Unique Binary Search Trees 解答

Question

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

Solution

Key to the problem here is to separate this problem into two smaller problems, unique BST's number of right child tree and left child tree.

The pseudocode is like:

for (int i = 1; i <= n; i++) {

　　result = result + nums[1 ~ i - 1] + nums[i + 1 ~ n]

}

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