tailieunhanh - Memory VOL.2 Episode 1

The first use of the word "computer" was recorded in 1613 in a book called "The yong mans gleanings" by English writer Richard Braithwait I haue read the truest computer of Times, and the best Arithmetician that euer breathed, and he reduceth thy dayes into a short number. It referred to a person who carried out calculations, or computations, and the word continued with the same meaning until the middle of the 20th century. From the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations.[3]. | Notes for the course advanced algorithms January 2000 Johan Hastad email johanh@ 2 Contents 1 Introduction 7 2 Notation and basics 9 A couple of basic algorithms. 9 Greatest common divisor . 9 Systems of linear equations. 11 Depth first search . 11 3 Primality testing 13 Chinese remainner theorem. 11 Chinese remainder theorem in practice. 15 The Miller-Rabin primality test. 16 Some notes on the algorithm. 20 Other tests for primality. 20 4 Factoring integers 23 The naive algorithm. 23 Pollard s p-method. 23 A method used by Fermat. 25 Comainine eeqat onn. 22 Implementation tricks. 28 Other methods. 28 Continued fractions . 32 5 Discrete Logarithms 35 A digression. 36 A naive algorithm . 36 The baby step giant step algorithm . 36 Pollard s p-algorithm for discrete logarithms. 37 The algorithm by Pohlig and Hellman. 38 An even faster randomized algorithm. 40 6 Quantum computation 43 Some quantum mechanics. 43 Operating on qubits. 44 Simulating deterministic computations. 46 Relations to other models of computation. 48 Relation to probabilistic models . 48