Skip to content

516. Longest Palindromic Subsequence 👍

Approach 1: Top-down

  • Time: $O(n^2)$
  • Space: $O(n^2)$
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
class Solution {
 public:
  int longestPalindromeSubseq(string s) {
    const int n = s.length();
    // dp[i][j] := LPS's length in s[i..j]
    dp.resize(n, vector<int>(n));
    return lps(s, 0, n - 1);
  }

 private:
  vector<vector<int>> dp;

  int lps(const string& s, int i, int j) {
    if (i > j)
      return 0;
    if (i == j)
      return 1;
    if (dp[i][j])
      return dp[i][j];

    if (s[i] == s[j])
      dp[i][j] = 2 + lps(s, i + 1, j - 1);
    else
      dp[i][j] = max(lps(s, i + 1, j), lps(s, i, j - 1));

    return dp[i][j];
  }
};
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
class Solution {
  public int longestPalindromeSubseq(String s) {
    final int n = s.length();
    // dp[i][j] := LPS's length in s[i..j]
    dp = new int[n][n];
    return lps(s, 0, n - 1);
  }

  private int[][] dp;

  private int lps(final String s, int i, int j) {
    if (i > j)
      return 0;
    if (i == j)
      return 1;
    if (dp[i][j] > 0)
      return dp[i][j];

    if (s.charAt(i) == s.charAt(j))
      dp[i][j] = 2 + lps(s, i + 1, j - 1);
    else
      dp[i][j] = Math.max(lps(s, i + 1, j), lps(s, i, j - 1));

    return dp[i][j];
  }
}

Approach 2: Bottom-up

  • Time: $O(n^2)$
  • Space: $O(n^2)$
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
class Solution {
 public:
  int longestPalindromeSubseq(string s) {
    const int n = s.length();
    // dp[i][j] := LPS's length in s[i..j]
    vector<vector<int>> dp(n, vector<int>(n));

    for (int i = 0; i < n; ++i)
      dp[i][i] = 1;

    for (int d = 1; d < n; ++d)
      for (int i = 0; i + d < n; ++i) {
        const int j = i + d;
        if (s[i] == s[j])
          dp[i][j] = 2 + dp[i + 1][j - 1];
        else
          dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
      }

    return dp[0][n - 1];
  }
};
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
class Solution {
  public int longestPalindromeSubseq(String s) {
    final int n = s.length();
    // dp[i][j] := LPS's length in s[i..j]
    int[][] dp = new int[n][n];

    for (int i = 0; i < n; ++i)
      dp[i][i] = 1;

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

    return dp[0][n - 1];
  }
}
Back to top