Construct BST from its given level order traversal

Construct the BST (Binary Search Tree) from its given level order traversal.

Examples:

Input : arr[] = {7, 4, 12, 3, 6, 8, 1, 5, 10}
Output : BST: 
        7        
       /        
      4   12      
     /   /     
    3  6 8    
   /  /   
  1   5   10

The idea is to use a queue to construct tree. Every element of queue has a structure say NodeDetails which stores details of a tree node. The details are pointer to the node, and two variables min and max where min stores the lower limit for the node values which can be a part of the left subtree and max stores the upper limit for the node values which can be a part of the right subtree for the specified node in NodeDetails structure variable. For the 1st array value arr[0], create a node and then create a NodeDetails structure having pointer to this node and min = INT_MIN and max = INT_MAX. Add this structure variable to a queue. This Node will be the root of the tree. Move to 2nd element in arr[] and then perform the following steps:

Pop NodeDetails from the queue in temp.
Check whether the current array element can be a left child of the node in temp with the help of min and temp.node data values. If it can, then create a new NodeDetails structure for this new array element value with its proper ‘min’ and ‘max’ values and push it to the queue, make this new node as the left child of temp’s node and move to next element in arr[].
Check whether the current array element can be a right child of the node in temp with the help of max and temp.node data values. If it can, then create a new NodeDetails structure for this new array element value with its proper ‘min’ and ‘max’ values and push it to the queue, make this new node as the right child of temp’s node and move to next element in arr[].
Repeat steps 1, 2 and 3 until there are no more elements in arr[].

For a left child node, its min value will be its parent’s ‘min’ value and max value will be the data value of its parent node. For a right child node, its min value will be the data value of its parent node and max value will be its parent’s ‘max’ value.

Below is C++ implementation of above approach:

// C++ implementation to construct a BST 
// from its level order traversal 
#include <bits/stdc++.h> 
  
using namespace std; 
  
// node of a BST 
struct Node 
{ 
    int data; 
    Node *left, *right; 
}; 
  
// to store details of a node like 
// pointer to the node, 'min' and 'max'  
// to obtain the range of values where 
// node's left and right child's could lie 
struct NodeDetails 
{ 
    Node *ptr; 
    int min, max; 
}; 
  
// function to get a new node 
Node* getNode(int data) 
{ 
    // Allocate memory 
    Node *newNode = 
        (Node*)malloc(sizeof(Node)); 
      
    // put in the data     
    newNode->data = data; 
    newNode->left = newNode->right = NULL;     
    return newNode; 
} 
  
// function to construct a BST from 
// its level order traversal 
Node* constructBst(int arr[], int n) 
{ 
    // if tree is empty 
    if (n == 0) 
        return NULL; 
      
    Node *root; 
      
    // queue to store NodeDetails 
    queue<NodeDetails> q; 
      
    // index variable to access array elements 
    int i=0; 
      
    // node details for the  
    // root of the BST 
    NodeDetails newNode; 
    newNode.ptr = getNode(arr[i++]); 
    newNode.min = INT_MIN; 
    newNode.max = INT_MAX; 
    q.push(newNode); 
      
    // getting the root of the BST 
    root = newNode.ptr; 
      
    // until there are no more elements  
    // in arr[] 
    while (i != n)         
    { 
        // extracting NodeDetails of a 
        // node from the queue 
        NodeDetails temp = q.front(); 
        q.pop(); 
          
        // check whether there are more elements  
        // in the arr[] and arr[i] can be left child  
        // of 'temp.ptr' or not  
        if (i < n && (arr[i] < temp.ptr->data &&  
                          arr[i] > temp.min)) 
        { 
            // Create NodeDetails for newNode  
            /// and add it to the queue 
            newNode.ptr = getNode(arr[i++]); 
            newNode.min = temp.min; 
            newNode.max = temp.ptr->data; 
            q.push(newNode); 
              
            // make this 'newNode' as left child 
            // of 'temp.ptr' 
            temp.ptr->left = newNode.ptr;             
        } 
          
        // check whether there are more elements  
        // in the arr[] and arr[i] can be right child  
        // of 'temp.ptr' or not  
        if (i < n && (arr[i] > temp.ptr->data && 
                               arr[i] < temp.max)) 
        { 
            // Create NodeDetails for newNode  
            /// and add it to the queue 
            newNode.ptr = getNode(arr[i++]); 
            newNode.min = temp.ptr->data; 
            newNode.max = temp.max; 
            q.push(newNode); 
              
            // make this 'newNode' as right child 
            // of 'temp.ptr' 
            temp.ptr->right = newNode.ptr; 
        }         
    } 
      
    // root of the required BST 
    return root; 
} 
  
// function to print the inorder traversal 
void inorderTraversal(Node* root) 
{ 
    if (!root) 
        return; 
      
    inorderTraversal(root->left); 
    cout << root->data << " "; 
    inorderTraversal(root->right);     
} 
  
// Driver program to test above 
int main() 
{ 
    int arr[] = {7, 4, 12, 3, 6, 8, 1, 5, 10}; 
    int n = sizeof(arr) / sizeof(arr[0]); 
      
    Node *root = constructBst(arr, n); 
      
    cout << "Inorder Traversal: "; 
    inorderTraversal(root); 
    return 0;     
}  

Output:

Inorder Traversal: 1 3 4 5 6 7 8 10 12

Time Complexity : O(n)

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Construct BST from its given level order traversal

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