最长连续回文子串

来源：互联网发布：淘宝游戏包编辑：程序博客网时间：2024/06/09 14:51

题目：

给出一个字符串S，找到一个最长的连续回文串。

注意可有2中形态：aba（奇数型）或 abba（偶数型）

解法一：逐个遍历法：

<?php$str = "ababa";$re = longestPalindrome($str);function preProcess($str) {$n = strlen($str);$ret = "";for($i = 0; $i < $n; $i++) {$ret .= "#".substr($str,$i,1); }$ret .= "#";return $ret;}function longestPalindrome($str) {$s = preProcess($str); $n = strlen($s);$p = array();$maxLen = 0;$center = 0;for($i = 1; $i < $n-1; $i++) {$p[$i] = 0;$j = 1;while($i-$j >= 0 && $i+$j <= $n-1  &&  $s[$i-$j] == $s[$i+$j]) {$p[$i]++;$j++;}if($p[$i] > $maxLen) {$maxLen = $p[$i];$center = $i;}echo "i:$i p[$i]:$p[$i] center:$center maxLen:$maxLen<br>";}echo substr($str,($center)/2-$maxLen/2,$maxLen);}

解法二：Manacher’s Algorithm

参考：http://blog.csdn.net/hopeztm/article/details/7932245

参考：http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html

<?php$str = "aaaa";$re = longestPalindrome($str);function preProcess($str) {$n = strlen($str);$ret = "";for($i = 0; $i < $n; $i++) {$ret .= "#".substr($str,$i,1); }$ret .= "#";return $ret;}function longestPalindrome($str) {$s = preProcess($str); $n = strlen($s);$p = array();$maxLen = 0;$center = 0;$right = 0;for($i = 1; $i < $n-1; $i++) {$i_mirror = 2*$center - $i;$p[$i] = $i<$right ? min($p[$i_mirror],$right-$i) : 0;while($i-1-$p[$i] >= 0 && $i+1+$p[$i] <= $n-1 && $s[$i+1+$p[$i]] == $s[$i-1-$p[$i]]) {echo "$i";echo "<br>";$p[$i]++;}if($right-$i < $p[$i]){$center = $i;$right = $i + $p[$i];}echo "i:$i  right:$right p[$i]:$p[$i] center:$center <br>";if($p[$i] > $maxLen) {$maxLen = $p[$i];$centerIndex = $i;} }echo substr($str,($centerIndex-$maxLen)/2,$maxLen);}