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feat: add solutions to lc problem: No.0516. Longest Palindromic
Subsequence
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‎README.md

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- [不同路径 II](./solution/0000-0099/0063.Unique%20Paths%20II/README.md)
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- [最小路径和](./solution/0000-0099/0064.Minimum%20Path%20Sum/README.md)
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- [最长回文子串](./solution/0000-0099/0005.Longest%20Palindromic%20Substring/README.md)
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- [最长回文子序列](.solution/0500-0599/0516.Longest%20Palindromic%20Subsequence/README.md)
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- [礼物的最大价值](./lcof/面试题47.%20礼物的最大价值/README.md)
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- [最长上升子序列](./solution/0300-0399/0300.Longest%20Increasing%20Subsequence/README.md)
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- [俄罗斯套娃信封问题](./solution/0300-0399/0354.Russian%20Doll%20Envelopes/README.md)

‎README_EN.md

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@@ -187,6 +187,7 @@ Complete solutions to [LeetCode](https://leetcode.com/problemset/all/), [LCOF](h
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- [Unique Paths II](./solution/0000-0099/0063.Unique%20Paths%20II/README_EN.md)
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- [Minimum Path Sum](./solution/0000-0099/0064.Minimum%20Path%20Sum/README_EN.md)
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- [Longest Palindromic Substring](./solution/0000-0099/0005.Longest%20Palindromic%20Substring/README_EN.md)
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- [Longest Palindromic Subsequence](.solution/0500-0599/0516.Longest%20Palindromic%20Subsequence/README_EN.md)
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- [Longest Increasing Subsequence](./solution/0300-0399/0300.Longest%20Increasing%20Subsequence/README_EN.md)
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- [Russian Doll Envelopes](./solution/0300-0399/0354.Russian%20Doll%20Envelopes/README_EN.md)
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- [Longest Common Subsequence](./solution/1100-1199/1143.Longest%20Common%20Subsequence/README_EN.md)

‎solution/0500-0599/0516.Longest Palindromic Subsequence/README.md

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<li><code>s</code> 只包含小写英文字母</li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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动态规划。
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设 `dp[i][j]` 表示字符串 `s[i..j]` 中的最长回文子序列的长度。初始化 `dp[i][i] = 1`(`i∈[0, n-1]`)。
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- 对于 `s[i] == s[j]`，`dp[i][j] = dp[i + 1][j - 1] + 2`；
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- 对于 `s[i] != s[j]`，`dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])`。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def longestPalindromeSubseq(self, s: str) -> int:
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n = len(s)
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dp = [[0] * n for _ in range(n)]
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for i in range(n):
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dp[i][i] = 1
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for j in range(1, n):
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for i in range(j - 1, -1, -1):
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if s[i] == s[j]:
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dp[i][j] = dp[i + 1][j - 1] + 2
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else:
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
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return dp[0][-1]
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public int longestPalindromeSubseq(String s) {
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int n = s.length();
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int[][] dp = new int[n][n];
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s.charAt(i) == s.charAt(j)) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int longestPalindromeSubseq(string s) {
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int n = s.size();
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vector<vector<int>> dp(n, vector<int>(n, 0));
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s[i] == s[j]) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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};
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```
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### **Go**
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```go
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func longestPalindromeSubseq(s string) int {
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n := len(s)
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dp := make([][]int, n)
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for i := 0; i < n; i++ {
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dp[i] = make([]int, n)
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dp[i][i] = 1
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}
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for j := 1; j < n; j++ {
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for i := j - 1; i >= 0; i-- {
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if s[i] == s[j] {
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dp[i][j] = dp[i+1][j-1] + 2
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} else {
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dp[i][j] = max(dp[i+1][j], dp[i][j-1])
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}
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}
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}
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return dp[0][n-1]
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/0500-0599/0516.Longest Palindromic Subsequence/README_EN.md

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<li><code>s</code> consists only of lowercase English letters.</li>
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</ul>
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## Solutions
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<!-- tabs:start -->
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### **Python3**
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```python
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class Solution:
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def longestPalindromeSubseq(self, s: str) -> int:
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n = len(s)
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dp = [[0] * n for _ in range(n)]
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for i in range(n):
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dp[i][i] = 1
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for j in range(1, n):
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for i in range(j - 1, -1, -1):
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if s[i] == s[j]:
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dp[i][j] = dp[i + 1][j - 1] + 2
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else:
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
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return dp[0][-1]
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```
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### **Java**
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```java
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class Solution {
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public int longestPalindromeSubseq(String s) {
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int n = s.length();
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int[][] dp = new int[n][n];
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s.charAt(i) == s.charAt(j)) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int longestPalindromeSubseq(string s) {
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int n = s.size();
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vector<vector<int>> dp(n, vector<int>(n, 0));
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s[i] == s[j]) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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};
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```
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### **Go**
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```go
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func longestPalindromeSubseq(s string) int {
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n := len(s)
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dp := make([][]int, n)
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for i := 0; i < n; i++ {
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dp[i] = make([]int, n)
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dp[i][i] = 1
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}
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for j := 1; j < n; j++ {
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for i := j - 1; i >= 0; i-- {
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if s[i] == s[j] {
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dp[i][j] = dp[i+1][j-1] + 2
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} else {
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dp[i][j] = max(dp[i+1][j], dp[i][j-1])
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}
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}
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}
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return dp[0][n-1]
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/0500-0599/0516.Longest Palindromic Subsequence/Solution.cpp

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class Solution {
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public:
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int longestPalindromeSubseq(string s) {
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int n = s.size();
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vector<vector<int>> dp(n, vector<int>(n, 0));
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s[i] == s[j]) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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};

‎solution/0500-0599/0516.Longest Palindromic Subsequence/Solution.go

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func longestPalindromeSubseq(s string) int {
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n := len(s)
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dp := make([][]int, n)
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for i := 0; i < n; i++ {
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dp[i] = make([]int, n)
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dp[i][i] = 1
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}
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for j := 1; j < n; j++ {
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for i := j - 1; i >= 0; i-- {
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if s[i] == s[j] {
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dp[i][j] = dp[i+1][j-1] + 2
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} else {
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dp[i][j] = max(dp[i+1][j], dp[i][j-1])
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}
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}
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}
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return dp[0][n-1]
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}

‎solution/0500-0599/0516.Longest Palindromic Subsequence/Solution.java

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class Solution {
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public int longestPalindromeSubseq(String s) {
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int n = s.length();
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int[][] dp = new int[n][n];
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for (int i = 0; i < n; ++i) {
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dp[i][i] = 1;
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}
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for (int j = 1; j < n; ++j) {
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for (int i = j - 1; i >= 0; --i) {
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if (s.charAt(i) == s.charAt(j)) {
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dp[i][j] = dp[i + 1][j - 1] + 2;
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} else {
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dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
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}
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}
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}
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return dp[0][n - 1];
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}
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}

‎solution/0500-0599/0516.Longest Palindromic Subsequence/Solution.py

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class Solution:
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def longestPalindromeSubseq(self, s: str) -> int:
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n = len(s)
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dp = [[0] * n for _ in range(n)]
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for i in range(n):
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dp[i][i] = 1
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for j in range(1, n):
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for i in range(j - 1, -1, -1):
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if s[i] == s[j]:
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dp[i][j] = dp[i + 1][j - 1] + 2
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else:
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dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
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return dp[0][-1]

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