LeetCode [96] Unique Binary Search Trees

 96. Unique Binary Search Trees

Medium

Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?

Example:

Input: 3
Output: 5
Explanation:
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

 

Constraints:

• 1 <= n <= 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

//C++: Recursive TLE class Solution { public: int numTrees(int n) { if(n==0||n==1) return 1; int res = 0; for(int i=1; i<=n; ++i){ res += numTrees(i-1)*numTrees(n-i); } return res; } }; class Solution { public: int numTrees(int n) { int dp[N] = {0}; dp[0] = 1; for(int i=1; i<=n; ++i){ for(int j=1; j<=i; ++j){ dp[i] += dp[j-1]*dp[i-j]; } } return dp[n]; } }; //Java class Solution { public int numTrees(int n) { int[] dp = new int[n+1]; dp[0] = 1; for(int i=1; i<=n; ++i){ for(int j=1; j<=i; ++j){ dp[i] += dp[j-1]*dp[i-j]; } } return dp[n]; } }