Valid BST Permutations

Problem Preview

"### Problem A binary tree is a data structure characterized by the following properties: - It can be an empty tree where root = null. - It can consist of a root node that contains a value and two sub-trees labeled "left" and "right". - Each sub-tree also follows the definition of a binary tree. A binary tree is a binary search tree (BST) if all the non-empty nodes follow these two rules: - If a node has a left sub-tree, then all the values in its left sub-tree are smaller than its value. - If a node has a right sub-tree, then all the values in its right sub-tree are greater than its value. Given an integer, determine the number of valid BSTs that can be created by nodes numbered from 1 to that integer. Please see the samples below for diagrams based on 1, 2 or 3 nodes. ### Function Description Complete the function numBST in the editor below. numBST has the following parameter(s): int nodeValues[n]: the number of node values to analyze Returns: int[n]:the number of different binary search trees that can be created for each test case modulo 1000000007(10^9 + 7). ### Constraints - 1 ≤ n ≤ 1000 - 1 ≤ nodeValues[i] ≤ 1000 ### Input Format for Custom Testing ### Sample Case 0 Sample Input STDIN Function 5 nodeValues[] size n = 5 nodeValues = [1, 2, 3, 4, 100] ### Output The function returns an array of integers, each representing the number of unique BSTs for the corresponding input value modulo 1000000007."