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]; } } |
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