Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?
GeeksforGeeks
Input: 3
Output: 5
Explanation: Given n = 3, there are a total of 5 unique BST's,
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/**
* Time complexity : The main computation of the algorithm is done at the
* statement with G[i]. So the time complexity is essentially the number
* of iterations for the statement, which is ∑(i=2 to n) i = (2+n)(n−1)/2,
* to be exact, therefore the time complexity is O(N^2).
* Space complexity : The space complexity of the above algorithm is mainly
* the storage to keep all the intermediate solutions, therefore O(N).
*/
class Solution {
public int numTrees(int n) {
int[] dp = new int[n+1];
dp[0] = 1;
dp[1] = 1;
for(int i = 2; i <= n; i++) {
for(int j = 0; j < i; j++) {
dp[i] += (dp[j] * dp[i-j-1]);
}
}
return dp[n];
}
}