Popular Python recipes tagged "theory"http://code.activestate.com/recipes/langs/python/tags/theory/2013-01-31T23:41:21-08:00ActiveState Code RecipesEvolutionary Algorithm (Generation of Prime Numbers) (Python) 2011-11-27T06:45:00-08:00Alexander James Wallarhttp://code.activestate.com/recipes/users/4179768/http://code.activestate.com/recipes/577964-evolutionary-algorithm-generation-of-prime-numbers/ <p style="color: grey"> Python recipe 577964 by <a href="/recipes/users/4179768/">Alexander James Wallar</a> (<a href="/recipes/tags/algorithm/">algorithm</a>, <a href="/recipes/tags/example/">example</a>, <a href="/recipes/tags/genetic/">genetic</a>, <a href="/recipes/tags/genetic_algorithm/">genetic_algorithm</a>, <a href="/recipes/tags/genetic_algorithms/">genetic_algorithms</a>, <a href="/recipes/tags/list/">list</a>, <a href="/recipes/tags/number/">number</a>, <a href="/recipes/tags/of/">of</a>, <a href="/recipes/tags/prime/">prime</a>, <a href="/recipes/tags/primelist/">primelist</a>, <a href="/recipes/tags/primes/">primes</a>, <a href="/recipes/tags/theory/">theory</a>). </p> <p>This is an evolutionary algorithm that returns a random list of prime numbers. This code is highly inefficient for a reason. This algorithm is more of a proof of concept that if a prime was a heritable trait, it would not be a desired one. </p> <p>Parameters:</p> <p>isPrime --> n: number to check if it is prime allPrimes --> n: size of list of random primes, m: the primes in the list will be between 0 and m</p> primeList (Python) 2011-11-05T23:42:37-07:00Alexander James Wallarhttp://code.activestate.com/recipes/users/4179768/http://code.activestate.com/recipes/577935-primelist/ <p style="color: grey"> Python recipe 577935 by <a href="/recipes/users/4179768/">Alexander James Wallar</a> (<a href="/recipes/tags/list/">list</a>, <a href="/recipes/tags/numbers/">numbers</a>, <a href="/recipes/tags/prime/">prime</a>, <a href="/recipes/tags/primelist/">primelist</a>, <a href="/recipes/tags/primes/">primes</a>, <a href="/recipes/tags/theory/">theory</a>). Revision 3. </p> <p>This module returns all the prime numbers strictly less than n. For this code to print out all of the primes n inclusive, in the range, n+1 must be substituted for n.</p> Simple graph algorithms with a modular design (Python) 2011-04-21T13:40:32-07:00jimmy2timeshttp://code.activestate.com/recipes/users/4177690/http://code.activestate.com/recipes/577668-simple-graph-algorithms-with-a-modular-design/ <p style="color: grey"> Python recipe 577668 by <a href="/recipes/users/4177690/">jimmy2times</a> (<a href="/recipes/tags/algorithms/">algorithms</a>, <a href="/recipes/tags/breadth/">breadth</a>, <a href="/recipes/tags/depth/">depth</a>, <a href="/recipes/tags/directed/">directed</a>, <a href="/recipes/tags/first/">first</a>, <a href="/recipes/tags/graph/">graph</a>, <a href="/recipes/tags/object/">object</a>, <a href="/recipes/tags/oriented/">oriented</a>, <a href="/recipes/tags/python/">python</a>, <a href="/recipes/tags/search/">search</a>, <a href="/recipes/tags/theory/">theory</a>, <a href="/recipes/tags/undirected/">undirected</a>, <a href="/recipes/tags/visit/">visit</a>). Revision 7. </p> <p>The purpose of this recipe is to look at algorithmic graph theory from an object-oriented perspective.</p> <p>A graph is built on top of a dictionary indexed by its vertices, each item being the set of neighbours of the key vertex. This ensures that iterating through the neighbours of a vertex is still efficient in sparse graphs (as with adjacency lists) while at the same time checking for adjacency is expected constant-time (as with the adjacency matrix).</p> <p>Any valid class of graph must implement the interface defined by AbstractGraph.</p> <p>A generic search algorithm takes as input a graph, source and target vertices and a queue. A queue must implement the methods Q.get(), Q.put() and Q.empty() in such a way to get the desired order in visiting the vertices.</p> <p>Given this pattern, breadth-first and depth-first search are essentially defined by the corresponding expansion policies: the first one uses an actual FIFO queue, the second one a LIFO queue (or stack).</p> Inverse modulo p (Python) 2013-01-31T23:41:21-08:00Justin Shawhttp://code.activestate.com/recipes/users/1523109/http://code.activestate.com/recipes/576737-inverse-modulo-p/ <p style="color: grey"> Python recipe 576737 by <a href="/recipes/users/1523109/">Justin Shaw</a> (<a href="/recipes/tags/mod/">mod</a>, <a href="/recipes/tags/modulo/">modulo</a>, <a href="/recipes/tags/number/">number</a>, <a href="/recipes/tags/prime/">prime</a>, <a href="/recipes/tags/theory/">theory</a>). Revision 4. </p> <p>Very rarely it is necessary to find the multiplicative inverse of a number in the ring of integers modulo p. Thie recipe handles those rare cases. That is, given x, an integer, and p the modulus, we seek a integer x^-1 such that x * x^-1 = 1 mod p. For example 38 is the inverse of 8 modulo 101 since 38 * 8 = 304 = 1 mod 101. The inverse only exists when a and p are relatively prime.</p>