学步园

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.

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

class Solution {
public:
    int numTrees(int n) {
        if(n==1)
            return 1;
        else
            return numTrees(n-1)*(4*n-2)/(n+1);
    }
};

卡特兰数:

f(n) = f(n-1)*(4n-2)/(n + 1)

f(0) = 1;

f(1) = 1

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670,
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