96. Unique Binary Search Trees

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

int numTrees(int n) {
    if (n <= 0) {
        return 0;
    }
    // 用于计数
    int counts[n + 1];
    counts[0] = 1;
    counts[1] = 1;
    
    
    int inds;
    int partition;
    int tmp_count;
    for (inds = 2; inds <= n; ++inds) {
        tmp_count = 0;
        for(partition = 1; partition <= inds; ++partition) {
            tmp_count += counts[partition - 1] * counts[inds - partition];
        }
        counts[inds] = tmp_count;
    }
    return counts[n];
}

思想：