两个字符串最长的公共字串问题（LCS）

两种方法动态规划和后缀树

#!/usr/bin/env python
# --*-- coding: utf8 --*--
#
#Longest common substring

def display_matrix(matrix):
    print '###############################'
    for x in matrix:
        print x
    print '###############################'

def dynamic(str1, str2):
    #dynamic programming
    m = [ [ 0 for x in str1 ] for y in str2 ]
    maxlen = 0
    mj = 0

    display_matrix(m)

    for i in range(len(str2)):
        for j in range(len(str1)):
            if str1[j] == str2[i]:
                if i == 0 or j == 0:
                    m[i][j] = 1
                else:
                    m[i][j] = m[i-1][j-1] + 1

                if m[i][j] > maxlen:
                    maxlen = m[i][j]
                    mj = j

    display_matrix(m)

    print maxlen, str1[j-maxlen:j]

dynamic('abcdefgh', 'abyyixyqcdefgoo')

def display_tree(tr, lvl):
    for k, v in tr.items():
        print '--'*lvl, k, ' : ', v['sid']
        display_tree(tr[k]['sub'], lvl + 1)

def add_str(tr, s, num):
    for begin in range(len(s)):
        tmplvl = tr
        for w in s[begin:]:
            if w in tmplvl:
                tmplvl[w]['sid'].add(num)
            else:
                tmplvl[w] = {'sid': set([num]), 'sub':{}}
            tmplvl = tmplvl[w]['sub']

def findcommon(tr):
    maxstr = ''
    maxlen = 0

    for k, v in tr.items():
        if len(v['sid']) < 2:
            continue
        else:
            tmpstr = k + findcommon(v['sub'])
            if len(tmpstr) > maxlen:
                maxlen = len(tmpstr)
                maxstr = tmpstr
    return maxstr

def suffixTree(str1, str2):
    #suffix tree
    #use dict simulate suffix tree
    tree = {}
    add_str(tree, str1, 1)
    add_str(tree, str2, 2)
    display_tree(tree, 0)

    print findcommon(tree)


suffixTree('abcdeafg', 'abopiuocdeafuo')