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

For example,
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

求方案的个数，一般是用动归做

  • State: dp[i] 指有i个节点的BST有多少种组成方案
  • Function: dp[i] = dp[0] dp[i - 1] + dp[1] dp[i - 2] + … + dp[i - 1] * dp[0]
  • Init: dp[0] = 1
  • Answer: dp[n]
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public int numTrees(int n) {
    if (n < 0)
        return -1;
    int[] dp = new int[n + 1];
    dp[0] = 1;
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j < i; j++) {
            dp[i] = dp[i] + dp[j] * dp[i - j - 1];
        }
    }
    return dp[n];
}