查找所有公共的、不重叠的子字符串

Question

给定两个字符串，我想识别从最长到最短的所有公共子字符串。

string1 = '51234'

string2 = '12345'

result = ['1234', '5']

string1 = '12345623456'

string2 = '623456'

result = ['623456', '23456']

最后，我需要检查一个字符串与数千个字符串的固定列表。我不确定在散列出这些字符串中的所有子字符串时是否有一个明智的步骤。

先前的答复：

在这个线程中，发现了一个动态编程解决方案，它需要O（nm）时间，其中n和m是字符串的长度。我对一种更有效的方法感兴趣，它将使用后缀树。

背景：

我正在根据旋律片段创作歌曲旋律。有时，一个组合会产生一个旋律，与现有的一行中的太多音符相匹配。

Answer 1

让我们从树开始

from collections import defaultdict
def identity(x):
    return x


class TreeReprMixin(object):
    def __repr__(self):
        base = dict(self)
        return repr(base)


class PrefixTree(TreeReprMixin, defaultdict):
    '''
    A hash-based Prefix or Suffix Tree for testing for
    sequence inclusion. This implementation works for any
    slice-able sequence of hashable objects, not just strings.
    '''
    def __init__(self):
        defaultdict.__init__(self, PrefixTree)
        self.labels = set()

    def add(self, sequence, label=None):
        layer = self
        if label is None:
            label = sequence
        if label:
            layer.labels.add(label)
        for i in range(len(sequence)):
            layer = layer[sequence[i]]
            if label:
                layer.labels.add(label)

        return self

    def add_ngram(self, sequence, label=None):
        if label is None:
            label = sequence
        for i in range(1, len(sequence) + 1):
            self.add(sequence[:i], label)

    def __contains__(self, sequence):
        layer = self
        j = 0
        for i in sequence:
            j += 1
            if not dict.__contains__(layer, i):
                break
            layer = layer[i]
        return len(sequence) == j

    def depth_in(self, sequence):
        layer = self
        count = 0
        for i in sequence:
            if not dict.__contains__(layer, i):
                print "Breaking"
                break
            else:
                layer = layer[i]
            count += 1
        return count

    def subsequences_of(self, sequence):
        layer = self
        for i in sequence:
            layer = layer[i]
        return layer.labels

    def __iter__(self):
        return iter(self.labels)


class SuffixTree(PrefixTree):
    '''
    A hash-based Prefix or Suffix Tree for testing for
    sequence inclusion. This implementation works for any
    slice-able sequence of hashable objects, not just strings.
    '''
    def __init__(self):
        defaultdict.__init__(self, SuffixTree)
        self.labels = set()

    def add_ngram(self, sequence, label=None):
        if label is None:
            label = sequence
        for i in range(len(sequence)):
            self.add(sequence[i:], label=label)

要填充树，可以使用.add\ngram方法。

下一部分有点棘手，因为您正在寻找字符串的并发遍历，同时跟踪树坐标。为了实现这一切，我们需要一些对树和查询字符串进行操作的函数

def overlapping_substrings(string, tree, solved=None):
    if solved is None:
        solved = PrefixTree()
    i = 1
    last = 0
    matching = True
    solutions = []
    while i < len(string) + 1:
        if string[last:i] in tree:
            if not matching:
                matching = True
            else:
                i += 1
                continue
        else:
            if matching:
                matching = False
                solutions.append(string[last:i - 1])
                last = i - 1
                i -= 1
        i += 1
    if matching:
        solutions.append(string[last:i])
    for solution in solutions:
        if solution in solved:
            continue
        else:
            solved.add_ngram(solution)
            yield solution

def slide_start(string):
    for i in range(len(string)):
        yield string[i:]

def seek_subtree(tree, sequence):
    # Find the node of the search tree which
    # is found by this sequence of items
    node = tree
    for i in sequence:
        if i in node:
            node = node[i]
        else:
            raise KeyError(i)
    return node

def find_all_common_spans(string, tree):
    # We can keep track of solutions to avoid duplicates
    # and incomplete prefixes using a Prefix Tree
    seen = PrefixTree()
    for substring in slide_start(string):
        # Drive generator forward
        list(overlapping_substrings(substring, tree, seen))
    # Some substrings are suffixes of other substrings which you do not
    # want
    compress = SuffixTree()
    for solution in sorted(seen.labels, key=len, reverse=True):
        # A substrings may be a suffix of another substrings, but that substrings
        # is actually a repeating pattern. If a solution is
        # a repeating pattern, `not solution in seek_subtree(tree, solution)` will tell us.
        # Otherwise, discard the solution
        if solution in compress and not solution in seek_subtree(tree, solution):
            continue
        else:
            compress.add_ngram(solution)
    return compress.labels

def search(query, corpus):
    tree = SuffixTree()
    if isinstance(corpus, SuffixTree):
        tree = corpus
    else:
        for elem in corpus:
            tree.add_ngram(elem)
    return list(find_all_common_spans(query, tree))

所以现在要做你想做的事，就这样做：

search("12345", ["51234"])
search("623456", ["12345623456"])

如果有什么不清楚的地方，请告诉我，我会尽力澄清。