Longest common subsequence problem is a good example of dynamic programming, and also has its significance in biological applications.
For more information about LCS, please see: http://en.wikipedia.org/wiki/Longest_common_subsequence_problem
Also, here, I use a 'cached' decorator to keep core algorithm neat. You can see how great the decorator could be. :)
Also note that, this recipe is just a demonstration of LCS and the usage of a python decorator. However, the memory is not used very efficiently. If the problem is very large-scaled, it may lead to stack overflow or memory error.
So, do not use this recipe to deal with large-scaled problems. ;)
Python, 93 lines
Download
Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | """
A Longest common subsequence (LCS) problem solver.
This problem is a good example of dynamic programming, and also has its
significance in biological applications.
For more information about LCS, please see:
http://en.wikipedia.org/wiki/Longest_common_subsequence_problem
Copyright 2009 Shao-Chuan Wang <shaochuan.wang@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
__author__ = "Shao-Chuan Wang"
__email__ = "shaochuan.wang@gmail.com"
__version__ = "1.0"
__URL__ = "http://shao-chuan.appspot.com"
import functools
def cached(func):
cache = {}
def template(*args): #: template is wrapper; func is wrapped
key = (func, )+args
try:
ret = cache[key]
except KeyError:
ret = func(*args)
cache[key] = ret
else:
pass
return ret
functools.update_wrapper(template, func)
return template
@cached
def LCSLength(str1, str2):
if len(str1)==0 or len(str2)==0:
return 0
if str1[-1] == str2[-1]:
return LCSLength(str1[:-1], str2[:-1])+1
else:
return max(LCSLength(str1, str2[:-1]), LCSLength(str1[:-1], str2))
@cached
def LCS(str1, str2):
if len(str1)==0 or len(str2)==0:
return ''
if str1[-1] == str2[-1]:
return ''.join([LCS(str1[:-1], str2[:-1]), str1[-1]])
else:
candidate1 = LCS(str1[:-1], str2)
candidate2 = LCS(str1, str2[:-1])
if len(candidate1) >= len(candidate2):
return candidate1
else:
return candidate2
if __name__=='__main__':
# a simple example
lcs = LCS('abcbdab', 'bdcaba')
assert len(lcs) == LCSLength('abcbdab', 'bdcaba')
print 'Length of Longest common subsequence: %d' %(len(lcs),)
print 'Longest common subsequence: %s' % (lcs,)
# a complex example:
strA = '''abcdefgabcdefgaabcdefgabcdefgabcdesdqfgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg'''
strB = '''gdebcdehhglkjlkabvhgdebcdehhgdebcdehhgdebcdeoshhgdebcdehhgdebcdehhgdebcdehhgdebcdehh'''
lcs = LCS(strA, strB)
assert len(lcs) == LCSLength(strA, strB)
print 'Length of Longest common subsequence: %d' %(len(lcs),)
print 'Longest common subsequence: '
print lcs
|
