CS Data Structure Spring Answer Key- Assignment #3

Transcription

1 CS Data Structure Spring Answer Key- Assignment #3 Due Sunday, Mar 3 rd. Q1): Find Big-O for binary search algorithm, show your steps. Solution 1- The task is to search for a given value (called key) inside a sorted array; if the middle element of the array = the given value (key), then it is found and stop; Otherwise, there are two possible cases to happen: 2. If the key value is less than the middle element of the array. So, get the 1 st half of the array and repeat step 1 recursively. 3. If the key value is greater than the middle element of the array. So, get the 2 nd half of the array and repeat step 1 recursively. int binarysearch(int arr[], int value, int left, int right) while (left <= right) int middle = (left + right) / 2; return -1; if (arr[middle] == value) return middle; if (arr[middle] > value) right = middle - 1; left = middle + 1; Complexity analysis Steps : T(n)=1+T(n/2) T(n)=1+1+T(n/4) T(n) = k+t (n/2 k ) 1

2 Suppose : n = 2 k T(n) = k+t( 2 k /2 k ) T(n) = k+o(1) n=2 k k = log n T(n) = O(log n) Q2) Assume that a double linked list is implemented with a header node, and tail node. Write a class that includes methods to: a. return the size of the linked list b. print the linked list c. test if a value x is contained in the linked list d. add a value x if it is not already contained in the linked list and maintain the linked list sorted e. remove a value x if it is contained in the linked list. Solution: /* Name: ID: Description: Qs 2 - Double Linked List Hw # : 3 */ #include <iostream> using namespace std; // Structure to identify a node struct node int data; node * next; // pointer for next node node *prev; node(int _data, node * _next, node *_prev) data=_data; next=_next; prev=_prev; // pointer for previous node ; // class declaration to form a double linked list class dlinklist private: node *head; public: //CONSTRUCTOR dlinklist() head=null; //INSERT an element void insert(int x) head=new node(x,null,null); // create the first node 2

3 if(x < head->data) // given data value < the value of 1st node node *p=new node(x,head,null); head->prev = p; head = p; node *q = head ; while (q->next!=null) if( x==q->data ) cout<<x<<" This number is exist "<<endl; break; //check the data of the next node if( x < q->next->data) node *p=new node(x, q->next, q); q->next->prev = p; q->next = p; break ; q = q->next ; //reaching the end of the linked List if(q->next == NULL) node *p = new node(x, NULL, q); q->next = p; //Return the SIZE of a Linked list. int size() int count=0; node *p=head; if (p==null) return count; while(p!=null) // Empty Linked List 3

4 count++; p=p->next; return count; //SEARCH for an element bool search(int x) node *p=head; while(p!=null) if(p->data==x) return true; p=p->next; // empty Linked List // the key is found //PRINT elements inside the Linked list. void print() cout<<endl; node *p=head; if(p==null) cout<<" << Empty linkedlist >>"<<endl; while(p!=null) cout<<p->data<<"->"; p=p->next; cout<<endl; //DELETE an element from the list. void delet(int key) cout<<"<< No values to delete >>"<<endl; if(head->data==key) head=head->next; cout<<"<< Removed.. >> "<<endl; 4

5 node *p = head; while(p->next!=null) if(p->next->data==key) if(p->next->next==null) p->next->prev = NULL; p->next = NULL; cout<<" << Deleted >> "<<endl; p->next = p->next->next; p->next->prev = p; cout<<" << deleted >> "<<endl; break; p=p->next; int main() dlinklist a; int n; cout<<" The Menu "<<endl; cout<<" "<<endl; cout<<endl; cout<<" 1- for return the size of linked list "<<endl; cout<<" 2- for print "<<endl; cout<<" 3- for search "<<endl; cout<<" 4- for add value "<<endl; cout<<" 5- for remove value "<<endl; cout<<" 6- To Exit "<<endl; cout<<" "<<endl; cout<<endl; cout<<" chose your option from the menu "<<endl; cin>>n; while(n!=6) if(n==1) cout<<" the size is = "<<a.size()<<endl; if(n==2) a.print(); if(n==3) int key; 5

6 cout<<" Enter the number that you are searching for "<<endl; cin>>key; if(a.search(key)) cout<<" ** Found ** "<<endl; cout<<" ** Not Found ** "<<endl; if(n==4) int n; cout<<" Enter your value... or Press -1 to stop >> " <<endl; cin>>n; while( n!= -1) a.insert(n); cin>>n; if(n==5) int n; cout<<" Enter the value that you want to remove"<<endl; cin>>n; a.delet(n); if(n==6) int x; cout<<" Enter the number that you want to swap"<<endl; cin>>x; a.swap(x); cout<<endl; cout<<" ** Chose your option from the main menu ** "<<endl; cin>>n; Q3) Write a function to swap two adjacent elements by adjusting only the links (and not the data) using: a. Singly linked lists. b. Doubly linked lists. c. What the difference between them. Solution: /* Name: ID: Description: Qs 3 swap methods of Linked Lists Hw # : 3 */ 6

7 //swap method for double Linked List void swap(int key) cout<<" Empty link list "<<endl; if(head->data==key) if(head->next!=null) node *c = head->next; head->next = c->next; head->next->prev = head; c->prev = NULL; c->next = head; head->prev = c; head = c; node *c=head; while(c->next!=null) if(c->data == key) node *p = c->next; p->prev = c->prev; c->next = p->next; p->next = c ; c->prev = p; p->prev->next = p; if(c->next!=null) c->next->prev = c; break; c = c->next; At a singly linked list we have to exchange the next pointer for the swapped nodes. But, at a double linked list we have to exchange the previous pointer and the next pointer for the swapped nodes. 7

8 Q4) Efficiently implement a stack class with the following methods: 1- push(x): Insert item x on the top of the stack. 2- pop() : Remove the top item from the stack and return it. 3- isempty(): Return true if the stack is empty. 4- Solution: /* Question 4 : Name: ID: Description: Qs 4 Implement a STACK Hw # : 3 */ #include<iostream> using namespace std; //construct a node struct node int data; node *next; node(int _data, node * _next) data = _data; next = _next; //construct a class stack class stack node *head; public: stack() head=null; // to insert (push) an element into a stack void push(int x) head=new node(x,null); node *p=new node(x,head); head=p; // to pop (delete) an element from a stack int pop() int s; 8

9 cout<<" empty stack "<<endl; s=head->data; head=head->next; return s; bool isempty() return true; void print() node *p=head; if( isempty() ) cout<<"empty stack"<<endl; while(p!=null) cout<<p->data<<"->"; p=p->next; Q5) Using stack class write a program to check for balancing symbols /* */, (), [], and. Solution: /* Question 5 : Name: ID: Description: Qs 4 Balanced STACK Hw # : 3 */ #include<iostream> using namespace std; struct node int data; node * next; node(int _data, node * _next) data=_data; next=_next; ; class stack public: 9

10 node *head; public: stack() head=null; bool isempty() //method empty to check the stack return head==null; void push(int x) //to insert an element in front of a stack head=new node(x,head); int pop() // to delete an element from front of stack if(isempty()) cout<<"the stack is empty"<<endl; int x; x=head->data; head=head->next; return x; void print() node *z=head; if(z==null) cout<<"stack is Empty "<<endl; while(z!=null) cout<<z->data<<","; z=z->next; bool balance() // method to check the balancing expr char s[10]; char c; char z; cout<<"enter the expression that you would like to check: "<<endl; cin>>s; int i=0; while(s[i]!= '\0') 10

11 if(s[i] == '' s[i]=='[' s[i]== '(') push(s[i]); if(s[i]== '/') push(s[i]); i++; push(s[i]); i++; continue; if(s[i]== '') c=pop(); if(c!='') if(s[i]== ']') c=pop(); if(c!='[') if(s[i]==')') c=pop(); if(c!='(') if(s[i]=='*') c=pop(); z=pop(); i++; if(c!='*' z!='/') i++; if(isempty()) return true; ; int main() // main method stack a; if(a.balance()) cout<<"the expression is balanced "<<endl; cout<<"the expression isnot balanced"<<endl; system("pause"); return 0; 11

12 Q6) Using Stack Write a program to evaluate a postfix expression. Solution: /* Name: ID: Description: Qs 6 - Postfix Expression using Stack Hw # : 3 */ #include<iostream> #include<string> #include<sstream> using namespace std; struct stacktype ; int element[10]; int top; // creating the stack for 1 st time void create (stacktype &stack) stack.top=-1; // add data to the stack void push(stacktype & stack,int c) stack.top++; stack.element[stack.top]=c; // pop data from the stack int pop(stacktype &stack) int x; x=stack.element[stack.top]; stack.top--; return x; // check whether the stack is empty bool empty(stacktype stack ) if (stack.top ==-1) return true; int main() stacktype stack; 12

13 int num,num2,r,result; string str; int p; int i=0; create(stack); cout<<"enter Your Expressoin"<<endl; cin>>str; p=str[i]; while(p!='\0') // till end of string // if data contains a digit value is encountered if (isdigit(p)) push(stack,p); // operations are encountered if(p=='+') num=pop(stack); num2=pop(stack); r=num+num2 ; push(stack,r); if(p=='-') num=pop(stack); num2=pop(stack); r=num-num2; push(stack,r); if(p=='*') num=pop(stack); num2=pop(stack); r=num*num2; push(stack,r); if(p=='/') num=pop(stack); num2=pop(stack); r=num/num2; push(stack,r); i++; p=str[i]; /* displays the result */ cout<<"the result"<<" "<<pop(stack)<<endl; system ("pause"); return 0; 13