Added Longest Plaindromic subsequence

Dynamic-Programming/LongestPalindromicSubsequence.js

@@ -0,0 +1,39 @@
+/*
+  LeetCode -> https://leetcode.com/problems/longest-palindromic-subsequence/
+
+  Given a string s, find the longest palindromic subsequence's length in s.
+  You may assume that the maximum length of s is 1000.
+
+*/
+
+const longestPalindromeSubsequence = function (s) {
+  const n = s.length
+
+  const dp = new Array(n).fill(0).map(item => new Array(n).fill(0).map(item => 0))
+
+  // fill predefined for single character
+  for (let i = 0; i < n; i++) {
+    dp[i][i] = 1
+  }
+
+  for (let i = 1; i < n; i++) {
+    for (let j = 0; j < n - i; j++) {
+      const col = j + i
+      if (s[j] == s[col]) {
+        dp[j][col] = 2 + dp[j + 1][col - 1]
+      } else {
+        dp[j][col] = Math.max(dp[j][col - 1], dp[j + 1][col])
+      }
+    }
+  }
+
+  return dp[0][n - 1]
+}
+
+const main = () => {
+  console.log(longestPalindromeSubsequence('bbbab')) // 4
+  console.log(longestPalindromeSubsequence('axbya')) // 3
+  console.log(longestPalindromeSubsequence('racexyzcxar')) // 7
+}
+
+main()