algorithm - How to construct a binary tree using a level order traversal sequence

Question

How to construct a binary tree using a level order traversal sequence, for example from sequence {1,2,3,#,#,4,#,#,5}, we can construct a binary tree like this:

     1
    / 
   2   3
      /
     4
      
       5

where '#' signifies a path terminator where no node exists below.

Finally I implement Pham Trung's algorithm by c++

struct TreeNode
{
    TreeNode *left;
    TreeNode *right;
    int val;

    TreeNode(int x): left(NULL), right(NULL), val(x) {}
};
TreeNode *build_tree(char nodes[], int n)
{
    TreeNode *root = new TreeNode(nodes[0] - '0'); 
    queue<TreeNode*> q;
    bool is_left = true;
    TreeNode *cur = NULL;
    q.push(root);

    for (int i = 1; i < n; i++) {
        TreeNode *node = NULL;
        if (nodes[i] != '#') {
            node = new TreeNode(nodes[i] - '0');
            q.push(node);
        }

        if (is_left) {
            cur = q.front();
            q.pop();
            cur->left = node;
            is_left = false;
        } else {
            cur->right = node;
            is_left = true;
        }
    }

    return root;
}

Answer 1

Assume using array int[]data with 0-based index, we have a simple function to get children:

• Left child

    int getLeftChild(int index){
       if(index*2 + 1 >= data.length)
          return -1;// -1 Means out of bound
       return data[(index*2) + 1];
    }
  

• Right child

    int getRightChild(int index){
       if(index*2 + 2 >= data.length)
          return -1;// -1 Means out of bound           
       return data[(index*2) + 2];
    }
  

Edit: Ok, so by maintaining a queue, we can build this binary tree.

We use a queue to maintain those nodes that are not yet processed.

Using a variable count to keep track of the number of children added for the current node.

First, create a root node, assign it as the current node. So starting from index 1 (index 0 is the root), as the count is 0, we add this node as left child of the current node. Increase count. If this node is not '#', add it to the queue.

Moving to the next index, the count is 1, so we add this as right child of current node, reset count to 0 and update current node (by assigning the current node as the first element in the queue). If this node is not '#', add it to the queue.

     int count = 0;
     Queue q = new Queue();
     q.add(new Node(data[0]);
     Node cur = null;
     for(int i = 1; i < data.length; i++){
        Node node = new Node(data[i]);
        if(count == 0){
           cur = q.dequeue();           
        }
        if(count==0){
          count++;
          cur.leftChild = node;
        }else {
          count = 0;
          cur.rightChild = node;
        }
        if(data[i] != '#'){
          q.enqueue(node);
        }
     }    



    class Node{
       int data;
       Node leftChild, rightChild;
    } 

Note: this should only work for a binary tree and not BST.