Longest Palindromic Substring

Author: shangchun

longestPalindromicSubstring.js

@@ -0,0 +1,78 @@
+/*jshint node:true, white:true*/
+var assert = require('assert');
+
+/**
+ * 最长回文，线性复杂度
+ * @link http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html
+ * @method longestPalindrome
+ * @param {String} s
+ * @return {String}
+ */
+function longestPalindrome(s) {
+    var T = preProcess(s),
+        len = T.length,
+        P = [],
+        C = 0,
+        R = 0,
+        i,
+        iMirror,
+        maxLen = 0,
+        centerIndex = 0;
+
+    for (i = 1; i < len - 1; ++i) {
+        iMirror = 2 * C - i; // equals to i' = C - (i-C)
+
+        P[i] = (R > i) ? Math.min(R - i, P[iMirror]) : 0;
+        
+        // Attempt to expand palindrome centered at i
+        while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) {
+            P[i]++;
+        }
+    
+        // If palindrome centered at i expand past R,
+        // adjust center based on expanded palindrome.
+        if (i + P[i] > R) {
+            C = i;
+            R = i + P[i];
+        }
+    }
+ 
+    // Find the maximum element in P.
+    for (i = 1; i < len - 1; ++i) {
+        if (P[i] > maxLen) {
+            maxLen = P[i];
+            centerIndex = i;
+        }
+    }
+    
+    return s.substr((centerIndex - 1 - maxLen) / 2, maxLen);
+}
+
+/**
+ * Transform S into T.
+ * For example, S = "abba", T = "^#a#b#b#a#$".
+ * ^ and $ signs are sentinels appended to each end to avoid bounds checking
+ * @method preProcess
+ * @param {String} s
+ * @return {String}
+ */
+function preProcess(s) {
+    var len = s.length,
+        i,
+        ret;
+    if (len === 0) return "^$";
+
+    ret = "^";
+    for (i = 0; i < len; ++i) {
+        ret += "#" + s.substr(i, 1);
+    }
+    ret += "#$";
+    return ret;
+}
+ 
+assert.equal(longestPalindrome(''), '', 'empty');
+assert.equal(longestPalindrome('abcd'), 'a', 'trivial solution');
+assert.equal(longestPalindrome('aba'), 'aba', 'full palindromic');
+assert.equal(longestPalindrome('abac'), 'aba', 'part palindromic');
+assert.equal(longestPalindrome('caba'), 'aba', 'part palindromic');
+assert.equal(longestPalindrome('babcbabcbaccba'), 'abcbabcba', 'part palindromic');