題目：

Given a string S, find the longest palindromic substring in S. You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.

題解：

第一種方法就是挨個檢查，維護全局最長，時間復雜度為O(n3)，會TLE。

代碼如下：

1?public?String?longestPalindrome(String?s)?{

2

3?????int?maxPalinLength?=?0;

4?????String?longestPalindrome?=?null;

5?????int?length?=?s.length();

6

7?????//check?all?possible?sub?strings8?????for?(int?i?=?0;?i?

9?????????for?(int?j?=?i?+?1;?j?

10?????????????int?len?=?j?-?i;

11?????????????String?curr?=?s.substring(i,?j?+?1);

12?????????????if?(isPalindrome(curr))?{

13?????????????????if?(len?>?maxPalinLength)?{

14?????????????????????longestPalindrome?=?curr;

15?????????????????????maxPalinLength?=?len;

16?????????????????}

17?????????????}

18?????????}

19?????}

20

21?????return?longestPalindrome;

22?}

23

24?public?boolean?isPalindrome(String?s)?{

25

26?????for?(int?i?=?0;?i?

27?????????if?(s.charAt(i)?!=?s.charAt(s.length()?-?1?-?i))?{

28?????????????return?false;

29?????????}

30?????}

31

32?????return?true;

33?}

第二種方法“是對于每個子串的中心(可以是一個字符，或者是兩個字符的間隙，比如串abc,中心可以是a,b,c,或者是ab的間隙，bc的間隙，例如aba是回文，abba也是回文，這兩種情況要分情況考慮)往兩邊同時進

行掃描，直到不是回文串為止。假設字符串的長度為n,那么中心的個數為2*n-1(字符作為中心有n個，間隙有n-1個)。對于每個中心往兩邊掃描的復雜

度為O(n),所以時間復雜度為O((2*n-1)*n)=O(n^2),空間復雜度為O(1)?！币訡ode ganker(http://codeganker.blogspot.com/2014/02/longest-palindromic-substring-leetcode.html)

代碼如下：

1?????public?String?longestPalindrome(String?s)?{

2?????????if?(s.isEmpty()||s==null||s.length()?==?1)

3?????????????return?s;

4

5?????????String?longest?=?s.substring(0,?1);

6?????????for?(int?i?=?0;?i?

7?????????????//get?longest?palindrome?with?center?of?i8?????????????String?tmp?=?helper(s,?i,?i);

9

10?????????????if?(tmp.length()?>?longest.length())

11?????????????????longest?=?tmp;

12

13?????????????//get?longest?palindrome?with?center?of?i,?i+114?????????????tmp?=?helper(s,?i,?i?+?1);

15?????????????if?(tmp.length()?>?longest.length())

16?????????????????longest?=?tmp;

17?????????}

18

19?????????return?longest;

20?????}

21

22?????//Given?a?center,?either?one?letter?or?two?letter,23?//Find?longest?palindrome24?????public?String?helper(String?s,?int?begin,?int?end)?{

25?????????while?(begin?>=?0?&&?end?<=?s.length()?-?1?&&?s.charAt(begin)?==?s.charAt(end))?{

26?????????????begin--;

27?????????????end++;

28?????????}

29?????????return?s.substring(begin?+?1,?end);

30?????}

Reference:

http://www.programcreek.com/2013/12/leetcode-solution-of-longest-palindromic-substring-java/

http://codeganker.blogspot.com/2014/02/longest-palindromic-substring-leetcode.html

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