1 """ 2 Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n? 3 Example: 4 Input: 3 5 Output: 5 6 Explanation: 7 Given n = 3, there are a total of 5 unique BST's: 8 9 1 3 3 2 1 10 / / / 11 3 2 1 1 3 2 12 / / 13 2 1 2 3 14 """ 15 """ 16 数学分析，让每个值作为根结点，再讨论 17 左右子树结点的数量，能得到 18 res[1]=1 19 res[2]=res[1]*res[0]+res[0]*res[1] 20 res[3]=(res[0]*res[2])+(res[1]*res[1])+(res[2]*res[0]) 21 令res[0]=1保证树的一边为空存在 22 """ 23 class Solution: 24 def numTrees(self, n): 25 res = [0]*(n+1) 26 res[0], res[1] = 1, 1 27 for i in range(2, n+1): 28 for j in range(i): 29 res[i] += res[j]*res[i-j-1] 30 return res[n]