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
Solution
dp
Code
public class Solution {
public int numTrees_1(int n) {
int[] dp = new int[n+1];
dp[0] = 1;
for (int i = 1; i <= n; ++i)
for (int j = 0; j < i; j++)
dp[i] += dp[j] * dp[i-j-1];
return dp[n];
}
public int numTrees(int n) {
if (n < 0) return 0;
int[] dp = new int[n+1];
dp[0] = 1; dp[1] = 1;
for(int i = 2;i <= n; ++i){
dp[i] = dp[i-1] * (4 * i - 2)/(i + 1);
}
return dp[n];
}
}