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POHow can memoization be applied to this algorithm?
 

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    <p>After finding the <code>difflib.SequenceMatcher</code> class in Python's standard library to be unsuitable for my needs, a generic "diff"-ing module was written to solve a problem space. After having several months to think more about what it is doing, the recursive algorithm appears to be searching more than in needs to by re-searching the same areas in a sequence that a separate "search thread" may have also examined.</p> <p>The purpose of the <code>diff</code> module is to compute the difference and similarities between a pair of sequences (list, tuple, string, bytes, bytearray, et cetera). The initial version was much slower than the code's current form, having seen a speed increase by a factor of ten. How can memoization be applied to the following code? What is the best way to rewrite the algorithm to further increase any possible speed?</p> <hr> <pre><code>class Slice: __slots__ = 'prefix', 'root', 'suffix' def __init__(self, prefix, root, suffix): self.prefix = prefix self.root = root self.suffix = suffix ################################################################################ class Match: __slots__ = 'a', 'b', 'prefix', 'suffix', 'value' def __init__(self, a, b, prefix, suffix, value): self.a = a self.b = b self.prefix = prefix self.suffix = suffix self.value = value ################################################################################ class Tree: __slots__ = 'nodes', 'index', 'value' def __init__(self, nodes, index, value): self.nodes = nodes self.index = index self.value = value ################################################################################ def search(a, b): # Initialize startup variables. nodes, index = [], [] a_size, b_size = len(a), len(b) # Begin to slice the sequences. for size in range(min(a_size, b_size), 0, -1): for a_addr in range(a_size - size + 1): # Slice "a" at address and end. a_term = a_addr + size a_root = a[a_addr:a_term] for b_addr in range(b_size - size + 1): # Slice "b" at address and end. b_term = b_addr + size b_root = b[b_addr:b_term] # Find out if slices are equal. if a_root == b_root: # Create prefix tree to search. a_pref, b_pref = a[:a_addr], b[:b_addr] p_tree = search(a_pref, b_pref) # Create suffix tree to search. a_suff, b_suff = a[a_term:], b[b_term:] s_tree = search(a_suff, b_suff) # Make completed slice objects. a_slic = Slice(a_pref, a_root, a_suff) b_slic = Slice(b_pref, b_root, b_suff) # Finish the match calculation. value = size + p_tree.value + s_tree.value match = Match(a_slic, b_slic, p_tree, s_tree, value) # Append results to tree lists. nodes.append(match) index.append(value) # Return largest matches found. if nodes: return Tree(nodes, index, max(index)) # Give caller null tree object. return Tree(nodes, index, 0) </code></pre> <hr> <p><strong>Reference:</strong> <a href="https://stackoverflow.com/questions/3220433">How to optimize a recursive algorithm to not repeat itself?</a></p>
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