Merge pull request #1379 from xiaofei-2020/dp53

添加（0516.最长回文子序列.md）：增加typescript版本

problems/0516.最长回文子序列.md

@@ -235,6 +235,35 @@ const longestPalindromeSubseq = (s) => {
 };
 ```
 
+TypeScript：
+
+```typescript
+function longestPalindromeSubseq(s: string): number {
+    /**
+        dp[i][j]：[i,j]区间内，最长回文子序列的长度 
+     */
+    const length: number = s.length;
+    const dp: number[][] = new Array(length).fill(0)
+        .map(_ => new Array(length).fill(0));
+    for (let i = 0; i < length; i++) {
+        dp[i][i] = 1;
+    }
+    // 自下而上，自左往右遍历
+    for (let i = length - 1; i >= 0; i--) {
+        for (let j = i + 1; j < length; j++) {
+            if (s[i] === s[j]) {
+                dp[i][j] = dp[i + 1][j - 1] + 2;
+            } else {
+                dp[i][j] = Math.max(dp[i][j - 1], dp[i + 1][j]);
+            }
+        }
+    }
+    return dp[0][length - 1];
+};
+```
+
+
+
 
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