Advanced Programming I and the Role of Algorithms

1
Advanced Programming Iand the Role of Algorithms

• Introduction to Algorithms

2
Algorithms

• Studying algorithms is about studying efficiency
• How fast does it run?
• Can I make it run faster?

3
Algorithms

• An algorithm is any well-defined computational
  procedure that takes some input and produces
  output
• A sequence of steps
• An algorithm is correct if for all input, it
  halts with the correct output
• We say that a correct algorithm solves the
  computational problem
• An incorrect algorithm may not halt!

4
Example Sorting Problem

• Input A sequence of n numberslta1, a2, , angt
• Output A permutation lta'1, a'2, , a'ngt of the
  original such that a'1 a'2 a'n
• Sorting is fundamental to computer science, so
  well be studying several different solutions to
  it

5
The Challenge

• Suppose we have 1 million numbers to sort
• Your computer executes 100 million ips
• Mine executes 1 million ips
• You have optimized compiler (take hit of 2)
• I have crummy compiler (take hit of 50)
• You use insertion sort (n2), I use merge sort (n
  log n)

20,000 secs 5.56 hours
2 (106)2 instrs
108 instruction/sec
1,000 secs 16.67 minutes
50(106lg 106) instrs
106 instruction/sec
6
I WIN!
7
What youll be studying

• The Design and Analysis of Algorithms
• Growth of Functions
• Recurrences
• Heapsort, Quicksort, Counting Sort
• Medians and Order Statistics
• Elementary Data Structures
• Hashing

8
What youll be studying

• Binary Search Trees
• Red-Black Trees
• Dynamic Programming
• Greedy Algorithms
• Amortized Analysis
• B-Trees
• Elementary Graph Algorithms

9
What youll be studying

• Minimum Spanning Trees
• Single-Source Shortest Paths
• All-Pairs Shortest Paths
• NP-Completeness
• Approximation Algorithms

10
A Most Excellent Quote

• Having a solid base of algorithmic knowledge and
  technique is one characteristic that separates
  the truly skilled programmers from the novices.