Question

我想找到通过添加尽可能少的部分来改变二进制数字符串之间的汉明距离的方法。我应该使用稀疏树和深度优先搜索，但我真的不知道如何使用它。

Answer 1

您可以使用此代码。如果二进制字符串，它计算列表中每对字符串之间的汉明距离。如果距离小于最小阈值，则仅修改两个弦中的一个，直到达到最小距离。这不是很正确，因为修改对中的一个字符串会导致一个字符串中的更多修改，因此更好的解决方案是修改一个字符串，然后再修改另一个字符串。但如果这看起来像你需要的话，你可以解决这个问题。

import Levenshtein as lv

min_distance = 3
numbers = {'1100010' ,'1001101', '1111111', '1111101', '1101001'}

for number in numbers:
    other_numbers = numbers - {number}
    for other_number in other_numbers:
        distance = lv.hamming(number, other_number)
        backup_other_number = other_number
        while lv.hamming(number, other_number) < min_distance:
            for count, (a, b) in enumerate(zip(number, other_number)):
                if a == b:
                    other_number = ''.join([
                        n if c != count else str(int(a != '1'))
                        for c, n in enumerate(other_number)
                    ])
                if lv.hamming(number, other_number) >= min_distance:
                    break
        print 'Old pair: {0}, distance: {1}'.format(
            (number, backup_other_number),
            distance
        )
        print 'New pair: {0}, distance: {1}'.format(
            (number, other_number),
            lv.hamming(number, other_number)
        )
    print '=' * 80

输出：

(tmp)➜  ~  python hamming.py
Old pair: ('1001101', '1111101'), distance: 2
New pair: ('1001101', '0111101'), distance: 3
Old pair: ('1001101', '1111111'), distance: 3
New pair: ('1001101', '1111111'), distance: 3
Old pair: ('1001101', '1100010'), distance: 5
New pair: ('1001101', '1100010'), distance: 5
Old pair: ('1001101', '1101001'), distance: 2
New pair: ('1001101', '0101001'), distance: 3
================================================================================
Old pair: ('1111101', '1001101'), distance: 2
New pair: ('1111101', '0001101'), distance: 3
Old pair: ('1111101', '1111111'), distance: 1
New pair: ('1111101', '0011111'), distance: 3
Old pair: ('1111101', '1100010'), distance: 5
New pair: ('1111101', '1100010'), distance: 5
Old pair: ('1111101', '1101001'), distance: 2
New pair: ('1111101', '0101001'), distance: 3
================================================================================
Old pair: ('1111111', '1001101'), distance: 3
New pair: ('1111111', '1001101'), distance: 3
Old pair: ('1111111', '1111101'), distance: 1
New pair: ('1111111', '0011101'), distance: 3
Old pair: ('1111111', '1100010'), distance: 4
New pair: ('1111111', '1100010'), distance: 4
Old pair: ('1111111', '1101001'), distance: 3
New pair: ('1111111', '1101001'), distance: 3
================================================================================
Old pair: ('1100010', '1001101'), distance: 5
New pair: ('1100010', '1001101'), distance: 5
Old pair: ('1100010', '1111101'), distance: 5
New pair: ('1100010', '1111101'), distance: 5
Old pair: ('1100010', '1111111'), distance: 4
New pair: ('1100010', '1111111'), distance: 4
Old pair: ('1100010', '1101001'), distance: 3
New pair: ('1100010', '1101001'), distance: 3
================================================================================
Old pair: ('1101001', '1001101'), distance: 2
New pair: ('1101001', '0001101'), distance: 3
Old pair: ('1101001', '1111101'), distance: 2
New pair: ('1101001', '0111101'), distance: 3
Old pair: ('1101001', '1111111'), distance: 3
New pair: ('1101001', '1111111'), distance: 3
Old pair: ('1101001', '1100010'), distance: 3
New pair: ('1101001', '1100010'), distance: 3
================================================================================
(tmp)➜  ~  
(tmp)➜  ~  python hamming.py
Old pair: ('1001101', '1111101'), distance: 2
New pair: ('1001101', '0111101'), distance: 3
Old pair: ('1001101', '1111111'), distance: 3
New pair: ('1001101', '1111111'), distance: 3
Old pair: ('1001101', '1100010'), distance: 5
New pair: ('1001101', '1100010'), distance: 5
Old pair: ('1001101', '1101001'), distance: 2
New pair: ('1001101', '0101001'), distance: 3
================================================================================
Old pair: ('1111101', '1001101'), distance: 2
New pair: ('1111101', '0001101'), distance: 3
Old pair: ('1111101', '1111111'), distance: 1
New pair: ('1111101', '0011111'), distance: 3
Old pair: ('1111101', '1100010'), distance: 5
New pair: ('1111101', '1100010'), distance: 5
Old pair: ('1111101', '1101001'), distance: 2
New pair: ('1111101', '0101001'), distance: 3
================================================================================
Old pair: ('1111111', '1001101'), distance: 3
New pair: ('1111111', '1001101'), distance: 3
Old pair: ('1111111', '1111101'), distance: 1
New pair: ('1111111', '0011101'), distance: 3
Old pair: ('1111111', '1100010'), distance: 4
New pair: ('1111111', '1100010'), distance: 4
Old pair: ('1111111', '1101001'), distance: 3
New pair: ('1111111', '1101001'), distance: 3
================================================================================
Old pair: ('1100010', '1001101'), distance: 5
New pair: ('1100010', '1001101'), distance: 5
Old pair: ('1100010', '1111101'), distance: 5
New pair: ('1100010', '1111101'), distance: 5
Old pair: ('1100010', '1111111'), distance: 4
New pair: ('1100010', '1111111'), distance: 4
Old pair: ('1100010', '1101001'), distance: 3
New pair: ('1100010', '1101001'), distance: 3
================================================================================
Old pair: ('1101001', '1001101'), distance: 2
New pair: ('1101001', '0001101'), distance: 3
Old pair: ('1101001', '1111101'), distance: 2
New pair: ('1101001', '0111101'), distance: 3
Old pair: ('1101001', '1111111'), distance: 3
New pair: ('1101001', '1111111'), distance: 3
Old pair: ('1101001', '1100010'), distance: 3
New pair: ('1101001', '1100010'), distance: 3
================================================================================

改变汉明距离

1 个答案: