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The Role of Algorithms

The Role of Algorithms. Introduction to Algorithms. Algorithms. Studying algorithms is about studying efficiency How fast does it run? Can I make it run faster?. Algorithms. An algorithm is any well-defined computational procedure that takes some input and produces output

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The Role of Algorithms

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  1. The Role of Algorithms Introduction to Algorithms Jeff Chastine

  2. Algorithms • Studying algorithms is about studying efficiency • How fast does it run? • Can I make it run faster? Jeff Chastine

  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! Jeff Chastine

  4. Example: Sorting Problem • Input: A sequence of n numbers<a1, a2, …, an> • Output: A permutation <a'1, a'2, …, a'n> of the original such that a'1 ≤ a'2 ≤ …≤ a'n • Sorting is fundamental to computer science, so we’ll be studying several different solutions to it Jeff Chastine

  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 Jeff Chastine

  6. I WIN! Jeff Chastine

  7. Problems to Think About… • Searching large amounts of information • Most efficient path from A to B (how many routes are there?) • Find a convex hull that contains all points • Travel to a series of points and return home • Best way to schedule classes • Impossible to solve problems? Jeff Chastine

  8. What you’ll be studying • The Design and Analysis of Algorithms • Growth of Functions • Recurrences • Heapsort, Quicksort, Counting Sort… • Medians and Order Statistics • Elementary Data Structures • Hashing Jeff Chastine

  9. What you’ll be studying • Binary Search Trees • Dynamic Programming • Greedy Algorithms • Amortized Analysis • Elementary Graph Algorithms Jeff Chastine

  10. What you’ll be studying • Minimum Spanning Trees • Single-Source Shortest Paths • All-Pairs Shortest Paths • NP-Completeness • Approximation Algorithms Jeff Chastine

  11. 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.” Jeff Chastine

  12. The Proof(and why you should pay attention) • http://www.geeksforgeeks.org/ Jeff Chastine

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