Constructing Binary Search Tree from Preorder Traversal

Day - 103 Construct Binary Search Tree from Preorder Traversal The problem - Given an array of integers preorder, which represents the preorder traversal of a BST (i.e., binary search tree), construct the tree and return its root. It is guaranteed that there is always possible to find a binary search tree with the given requirements for the given test cases. Brute Force - Sort the preorder array to get inorder traversal, then use both preorder and inorder arrays to reconstruct the BST (like standard tree construction). This gives O(n log n) time due to sorting, which is inefficient when BST properties can guide direct construction. Approach Used - •) If preorder.length == 0, return null (empty tree). •) Create root with first element, root = new TreeNode(preorder[0]). •) For i = 1 to preorder.length - 1, insert each element, insert(root, preorder[i]). •) Return root. Helper Function - insert(TreeNode root, int val) •) If val < root.val, insert in left subtree, - If root.left == null, create node, root.left = new TreeNode(val). - Else, recurse left, insert(root.left, val). •) Else (when val > root.val), insert in right subtree, - If root.right == null, create node, root.right = new TreeNode(val) - Else, recurse right, insert(root.right, val). Complexity - Time - O(n x h), where h = height of tree, n is number of nodes. Space - O(h), recursion stack depth. Note - Preorder traversal's first element is always the root. By leveraging BST insertion rules (smaller values go left, larger go right), we can sequentially insert each element from the preorder array. Each insertion automatically finds the correct position, building the BST without needing inorder traversal or sorting. #DSA #Java #SoftwareEngineering #InterviewPrep #LearnToCode #CodeDaily #ProblemSolving

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