CS113 Lecture Topics  (after Midterm)

Oct 29: Roberts 12, 17.3; Standish 6, 13

	Sorting and Algorithmic Efficiency
		What is Sorting?
		What is an Algorithm?
		Selection Sort 
		Big O
		Intro to MergeSort

Oct 31: Recursion

	pseudo-code and intuition for MergeSort
	easier recursive examples
		factorial
		fibonacci numbers
			wrapper functions
		string reversal (printing a string backwards)
		palindromes
	types of recursive decomposition
		left half and right half   [merge sort]
		first and rest 		   [factorial, string reversal]
		last and all but last 	   [bad algorithm for string reversal]
		outside and middle 	   [palindrome]

	
Nov 5:	Recursion
		binary search in sorted array
		towers of hanoi
	Big O
		linear, quadratic, logrithmic and exponential growth rates

Nov 7:	Sorting
		QuickSort
			worst case: O(n*n)
			ave case:   O(n log n)
			can choose pivot in ways which improve performance
		Big O, Big Omega, Big Theta
		O(n log n) is best for comparison-based sorting
			BigOmega(n log n) compares required
		Radix sort 
			O(n) algorithm 
			limited applicability
		Insertion sort
			O(n*n) in general
			performs well on nearly sorted array
			

Nov 12:	Table ADT
		Interface
	Linear implementations
		Sorted/unsroted array, sorted/unsorted linked list
		Performance
	Trees
		basic definitions/vocab
		better performance for table ADT
		how do we implement it?

Nov 14:	Binary Search Trees
		table.h
		finding things in a BST

Nov 19:	BST Implementation
		did		discussed
		---		---------
		New()		[Free()]
		Retrive()	[Update()]
		Traverse()	[Visit()]
		Insert()	[Delete()]

Nov 21:	Improving tree performance 
		Shape: AVL trees
			definition of AVL property 
			examples
			how to insert
			analysis (showing depth is at most O(log n))
		Tree Structure: 2-3 trees

	Other things to do with trees
		Heaps & Priority Queues
			Def. of heap:  shape and organization
			inserting items into a heap
			removing the largest item from a heap
		Sorting:  put things in and read them back out
			TreeSort (use BST or AVL-BST)
			HeapSort (use a heap)

Nov 26: Hashing: mapping a bunch of keys directly onto an array

	Inevitable collisions
	Special considerations for delete and enumerate
	Resolving collisions with linear probing; clustering
	Double hashing and permissible decrement rates
	Performance: If table is half-empty, Most operations are O(1)
		except for enumerate, which is O(n log n) and init, O(n)

	Makefiles: targets, dependencies, quirks, implicit rules	

Nov 28:	No class: Thanksgiving Recess

Dec  3:	Graphs
	Definitions: vertex, node, edge, augmented graph (labeled graph), 
		weight (of graph, of edge), directed, undirected, successor,
		predecessor, path, cycle, simple cycle, DAG (directed acyclic
		graph), connected, weakly connected, strongly connected,
		connected component, adjacency set, in degree, out degree
	Representations: adjacency lists, adjacency matrix
		advantages/disadvantages
	Traversal
		Recursive 
		Stack
		Queue
		depth-first/breadth first

Dec  5:	Graphs
	Spanning Trees
		min spanning tree algorithm (Prim's algorithm)
	Shortest Distance
		Dijkstra's algorithm
	Topological Order
		definition and algorithm
	Greedy Algorithms

Dec 10:	Graphs and hard problems


Dec 17: Final Exam (9 am)