516.Longest Palindromic Subsequence
===

###### tags: `Medium`,`String`,`DP`

[516. Longest Palindromic Subsequence](https://leetcode.com/problems/longest-palindromic-subsequence/)

### 題目描述

Given a string `s`, find *the longest palindromic **subsequence**'s length in* `s`.

A **subsequence** is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

### 範例

**Example 1:**

Input: s = "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb".

**Example 2:**

Input: s = "cbbd"
Output: 2
Explanation: One possible longest palindromic subsequence is "bb".

**Constraints**:

* 1 <= `s.length` <= 1000
* `s` consists only of lowercase English letters.

### 解答

#### Javascript

function longestPalindromeSubseq(s) {
  const n = s.length;
  const dp = new Array(n).fill(0).map(() => new Array(n).fill(0));

  for (let i = n - 1; i >= 0; i--) {
    dp[i][i] = 1;
    for (let j = i + 1; j < n; j++) {
      if (s[i] === s[j]) {
        dp[i][j] = dp[i + 1][j - 1] + 2;
      } else {
        dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
      }
    }
  }

  return dp[0][n - 1];
}

> [name=Marsgoat][time=Apr 15, 2023]

### Reference

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