[DP] Refactor the solution to Longest Palindromic Substring

DP/LongestPalindromicSubstring.swift

@@ -1,8 +1,7 @@
 /**
  * Question Link: https://leetcode.com/problems/longest-palindromic-substring/
- * Primary idea: 2D Dynamic Programming, update boolean array based on
- *               current two characters' equity and the previous boolean subarray
- * Time Complexity: O(n^2), Space Complexity: O(n^2)
+ * Primary idea: Find the longest palindrome string from every index at the center.
+ * Time Complexity: O(n^2), Space Complexity: O(1)
  *
  */
 
@@ -12,38 +11,28 @@ class LongestPalindromicSubstring {
             return s
         }
 
-        var sChars = Array(s)
-        let len = sChars.count
-        var maxLen = 1
-        var maxStart = 0
-        var isPalin = Array(repeating: Array(repeating: false, count : len), count : len)
+        let sChars = Array(s)
+        var maxLen = 0, start = 0
 
-        // set palindrome whose len is 1
-        for i in 0...len - 1 {
-            isPalin[i][i] = true
+        for i in 0..<sChars.count {
+            searchPalindrome(sChars, i, i, &start, &maxLen)
+            searchPalindrome(sChars, i, i + 1, &start, &maxLen)
         }
 
-        // set palindrome whose len is 2
-        for i in 0...len - 2 {
-            if sChars[i] == sChars[i + 1] {
-                isPalin[i][i + 1] = true
-                maxLen = 2
-                maxStart = i
-            }
-        }
+        return String(sChars[start..<start + maxLen])
+    }
+
+    private func searchPalindrome(_ chars: [Character], _ l: Int, _ r: Int, _ start: inout Int, _ maxLen: inout Int) {
+        var l = l, r = r
 
-        if len >= 3 {
-            for length in 3...len {
-                for i in 0...len - length {
-                    if sChars[i] == sChars[i + length - 1] && isPalin[i + 1][i + length - 2] {
-                        isPalin[i][i + length - 1] = true
-                        maxLen = length
-                        maxStart = i
-                    }
-                }
-            }
+        while l >= 0 && r < chars.count && chars[l] == chars[r] {
+            l -= 1
+            r += 1
         }
 
-        return String(sChars[maxStart...maxStart + maxLen - 1])
+        if maxLen < r - l - 1 {
+            start = l + 1
+            maxLen = r - l - 1
+        }
     }
 }