Unique Binary Search Trees
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
class Solution {
// when i=k is at root position
// trees possible = nBST(k-1)*nBST(n-k)
public int numTrees(int n) {
if (n == 0)
return 1;
int dp[] = new int[n + 1];
dp[0] = 1;
dp[1] = 1;
for (int i = 2; 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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