算法--最长公共子序列（LongestCommon Subsequence, LCS)

定义：

两个字符串共有的最长的子序列（可不连续），最长公共字符串（Longest CommonSubstring）是两个字符串共有的最长的连续字符串。

方法：穷举法，动态规划

动态规划法的简介：

《后补》

代码思路：

《后补》

Python 代码：

# -*- coding: utf-8 -*-
#!／usr/bin/env python
from random import randint

#generate a unsorted list
origin = []
LETTERS="abcdefghijklmnopqrstuvwxyz"
def randomList():
    strs = ""
    end = randint(5,10)
    for i in xrange(0,end,1):
        strs += LETTERS[randint(0,25)]
    return strs

def lcs(getRandomStr):
    stra = getRandomStr()
    strb = getRandomStr()
    la = len(stra)
    lb = len(strb)
    c = [[0]*(lb+1) for i in range(la+1)]
    print stra
    print strb
    for i in range(la-1,-1,-1):
        for j in range(lb-1,-1,-1):
            if stra[i] == strb[j]:
                c[i][j] = c[i+1][j+1] + 1
            else:
                c[i][j] = max({c[i+1][j],c[i][j+1]})
    #print the result
    i,j = 0,0
    ret = ''
    while i < la and j < lb:
        # print i,j
        if stra[i] == strb[j]:
            ret += stra[i]
            i += 1
            j += 1
        elif c[i+1][j] >= c[i][j+1] :
            i += 1
        else:
            j += 1
    print ret
if __name__ == '__main__':
    lcs(randomList)