CSE 310-Lecture2

CSE 310-Lecture2 - C M L Click to edit Master subtitle...

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Unformatted text preview: C M L Click to edit Master subtitle style 10/22/10 C M L CSE 310 Algorithms and Data Structures Aviral Shrivastava Assistant Professor Computer Science and Engineering Arizona State University C M L 10/22/10 C M L 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 C M L 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 C M L 10/22/10 C M L 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 Mandelbrot set C M L 10/22/10 C M L Karatsuba Multiply 2 n-digit numbers Kolmogorov 1960 conjecture: It takes (n2) operations In a lecture at Moscow State University In a week Karatsuba proved him wrong Developed scheme to multiply two numbers...
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This note was uploaded on 10/21/2010 for the course CSE 310 taught by Professor Davulcu,h during the Spring '08 term at ASU.

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CSE 310-Lecture2 - C M L Click to edit Master subtitle...

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