[LeetCode] Problem 96 - Unique Binary Search Trees

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Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?

Example

Input: 3

Output: 5

Explanation:
Given n = 3, there are a total of 5 unique BST’s:

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1         3     3      2      1
 \       /     /      / \      \
  3     2     1      1   3      2
 /     /       \                 \
2     1         2                 3

Code

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public int numTrees(int n) {
    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];
}