leetcode 459. Repeated Substring Pattern

Given a non-empty string check if it can be constructed by taking a substring of it and appending multiple copies of the substring together. You may assume the given string consists of lowercase English letters only and its length will not exceed 10000.

Example 1:

Input: "abab"

Output: True

Explanation: It's the substring "ab" twice.

Example 2:

Input: "aba"

Output: False

Example 3:

Input: "abcabcabcabc"

Output: True

Explanation: It's the substring "abc" four times. (And the substring "abcabc" twice.)

class Solution(object):
    def repeatedSubstringPattern(self, s):
        """
        :type s: str
        :rtype: bool
        """
        #return True if re.match(r"(w+)*", s) else False
        def is_repeat(s1, s2):            
            return s1 == s2*(len(s1)/len(s2))            
        
        l = len(s)
        for i in xrange(1, l/2+1):
            if l % i == 0:
                if is_repeat(s, s[:i]):
                    return True
        return False

 上面是暴力解法，下面是技巧解法：

class Solution(object):
    def repeatedSubstringPattern(self, s):
        """
        :type s: str
        :rtype: bool
        """
        #return True if re.match(r"(w+)*", s) else False
        if not s:
            return False            
        ss = (s + s)[1:-1]
        return ss.find(s) != -1

 解释：

Let's say T = S + S.
"S is Repeated => From T[1:-1] we can find S" is obvious.

If from T[1:-1] we found S at index p-1, which is index p in T and S.
let s1 = S[:p], S can be represented as s1s2...sn, where si stands for substring rather than character.
then we know T[p:len(S) + p] = s2s3...sn-1sns1 = S = s1s2...sn-2sn-1sn.
So s1 = s2, s2 = s3, ..., sn-1 = sn, sn = s1,Which means S is Repeated.

其实你自己画图下就知道了！！！假设:

s=s1s2s3s4

T=s1s2s3s4s1s2s3s4

去掉收尾，则有：T'=s2s3s4s1s2s3，如果在这里面找到了s1s2s3s4，假设找到的为0位置则：

s2s3s4s1=s1s2s3s4，说明：s2==s1,s3==s2,s4==s3,s1==s4，不就是单个字符重复了嘛！同样，假设出现的位置为1，也可以类似推导！