Recitation #2 Abstract Data Types, Collection Classes, and Linked List

Transcription

1 Recitation #2 Abstract Data Types, Collection Classes, and Linked List (1) Create an ADT Fraction that describes properties of fractions. Include the constructor, setter, getter, and tostring() methods and write the following operation methods in your Fraction class. (a) add, (b) subtract, (c) multiply, (d) divide, and (e) invert. Write a test class to test your Fraction ADT. Here are some operations on fractions: add a/b + c/d = (ad + bc)/bd subtract a/b - c/d = (ad - bc)/bd multiply a/b * c/d = ac/bd divide a/b c/d = ad/bc invert invert(a/b) = b/a Steps of ADT Design and Implementation: Study the properties of the data abstraction and develop a list of operations that it should provide. A fraction is the quotient of two numbers a/b, where a and b are both integers and b 0. a is called the numerator and b the denominator. So, the attributes for a fraction object: 1. int numerator 2. int denominator public class Fraction { private int num ;//numerator private int den ;//denominator public Fraction () { num = 0; den = 1; } public Fraction ( int n, int d ) // constructor { // assign num = n & den = d as long as d!= 0 if ( d == 0 ) { throw new IllegalArgumentException (); } else { num = n; den = d; }

2 } // getter methods public int getnum () { return this. num ; } public int getden () { return this. den ; } // setter methods public void setnum ( int n ) { this. num = n ; } public void setden ( int d ) { if ( d == 0 ) { throw new IllegalArgumentException (); } else { this. den = d; } } private static int gcd ( int x, int y) { /* gcd() method finds the greatest common divisor of * the 2 int variables passed and returns that value * */ int mod ; // hold a value temporarily to allow switch if ( x < y ) // always use the larger value as the divisor { mod = x; x = y; y = mod ; } int r = x % y ; // r holds the remainder of modulus division while ( r!= 0 )// while modulus division does not result in zero { x = y ; y = r; r = x % y ; } return y; } private Fraction reduce ( int n, int d) { int gcdnum = gcd ( n, d ); d = d / gcdnum ; // reduce the denominator using the gcd foun in gcd method n = n / gcdnum ; // reduce the numerator using the gcd foun in gcd method return new Fraction ( n, d ); // return the new fraction object in lowest form } // Operations public Fraction add ( Fraction b) { int num1 = ( this. num * b. den ) + ( b. num * this. den ); // cross multily and add int num2 = this. den * b. den ; // multiply the denominators to make them equivlent return reduce ( num1, num2 ); // calls reduce() method and returns a new Fraction object }

3 public Fraction subtract ( Fraction b) { int num1 = ( this. num * b. den ) - ( b. num * this. den ); // cross multiply and subtact int num2 = this. den * b. den; return reduce ( num1, num2 ); // sends to reduce method } public Fraction multiply ( Fraction b) { int num1 = this. num * b. num ; // multiplys straight accross int num2 = this. den * b. den; return reduce ( num1, num2 ); // sends to reduce method and returns the reduced fraction to the //tostring() method } public Fraction divide ( Fraction b) { int num1 = this. num * b. den ; //multiplys the inverse of 2nd fraction object to divide int num2 = this. den * b. num; return reduce ( num1, num2 ); // sends to reduce method } public Fraction invert () { return new Fraction ( this. den, this. num ); } public String tostring ()// *** convert to a mixed fraction for output only { if ( num > den && den > 1 ) //if true will show fraction object and mixed number return ( num + "/" + den + " or " + ( num / den ) + " " + ( num % den ) + "/" + den ); else return ( num + "/" + den ); //will not try to convert fraction object to mixed number } public static void main ( String args []) { Fraction x = new Fraction ( 1, 2 ); Fraction y = new Fraction ( 1, 3 ); Fraction z = x. add ( y ); System. out. println ( "Result: " + z. tostring ()); z = x. subtract ( y ); System. out. println ( "Result: " + z. tostring ()); z = x. multiply ( y ); System. out. println ( "Result: " + z. tostring ()); z = x. divide ( y ); System. out. println ( "Result: " + z. tostring ()); z = x. invert (); System. out. println ( "Result: " + z. tostring ()); } }

4 (2) Write a code to remove the duplicate elements of an array. import java. util. Arrays ; public class Duplicate { static void unique_array ( int [] my_array ) { //Assuming all elements in input array are unique int no_unique_elements = my_array. length ; //Comparing each element with all other elements for ( int i = 0 ; i < no_unique_elements ; i ++ ) { for ( int j = i + 1 ; j < no_unique_elements ; j ++ ) { //If any two elements are found equal if ( my_array [ i ] == my_array [ j ]) { //Replace duplicate element with last unique element my_array [ j ] = my_array [ no_unique_elements - 1 ]; no_unique_elements -- ; j -- ; } } } //Copying only unique elements of my_array into array1 int [] array1 = Arrays. copyof ( my_array, no_unique_elements ); //Printing arraywithoutduplicates for ( int i = 0 ; i < array1. length ; i ++ ) { System. out. print ( array1 [ i ] + "\t" ); } } public static void main ( String [] args ) { unique_array ( new int [] { 0, 3, - 2, 4, 3, 2 }); unique_array ( new int [] { 10, 22, 10, 20, 11, 22 }); } }

5 (3) Write a code to find the median of an array of integers with n elements. Hint: Sort the array (e.g., using insertion sort shown in class). If the array has odd number of elements return the middle element A[n/2], and it has even number of elements return (A[(n/2)-1]+A[n/2]) /2. (4) Given an array, a linked list, and a doubly linked list, determine which data structure(s) would be better for storing a collection of values in the following situations (and explain why) (a)elements are usually accessed in sequence (b)the initial size is unknown and can vary widely during execution (c)elements are frequently accessed randomly (d)elements are accessed sequentially, but sometimes in reverse order (a) Linked list/doubly linked list; as nodes can only be accessed by traversing the list in order (b) Linked list/doubly linked list; as nodes are only created as needed, array might need to be resized (c) Array, because you can access each element by index in O(1) time (d) Doubly linked list, because you have references to the next and previous node (5) Suppose you have a linked list with integer type data. Write a method called findmaxelement that returns a reference to the node of the linked list which contains the maximum element, by only traversing the list ONCE. public Node findmaxelement () { if ( head == null ) return null; Node maxelement = head; Node current = head; while ( current!= null ) { current = current. getnext(); if ( current!= null && current. getdata() > maxelement. getdata() ) { maxelement = current; } } return maxelement; } (6) What does the following function do for a given linked list if you call it with a head node? void method ( Node node ) { if ( node == null) return; method ( node. getnext ()); System. out. println ( node. getdata (). tostring ()); } What is the time complexity of this code?

6 Prints the nodes of the linked list in reverse order. This code takes O (n). (7) Write a function to return the middle element of a Linked List in one pass. public Node getmiddleelement () { if ( head == null ) return null; Node current = head; int length = 0; Node middle = head; while ( current. getnext ()!= null ){ length ++; if ( length % 2 == 0 ){ middle = middle. getnext (); } current = current. getnext (); } if ( length % 2 == 1 ){ middle = middle. getnext (); } return middle; }