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CSE 310-Lecture2

# CSE 310-Lecture2 - CSE 310 Algorithms and Data Structures...

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C M L Click to edit Master subtitle style 10/22/10 CSE 310 Algorithms and Data Structures Aviral Shrivastava Assistant Professor Computer Science and Engineering Arizona State University

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C M L 10/22/10 Announcements Class Schedule MW, 7:00 pm – 10:00 pm Assignment 1 is online Due by June 14, 2010
C M L 10/22/10 Recursion Fundamental way of solving problems Break the problem into smaller sub-problems Classical examples of recursion Fib(n) = 1, for n=0 and 1 Base Case Fib(n) = Fib(n-1)+F(n-2) for all n>2 Recursive Definition Fact(n) = 1, for n=1 Base Case Fact(n) = n*Fact(n-1) Recursive Definition GNU All programming languages are defined recursively C/C++, Java, Perl, Python Indian language “Sanskrit” was defined using recursion in 5 BC

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C M L 10/22/10 Fractals The Mandelbrot set M is defined by a family of complex quadratic polynomials given by, where c is a complex parameter. For each c , one considers the behavior of the sequence obtained by iterating Pc ( z ) starting at critical point z = 0. The sequence either escapes to infinity or stays within a disk of some finite radius. The Mandelbrot set is defined as the set of all points c such that the above sequence does not escape to infinity. Fractal: When computed and graphed on the complex plane, the Mandelbrot Set is seen to have an elaborate boundary, which does not simplify at any Mandelbrot set
C M L 10/22/10 Karatsuba Multiply 2 n-digit numbers Kolmogorov 1960 conjecture: It takes Ѳ(n2) operations In a lecture at Moscow State University In a week Karatsuba proved him wrong

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CSE 310-Lecture2 - CSE 310 Algorithms and Data Structures...

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