The other day I was doing a programming challenge that required me to find the longest palindrome within a string. The challenge was to do it in at least O(N)2 complexity. I found this to be fairly interesting. The challenge read like so:

*Given a string S, find the longest substring in S that is the same in reverse and print it to the standard output.*

So for example, if I had the string given was: s= “abcdxyzyxabcdaaa” . Then the longest palindrome within it is “xyzyx “. We need to write a function to find this for us. The nature of the challenge just needed me to write a function for a web back-end, so the example code below does not have main, or a defined string, etc. Also, there are O(N) solutions for this problem if you seek them, but they are a little more complicated.

#include <iostream> #include <string> using namespace std; void longest_palind(const string &s) { int n = s.length(); int longestBegin = 0; int maxLen = 1; bool table[100][100] = {false}; for (int i = 0; i < n; i++) { table[i][i] = true; } for (int i = 0; i < n-1; i++) { if (s[i] == s[i+1]) { table[i][i+1] = true; longestBegin = i; maxLen = 2; } } for (int len = 3; len <= n; len++) { for (int i = 0; i < n-len+1; i++) { int j = i+len-1; if (s[i] == s[j] && table[i+1][j-1]) { table[i][j] = true; longestBegin = i; maxLen = len; } } } cout << s.substr(longestBegin, maxLen); }