http://code.activestate.com/recipes/tags/theory-example/2013-01-31T23:41:21-08:00ActiveState Code Recipes2011-11-05T23:42:37-07:00Alexander 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>

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>

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>