick_sort(L1);

quick_sort(L2);merge(L,L1,L2,pivot_num);

}}

int pivot(list *L){

list ::iterator L_Iter;int N = L->size();int t = rand() % N;L_Iter = L->begin();for (int i=0; i< t; i++) L_Iter++;return *L_Iter;

}

Write C++ code for the functions partition and merge

void partition(list *L, list *L1, list

*L2, int pivot_num){

merge(list *L, list *L1, list *L2, int

pivot_num){

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Problem 6: Fill in the following table for the operation of Priority Queue ADT

No. Operation Output Priority Queue1 insertItem(10, C) - {(10,C)}2 insertItem(8, A)

3 insertItem(9, B)4 minElement()5 minKey()6 insertItem(7, D)7 size()8 removeMin()9 removeMin()10 removeMin()

Problem 7: Describe the sorting process using Radix-sort algorithm for the following sequence of 4-bit

unsigned number.

1100

0101

1101

1000

0110

1110

0111

Problem 8: Answer the following questions about Graph ADT

1. If the number of vertices is 10 , the maximum number of edges in the graph is

2. If the number of edges is 12 , the sum of degree of all vertices in the graph is3. If the number of vertices is n , and the number of edges is m , the running time of DFS is

4. If the number of vertices is n , and the number of edges is m , the running time of BFS is

5. If the number of vertices is n , and the number of edges is m , the running time of Dijkstrasalgorithm is

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Problem 9: Give the graph G below. Assume that the graph is implemented by a linked list with alphabetorder and numeric order. Find traversal of G using Depth first search (DFS) and Breadth first search (BFS)starting at S0.

Graph G Draw DFS traversal Draw BFS traversal S1

S3

S4 S5 S6

S0

S2

Problem 10: Apply Dijkstras algorithm to find Minimum Spanning Tree for the following graph.Describe step by step the shortest path finding process.Step 1:

A

B

C

D F

E

G

H23

24

25 13

1513

10

29

57

23

0

27

Step 2: Step 3:

Step 4: Step 5: Step 6:

Step 7: Step 8:

--------------------------------------------------- The end ------------------------------------------------------ Electronics Department Lecturer

Dr. Hoang Trang Dr. Truong Quang Vinh