+ problem 516

Author: fruit-in

Problemset/0516-Longest Palindromic Subsequence/README.md

@@ -0,0 +1,50 @@
+# 516. Longest Palindromic Subsequence
+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.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> s = "bbbab"
+<strong>Output:</strong> 4
+<strong>Explanation:</strong> One possible longest palindromic subsequence is "bbbb".
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> s = "cbbd"
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> One possible longest palindromic subsequence is "bb".
+</pre>
+
+#### Constraints:
+* `1 <= s.length <= 1000`
+* `s` consists only of lowercase English letters.
+
+## Solutions (Rust)
+
+### 1. Solution
+```Rust
+impl Solution {
+    pub fn longest_palindrome_subseq(s: String) -> i32 {
+        let s = s.as_bytes();
+        let mut dp = vec![vec![0; s.len()]; s.len()];
+
+        for i in 0..s.len() {
+            dp[i][i] = 1;
+        }
+
+        for size in 2..=s.len() {
+            for i in 0..s.len() - size + 1 {
+                dp[i][i + size - 1] =
+                    dp[i + 1][i + size - 2] + (s[i] == s[i + size - 1]) as i32 * 2;
+                dp[i][i + size - 1] = dp[i][i + size - 1]
+                    .max(dp[i][i + size - 2])
+                    .max(dp[i + 1][i + size - 1]);
+            }
+        }
+
+        dp[0][s.len() - 1]
+    }
+}
+```

Problemset/0516-Longest Palindromic Subsequence/README_CN.md

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+# 516. 最长回文子序列
+给你一个字符串 `s` ，找出其中最长的回文子序列，并返回该序列的长度。
+
+子序列定义为：不改变剩余字符顺序的情况下，删除某些字符或者不删除任何字符形成的一个序列。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> s = "bbbab"
+<strong>输出:</strong> 4
+<strong>解释:</strong> 一个可能的最长回文子序列为 "bbbb" 。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> s = "cbbd"
+<strong>输出:</strong> 2
+<strong>解释:</strong> 一个可能的最长回文子序列为 "bb" 。
+</pre>
+
+#### 提示:
+* `1 <= s.length <= 1000`
+* `s` 仅由小写英文字母组成
+
+## 题解 (Rust)
+
+### 1. 题解
+```Rust
+impl Solution {
+    pub fn longest_palindrome_subseq(s: String) -> i32 {
+        let s = s.as_bytes();
+        let mut dp = vec![vec![0; s.len()]; s.len()];
+
+        for i in 0..s.len() {
+            dp[i][i] = 1;
+        }
+
+        for size in 2..=s.len() {
+            for i in 0..s.len() - size + 1 {
+                dp[i][i + size - 1] =
+                    dp[i + 1][i + size - 2] + (s[i] == s[i + size - 1]) as i32 * 2;
+                dp[i][i + size - 1] = dp[i][i + size - 1]
+                    .max(dp[i][i + size - 2])
+                    .max(dp[i + 1][i + size - 1]);
+            }
+        }
+
+        dp[0][s.len() - 1]
+    }
+}
+```

Problemset/0516-Longest Palindromic Subsequence/Solution.rs

@@ -0,0 +1,22 @@
+impl Solution {
+    pub fn longest_palindrome_subseq(s: String) -> i32 {
+        let s = s.as_bytes();
+        let mut dp = vec![vec![0; s.len()]; s.len()];
+
+        for i in 0..s.len() {
+            dp[i][i] = 1;
+        }
+
+        for size in 2..=s.len() {
+            for i in 0..s.len() - size + 1 {
+                dp[i][i + size - 1] =
+                    dp[i + 1][i + size - 2] + (s[i] == s[i + size - 1]) as i32 * 2;
+                dp[i][i + size - 1] = dp[i][i + size - 1]
+                    .max(dp[i][i + size - 2])
+                    .max(dp[i + 1][i + size - 1]);
+            }
+        }
+
+        dp[0][s.len() - 1]
+    }
+}

README.md

@@ -349,6 +349,7 @@
 [513][513l]  |[Find Bottom Left Tree Value][513]                                                    |![py]
 [514][514l]  |[Freedom Trail][514]                                                                  |![rs]
 [515][515l]  |[Find Largest Value in Each Tree Row][515]                                            |![py]
+[516][516l]  |[Longest Palindromic Subsequence][516]                                                |![rs]
 [518][518l]  |[Coin Change 2][518]                                                                  |![rs]
 [519][519l]  |[Random Flip Matrix][519]                                                             |![py]
 [520][520l]  |[Detect Capital][520]                                                                 |![rs]
@@ -1935,6 +1936,7 @@
 [513]:Problemset/0513-Find%20Bottom%20Left%20Tree%20Value/README.md#513-find-bottom-left-tree-value
 [514]:Problemset/0514-Freedom%20Trail/README.md#514-freedom-trail
 [515]:Problemset/0515-Find%20Largest%20Value%20in%20Each%20Tree%20Row/README.md#515-find-largest-value-in-each-tree-row
+[516]:Problemset/0516-Longest%20Palindromic%20Subsequence/README.md#516-longest-palindromic-subsequence
 [518]:Problemset/0518-Coin%20Change%202/README.md#518-coin-change-2
 [519]:Problemset/0519-Random%20Flip%20Matrix/README.md#519-random-flip-matrix
 [520]:Problemset/0520-Detect%20Capital/README.md#520-detect-capital
@@ -3518,6 +3520,7 @@
 [513l]:https://leetcode.com/problems/find-bottom-left-tree-value/
 [514l]:https://leetcode.com/problems/freedom-trail/
 [515l]:https://leetcode.com/problems/find-largest-value-in-each-tree-row/
+[516l]:https://leetcode.com/problems/longest-palindromic-subsequence/
 [518l]:https://leetcode.com/problems/coin-change-2/
 [519l]:https://leetcode.com/problems/random-flip-matrix/
 [520l]:https://leetcode.com/problems/detect-capital/

README_CN.md

@@ -349,6 +349,7 @@
 [513][513l]  |[找树左下角的值][513]                                     |![py]
 [514][514l]  |[自由之路][514]                                           |![rs]
 [515][515l]  |[在每个树行中找最大值][515]                               |![py]
+[516][516l]  |[最长回文子序列][516]                                     |![rs]
 [518][518l]  |[零钱兑换 II][518]                                        |![rs]
 [519][519l]  |[随机翻转矩阵][519]                                       |![py]
 [520][520l]  |[检测大写字母][520]                                       |![rs]
@@ -1935,6 +1936,7 @@
 [513]:Problemset/0513-Find%20Bottom%20Left%20Tree%20Value/README_CN.md#513-找树左下角的值
 [514]:Problemset/0514-Freedom%20Trail/README_CN.md#514-自由之路
 [515]:Problemset/0515-Find%20Largest%20Value%20in%20Each%20Tree%20Row/README_CN.md#515-在每个树行中找最大值
+[516]:Problemset/0516-Longest%20Palindromic%20Subsequence/README_CN.md#516-最长回文子序列
 [518]:Problemset/0518-Coin%20Change%202/README_CN.md#518-零钱兑换-ii
 [519]:Problemset/0519-Random%20Flip%20Matrix/README_CN.md#519-随机翻转矩阵
 [520]:Problemset/0520-Detect%20Capital/README_CN.md#520-检测大写字母
@@ -3518,6 +3520,7 @@
 [513l]:https://leetcode.cn/problems/find-bottom-left-tree-value/
 [514l]:https://leetcode.cn/problems/freedom-trail/
 [515l]:https://leetcode.cn/problems/find-largest-value-in-each-tree-row/
+[516l]:https://leetcode.cn/problems/longest-palindromic-subsequence/
 [518l]:https://leetcode.cn/problems/coin-change-2/
 [519l]:https://leetcode.cn/problems/random-flip-matrix/
 [520l]:https://leetcode.cn/problems/detect-capital/