ConvertSortedListToBST.java

/**
 * Given a singly linked list where elements are sorted in ascending order,
 * convert it to a height balanced BST.
 * 
 * Tags: DFS, Linked list
 */
class ConvertSortedListToBST {
    public static void main(String[] args) {
        
    }
    
    private ListNode cur;
    
    public static TreeNode sortedListToBST(ListNode head) {
        if (head == null) return null;
        cur = head;
        return buildTree(lengthOfList(head));
    }
    
    public static int lengthOfList(ListNode node) {
        int length = 0;
        while (node != null) {
            node = node.next;
            length++;
        }
        return length;
    }
    
    /**
     * Bottom up approach, O(n) (Instead of top-down, O(nlogn)) 
     * 
     * STEP 1: Take left n/2 nodes and recursively construct the left sub tree.
     * 
     * STEP 2: After left sub tree is constructed, we allocate memory for root
     * and link the left sub tree with root.
     * 
     * STEP 3: Finally, we recursively construct the right sub tree and link it
     * with root.
     */
    public static TreeNode buildTree(int n) {
        if (n == 0) return null;
        TreeNode node = new TreeNode(0);
        node.left = buildTree(n / 2);
        node.val = cur.val;
        cur = cur.next;
        node.right = buildTree(n - n / 2 - 1); // why n - n/2 - 1? The # of nodes in right subtreeis total nodes - nodes in left subtree - root
        return node;
    }
}