[LeetCode]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

思路：采用动态规划，n = 0,1一种结果
n = 2 时，两种情况，根节点占一个，左1右0，左0右1；
n = 3时， 三种情况，根节点占一个，左2右0，左1右1，左0右2；
……

public int numTrees(int n) {
int[] dp = new int[n+1];
dp[0] = 1;
for (int i=1; i<=n; i++) {
//int sum = 0;
for (int j=1;j<=i;j++) {
dp[i] += dp[j-1] * dp[i-j];
}
//dp[i] = sum;
}
return dp
;
}