Question

link

Given preorder, construct the BST.

Solution

We can get Inorder traversal by sorting the given Preorder traversal. So we have the required two traversals to construct the Binary Search Tree.

A very similar approach would be always spliting the array by the head value. Time complexity is O(nlgn) for a balanced BST, or O(n²) for a screwed tree.

Howver, there’s O(n) solutions.

The trick is to set a range {min .. max} for every node. Initialize the range as {INT_MIN .. INT_MAX}. The first node will definitely be in range, so create root node. To construct the left subtree, set the range as {INT_MIN …root->data}. If a values is in the range {INT_MIN .. root->data}, the values is part part of left subtree. To construct the right subtree, set the range as {root->data..max .. INT_MAX}.

The key is the we need a public variable as a pointer (to traverse thru the array).

There’s another O(n) solution using stack. I wont' cover for now.

Code

written by me

It’s not an easy question, to be frank.

int p;

public TreeNode solution(int[] preorder) {
    p = 0;
    return helper(preorder, Integer.MIN_VALUE, Integer.MAX_VALUE);
}

private TreeNode helper(int[] A, int min, int max) {
    int len = A.length;
    if (p >= len) {
        return null;
    } else if (A[p] < min || A[p] > max) {
        return null;
    }
    TreeNode root = new TreeNode(A[p]);
    p++;
    root.left = helper(A, min, root.val);
    root.right = helper(A, root.val, max);
    return root;
}