This whole problem is known as “Common Subexpression Elimination” or CSE. It is a slightly smaller version of the problem called “Graph Reduction” faced by the implementer of compilers for functional programming languages. Googling “Common Subexpression elimination algorithm” gives lots of solutions, though none that I can see especially for the constraints given by matrix … Read more
Your intuition behind why the algorithm should be Θ(n2) is a good one, but most suffix trees are designed in a way that eliminates the need for this time complexity. Intuitively, it would seem that you need Θ(n2) different nodes to hold all of the different suffixes, because you’d need n + (n – 1) … Read more
The Linear solution can be found in this Way :: Prequisities: (1).You must know how to construct the suffix array in O(N) or O(NlogN) time. (2).You must know how to find the standard LCP Array ie. LCP between adjacent Suffixes i and i-1 ie . LCP [i]=LCP(suffix i in sorted array, suffix i-1 in sorted … Read more
An alternative to use argparse in Ipython notebooks is passing a string to: args = parser.parse_args() (line 303 from the git repo you referenced.) Would be something like: parser = argparse.ArgumentParser( description=’Searching longest common substring. ‘ ‘Uses Ukkonen\’s suffix tree algorithm and generalized suffix tree. ‘ ‘Written by Ilya Stepanov (c) 2013’) parser.add_argument( ‘strings’, metavar=”STRING”, … Read more
A suffix tree can be viewed as a data structure built on top of a trie where, instead of just adding the string itself into the trie, you would also add every possible suffix of that string. As an example, if you wanted to index the string banana in a suffix tree, you would build … Read more
The following is an attempt to describe the Ukkonen algorithm by first showing what it does when the string is simple (i.e. does not contain any repeated characters), and then extending it to the full algorithm. First, a few preliminary statements. What we are building, is basically like a search trie. So there is a … Read more