426. Convert Binary Search Tree to Sorted Doubly Linked List

Tags: ‘Linked List’, ‘Divide and Conquer’, ‘Tree’

Convert a BST to a sorted circular doubly-linked list in-place. Think of the left and right pointers as synonymous to the previous and next pointers in a doubly-linked list.

Let's take the following BST as an example, it may help you understand the problem better:

We want to transform this BST into a circular doubly linked list. Each node in a doubly linked list has a predecessor and successor. For a circular doubly linked list, the predecessor of the first element is the last element, and the successor of the last element is the first element.

The figure below shows the circular doubly linked list for the BST above. The "head" symbol means the node it points to is the smallest element of the linked list.

Specifically, we want to do the transformation in place. After the transformation, the left pointer of the tree node should point to its predecessor, and the right pointer should point to its successor. We should return the pointer to the first element of the linked list.

The figure below shows the transformed BST. The solid line indicates the successor relationship, while the dashed line means the predecessor relationship.

Solution

Iterative Inorder Traversal.

keep connecting the last node and curr node.

then connect the first node and last node.

/*
24% 6%
*/
class Solution {
  public Node treeToDoublyList(Node root) {
      if (root == null) return null;
        
      Node first = null, last = null, curr = root;
        
      Deque<Node> stack = new ArrayDeque<>();
      while (curr != null || !stack.isEmpty()) {
          while (curr != null) {
              stack.push(curr);
              curr = curr.left;
          }
          curr = stack.pop();
            
          // save first node
          if (first == null) first = curr;
          // connect last(previous node) if not null
          if (last != null) {
              last.right = curr;
              curr.left = last;
          }
            
          last = curr;
          curr = curr.right;
      }
        
      // connect head and tail
      first.left = last;
      last.right = first;
      return first;
  }
}

Recursive Inorder Traversal

also pass prev node to avoid global variable

Harder to understand. Draw a simple tree to help understanding

class Solution {
  public Node treeToDoublyList(Node root) {
      if (root == null) return null;
      Node dummy = new Node(0, null, null), prev = dummy;
      prev = inorder(root, prev);
      prev.right = dummy.right;
      dummy.right.left = prev;
      return dummy.right;
  }
    
  private Node inorder(Node node, Node prev) {
      if (node == null) return prev;
      prev = inorder(node.left, prev);
      prev.right = node;
      node.left = prev;
      prev = inorder(node.right, node); // now pass node as the prev
      return prev;
  }
}

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426. Convert Binary Search Tree to Sorted Doubly Linked List