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96. Unique Binary Search Trees 👍

  • Time: $O(n^2)$
  • Space: $O(n)$
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class Solution {
 public:
  int numTrees(int n) {
    // dp[i] := the number of unique BST's that store values 1..i
    vector<int> dp(n + 1);
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; ++i)
      for (int j = 0; j < i; ++j)
        dp[i] += dp[j] * dp[i - j - 1];

    return dp[n];
  }
};

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class Solution {
  public int numTrees(int n) {
    // dp[i] := the number of unique BST's that store values 1..i
    int[] dp = new int[n + 1];
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; ++i)
      for (int j = 0; j < i; ++j)
        dp[i] += dp[j] * dp[i - j - 1];

    return dp[n];
  }
}

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class Solution:
  def numTrees(self, n: int) -> int:
    # dp[i] := the number of unique BST's that store values 1..i
    dp = [1, 1] + [0] * (n - 1)

    for i in range(2, n + 1):
      for j in range(i):
        dp[i] += dp[j] * dp[i - j - 1]

    return dp[n]