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
This is a simple problem. Each number between 1 and n can be the root node.
1-d dynamical programming can be used to solve this problem.
public class Solution { public int numTrees(int n) { int num = 0; if(n > 0){ int[] trees = new int[n + 1]; trees[0] = 1; trees[1] = 1; if( n > 1){ for(int i = 2; i < n + 1; ++i){ trees[i] = 0; for(int j = 0; j < i; ++j){ trees[i] += trees[j] * trees[i - 1 - j]; } } } num = trees[n]; } return num; } }