寻找最接近字符串的回文

Question

我正在尝试编写一个 python 程序来找到最接近单词的回文。我可以在字符串的任何部分添加一个字母，从字符串的任何部分删除一个字母，或者在字符串的任何部分更改一个字母。我一直在研究使用 levenshtein 距离来找到帖子Edit Distance in Python 中两个单词之间所需的最少编辑次数。但我不确定如何以编程方式找到需要最少编辑次数的回文。我正在努力实现的一些示例：

palindrome('hello') = 'ollo'
#you can remove the h and then turn the e into an o, giving a palindrome in 2 steps
levenshtein('hello',palindrome('hello')) = 2

palindrome('test') = 'tet'
#you can remove the s to get a palindrome
levenshtein('test',palindrome('test')) = 1

palindrome('tart') = 'trart'
#adding an r or removing the r produces a palindrome, but both solutions only require 1 edit so either would be acceptable.
levenshtein('tart',palindrome('tart')) = 1

我能够使用链接帖子中的 levenshtein 代码来查找两个字符串之间的距离。我需要帮助编写一个回文（）函数，该函数接受一个字符串并返回最接近该字符串的回文。

Answer 1

这是我的 DFS 实现。它只搜索到word length-2 的距离，因为过去它变得微不足道（只删除一个字母，将每个字母都改成相同的）。

它会找到直到该距离限制的所有回文，并按距离对它们进行排序。

import time
word = "hello"
visited_cost = {}       # to keep track of non-palindromes we've considered
palindrome_cost = {}    # to store actual palindromes we've found


def find_palindrome(w, dist=0 ):
    # Don't go on forever
    if len(w) == 0 or len(w) > len(word) + 2 or dist > len(word) - 2:
        return []

    # Don't retry potential palindromes that we've tried before
    global visited_cost
    if w in visited_cost:
        if dist >= visited_cost[w]:
            return []
    visited_cost[w] = dist

    # check if we've found a palindrome
    if (reverse(w)) == w:
        if w in palindrome_cost:
            palindrome_cost[w] = min(palindrome_cost[w], dist)
        else:
            palindrome_cost[w] = dist
        return [w]

    palindromes = []
    if len(w) > 1:
        for x in drop_one(w):
            palindromes += find_palindrome(x, dist+1)
        for x in add_one(w):
            palindromes += find_palindrome(x, dist+1)
        for x in change_one(w):
            palindromes += find_palindrome(x, dist+1)
        return palindromes


# For a word w, gives all possible words obtained by dropping one letter
def drop_one(w):
    return [w[:i]+w[i+1:] for i in range(len(w))]


# For a word w, gives all possible words obtained by inserting a capital X
# at any position in the word. Of course "X" could be any letter
def add_one(w):
    return [w[:i]+"X"+ w[i:] for i in range(len(w))]


# For a word w, gives all possible words obtained by changing one letter 
# to another letter occurring in the word
def change_one(w):
    return [w[:i] +j +  w[i + 1:] for i in range(len(w)) for j in w]


def reverse(s):
    return "".join(reversed(s))

t0 = time.time()
results = set(find_palindrome(word))
s = sorted(results, key = lambda x: palindrome_cost[x])

for x in s:
    print x, palindrome_cost[x]
print "Found %i palindromes based on '%s' in %.3f seconds" %\
       (len(results), word, time.time() - t0)

输出：

ollo 2
olllo 2
elle 2
heleh 2
hllh 2
oeleo 2
hlllh 2
[...]
Found 46 palindromes based on 'hello' in 0.065 seconds