Longest Palindromic Substring @Leetcode

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Longest Palindromic Substring: Given a string S, find the longest palindromic substring in S.

My first thought came up is reversing the string then find the longest common substring of S and S'. While there is obvious flaw in this algorithm. 

Can take a look of solution over here. 
http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html
http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html

There is a O(n) solution over here which is very elegant and concise, while is a little bit hard to understand. Here is a good explanation in Chinese. Check it out. http://www.felix021.com/blog/read.php?2040

One problem that I want to think: When you design a algorithm for a problem, how could you prove that your algorithm is correct, complete and flawless in a systematic way? Everyone has blind point when thinking a problem. So how to avoid the blind point and think a problem completely? 

Here is the useful link of statistic information of difficulty and frequency of leetcode problems.
https://docs.google.com/spreadsheet/pub?key=0Aqt--wSNYfuxdGxQWVFsOGdVVWxQRlNUVXZTdEpOeEE&output=html