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Lec01_Introduction

Lec01_Introduction - CS333 Introduction to Algorithms...

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CS333 – CS333 – Introduction to Algorithms Introduction to Algorithms Problems Strategy Efficiency Analysis Order
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This class - Introduction http://www.cs.binghamton.edu/~lijun/CS333_Fall2009/2009Fall_CS333.html Goals Methods Examples
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Goals of the course: Prepare students for: Future technical challenges Using critical thinking for problem solving Implementing algorithms efficiently and correctly Arguing correctness Analyzing time complexity Presenting common algorithms Learning to design using well known methods Comparing algorithms Introduce: The theory of NP-completeness
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Basic Concepts Algorithm: - Applying a technique to a problem results in a step- by-step procedure for solving problem. The step-by-step procedure is called an algorithm for the problem. Example: - Sort a list S of n numbers in non-decreasing order. The answer is the numbers in sorted sequence. - Determine whether the number x is in the list S of n numbers. The answer is yes if x is in S, and no if it is not - solution: Sequential search; Binary search - Add array members - Matrix multiplication
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Importance of Algorithm Efficiency Time Storage Example - Sequential search versus binary search Basic operation: comparison Number of comparisons is grown in different rate - nth Fibonacci sequence Recursive versus iterative
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Example: search strategy Sequential search vs. binary search Problem: determine whether x is in the sorted array S of n keys Inputs: positive integer n, sorted (non-decreasing order) array of keys S indexed from 1 to n, a key x Output: location, the location of x in S (0 if x is not in S)
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