[DP] add Solution to Longest Palindromic Substring

DP/LongestPalindromicSubstring.swift

@@ -0,0 +1,49 @@
+/**
+ * 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)
+ *
+ */
+
+class LongestPalindromicSubstring {
+    func longestPalindrome(s: String) -> String {
+        guard s.characters.count > 1 else {
+            return s
+        }
+
+        var sChars = [Character](s.characters)
+        let len = sChars.count
+        var maxLen = 1
+        var maxStart = 0
+        var isPalin = Array(count: len, repeatedValue: [Bool](count: len, repeatedValue: false))
+
+        // set palindrome whose len is 1
+        for i in 0 ... len - 1 {
+            isPalin[i][i] = true
+        }
+
+        // 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
+            }
+        }
+
+        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
+                    }
+                }
+            }
+        }
+
+        return String(sChars[maxStart ... maxStart + maxLen - 1])
+    }
+}