Data Structures and Algorithms Notes

Transcription

1 Data Structures and Algorithms Notes Notes by Winst Course taught by Dr. G. R. Baliga ext Course started: September 4, 2012 Last generated: December 18, 2013 Interfaces - template for a class List - collection of things with operations that can be applied onto it. They are an abstract data type. Sorting Adding to front Adding to rear Size Removing the first thing Abstraction - Separation of how something is done versus what is being done. Linked list - no overhead with space wastage compared with ArrayList Singly linked list - only one link that links nodes together. Doubly linked list - links going in both directions. class Node { Object data ; Node next ; Node ( ) { data = null ; next = null ; Node ( Object data ){ this. data = data ; class LinkedList implements L i s t { int count ; Node f i r s t ; public void addfirst ( Object value ){ Node temp = new Node ( value ) ; temp. next = f i r s t ; f i r s t = temp ; count++; public void addlast ( Object value ){ Node temp = new Node ( value ) ; i f ( count == 0){ f i r s t = temp ; Office hours: TR from 10:30 to noon. 1

2 else { Node l a s t = f i r s t ; // while ( f i r s t. next!= n u l l ) for ( int i = 0 ; i < count 1 ; i++) l a s t = f i r s t. next ; l a s t. next=temp ; count++; You could start off a linked list with a dummy node that has no data, thus getting rid of the bothersome case checking. class LinkedList implements L i s t { int count ; Node f i r s t, l a s t ; public LinkedList ( ) { f i r s t = new Node ( ) ; l a s t = new Node ( ) ; f i r s t. next = l a s t ; count = 0 ; public addfirst ( Object value ){ Node temp = new Node ( value ) ; temp. next = f i r s t. next ; f i r s t. next = temp ; count++; public addlast ( Object value ){ Node temp = f i r s t ; for ( int i = 0 ; i < count ; i ++){ temp = temp. next ; Node n = new Node ( value ) ; n. next = l a s t ; temp. next = n ; Abstract Data Types Stack push pop Queue Deque enqueue dequeue Inheritance vs composition is a vs has a 1 Iterator 2

3 interface L i s t { L i s t I t e r a t o r l i s t I t e r a t o r ( ) ; L i s t I t e r a t o r { next ( ) ; hasnext ( ) ; p r e v i o u s ( ) ; hasprevious ( ) ; i n s e r t ( ) ; Implementable via Linked Lists: List Stack Queue Deque Sets Unordered collection. No duplicates. Listing 1: Inefficient method of implementation class Set { LinkedList l i s t ; add ( Object value ){ i f (! l i s t. c o n t a i n s ( value ) ) l i s t. addlast ( value ) ; boolean c o n t a i n s ( Object value ){ return l i s t s. c o n t a i n s ( value ) ; void remove ( Object value ){ int pos = l i s t. indexof ( value ) ; i f ( pos!= 1) l i s t. remove ( pos ) ; Better way Binary Trees 2 Binary Trees Removal by replacing rightmost left subnode or leftmost right subnode with the root. Any subnodes connected to this subnode can be reconnected with the above node. Infix, Prefix, Postfix (2 * 3) + (1+6/2) * 5 = 2 3 * / + 5 * + 3 Infix to Postfix use a stack to hold operators. use operator precedence. 4 Recursion Applies to linked lists. int findlength ( Node s t a r t ) { i f ( s t a r t==null ) 3

4 return 0 ; return 1 + findlength ( s t a r t. next ) ; int sumvalues ( Node s t a r t ){ i f ( s t a r t==null ) return 0 ; return s t a r t. data + sumvalues ( s t a r t. next ) ; int maxvalue ( Node s t a r t ){ i f ( s t a r t. next==null ) return s t a r t. data ; return Math. max( s t a r t. data, l a r g e s t ( s t a r t. next ) ) ; int count ( Node s t a r t, int value ){ i f ( s t a r t == null ) return 0 ; i f ( s t a r t. data == value ) return 1 + count ( s t a r t. next, value ) ; return count ( s t a r t. next, value ) ; 4.1 Binary trees class Node{ Node l e f t, r i g h t ; int data ; Listing 2: Binary tree Node implementation int count ( Node ) next ){ i f ( next == null ) return 0 ; return 1 + count ( root. l e f t ) + count ( root. r i g h t ) ; Composition - important word boolean e q u a l s ( Node A, Node B){ i f (A == null ) return (B == null ) ; i f (B == null ) return f a l s e ; // (A == n u l l ) ; Listing 3: Recursively check equality of 2 linked lists return A. data. e q u a l s (B. data ) && e q u a l s (A. next, B. next ) ; Listing 4: Recursively remove object N from a singly linked list Object remove ( Node s t a r t, int index ){ i f ( index < 0) return s t a r t ; i f ( s t a r t==null ) 4

5 return null ; i f ( index == 0){ return s t a r t. next ; else { s t a r t. next = remove ( s t a r t. next, index 1 ) ; return s t a r t ; Listing 5: Replace all instances of a given value V with a given W in a list public void r e p l a c e A l l ( Node n, Object v, Object w){ i f ( n == null ) return ; i f ( n. data. e q u a l s ( v ) ) { n. data = w; r e p l a c e A l l ( n. next, v, w) ; 5 Searching & Sorting Sequential search - looking in a sequential manner. Takes N time, where N is the size of the array. Binary search - Halves array each step. Takes lg n time. Comparable<T> interface // l o o k s l i k e bunches wrong here... Listing 6: Binary Search implementation int binarysearch (T value, T [ ] array, Comparator<t> comp, int startindex, int endindex ){ int l e f t, r i g h t, mid ; l e f t = s t a r t I n d e x ; r i g h t = endindex ; int answer = comp. compare ( a [ mid ], value ) ; while ( l e f t <= r i g h t ){ mid = ( l e f t + r i g h t ) / 2 ; i f ( answer == 0) return mid ; else i f ( answer < 0) l e f t = mid + 1 ; else r i g h t = mid 1 ; Listing 7: Sample implemetation for Comparator? Odd/Even splitting? class FunnyOrder implements Comparator<Integer >{ int compare ( I n t e g e r x, I n t e g e r y ){ i f ( ( x % 2 == 0) && ( y % 2 == 1 ) ) return 1; else i f ( ( x % 2 == 1) && ( y % 2 == 0 ) ) return 1 ; 5

6 6 Backtracking? N Queens - 8 queens not attacking each other on chess board Knight tour - Knights go on each square exactly once on a 6 6 or 5 5 board MVC - Model View Controller Separation of classes that handle the individual components (the model, the view, and the controlling of the interaction with the gui) Observer pattern Listing 8: Largest int in tree using recursion int l a r g e s t ( Node root ) { i f ( root. l e f t == null && root. r i g h t == null ) return root. data ; i f ( root. l e f t == null ) return Math. max( l a r g e s t ( root. r i g h t ), root. data ) i f ( root. r i g h t == null ) return Math. max( l a r g e s t ( root. l e f t ), root. data ) return Math. max(math. max( l a r g e s t ( root. r i g h t ), l a r g e s t ( root. l e f t ), data ) ) ; Listing 9: Largest int in tree using recursion (weak version) int l a r g e s t ( Node root ){ i f ( root == null ) return I n t e g e r.min VALUE; else return Math. max(math. max( l a r g e s t ( root. r i g h t ), l a r g e s t ( root. l e f t ), data ) ) ; 7 Set ADT Collection that does not allow duplicates. Generic. boolean add(t element) //returns true if added. boolean remove(t element) //false if doesn t exist boolean find(t element) Listing 10: Set structure class Set { // i n t e r n a l implementation uses binary search Node root ; // i n i t to point to dummy node class Node { T data ; Node l e f t, r i g h t ; public S e t ( Comparator<T> comparator ){ 6

7 8 Sorting Listing 11: Sort method signature void s o r t (T [ ] array, Comparator<T> comparator ) Selection sort selecting the smallest element and swapping it to it s correct index. Will need n 1 stages. Bubble sort exchanges adjacent pairs throughout. Doesn t always need n 1 stages. Insertion sort attempt to sort subarray, inserting new object to location it should be in, in the sorted subarray. Inserts by swapping item down into the subarray. Quicksort pick a value at random (pivot element). Partition the array so that all values equal to the picked end up in the middle, all values larger than the picked end up to the right, all values smaller end up on the left. 9 Interpolation Search Listing 12: Interpolation search method signature i n t e r p o l a t i o n S e a r c h (T value, T [ ] array, int s t a r t, int length, Comparator<T> compare, Evaluator <T> e v a l ) To use interpolation search on strings, would need some sort of evaluator (interface) to map from the strings to some numeric quantity (like doubles) Listing 13: Binary search method signature binarysearch (T value, T [ ] array, int s t a r t, int length, Comparator<T> compare ) ; Listing 14: Selection Sort method signature s e l e c t i o n S o r t (T [ ] array, Comparator<T> compare, int s t a r t, int numvalues ) ; 10 Hash Tables Chaining - when collision occurs, add to the linked list at the array s location Open addressing - when collision occurs, look one down till open spot is found. (this is more specifically called linear probing) 11 Traversals Inorder - left, root, right Postorder - left, right, root Preorder - root, left, right Use a stack for traversing 7