Print Binary Search Tree in Min Max Fashion

Given a Binary Search Tree (BST), the task is to print the BST in min-max fashion.

What is min-max fashion?
A min-max fashion means you have to print the maximum node first then the minimum then the second maximum then the second minimum and so on.

Examples:

Input:
100
/   \
20     500
/  \
10   30
\
40
Output: 10 500 20 100 30 40

Input:
40
/   \
20     50
/  \      \
10   35     60
/      /
25      55
Output: 10 60 20 55 25 50 35 40

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Create an array inorder[] and store the inorder traversal of the givrn binary search tree.
2. Since the inorder traversal of the binary search tree is sorted in ascending, initialise i = 0 and j = n – 1.
3. Print inorder[i] and update i = i + 1.
4. Print inorder[j] and update j = j – 1.
5. Repeat steps 3 and 4 until all the elements have been printed.

Below is the implementation of the above approach:

C++

 // C++ implementation of the approach #include using namespace std;    // Structure of each node of BST struct node {     int key;     struct node *left, *right; };    // A utility function to create a new BST node node* newNode(int item) {     node* temp = new node();     temp->key = item;     temp->left = temp->right = NULL;     return temp; }    /* A utility function to insert a new  node with given key in BST */ struct node* insert(struct node* node, int key) {     /* If the tree is empty, return a new node */     if (node == NULL)         return newNode(key);        /* Otherwise, recur down the tree */     if (key < node->key)         node->left = insert(node->left, key);     else if (key > node->key)         node->right = insert(node->right, key);        /* return the (unchanged) node pointer */     return node; }    // Function to return the size of the tree int sizeOfTree(node* root) {     if (root == NULL) {         return 0;     }        // Calculate left size recursively     int left = sizeOfTree(root->left);        // Calculate right size recursively     int right = sizeOfTree(root->right);        // Return total size recursively     return (left + right + 1); }    // Utility function to print the // Min max order of BST void printMinMaxOrderUtil(node* root, int inOrder[],                           int& index) {        // Base condition     if (root == NULL) {         return;     }        // Left recursive call     printMinMaxOrderUtil(root->left, inOrder, index);        // Store elements in inorder array     inOrder[index++] = root->key;        // Right recursive call     printMinMaxOrderUtil(root->right, inOrder, index); }    // Function to print the // Min max order of BST void printMinMaxOrder(node* root) {     // Store the size of BST     int numNode = sizeOfTree(root);        // Take auxiliary array for storing     // The inorder traversal of BST     int inOrder[numNode + 1];     int index = 0;        // Function call for printing     // element in min max order     printMinMaxOrderUtil(root, inOrder, index);     int i = 0;     index--;        // While loop for printing elements     // In front last order     while (i < index) {         cout << inOrder[i++] << " "              << inOrder[index--] << " ";     }     if (i == index) {         cout << inOrder[i] << endl;     } }    // Driver code int main() {     struct node* root = NULL;     root = insert(root, 50);     insert(root, 30);     insert(root, 20);     insert(root, 40);     insert(root, 70);     insert(root, 60);     insert(root, 80);        printMinMaxOrder(root);        return 0; }

Output:

20 80 30 70 40 60 50

Python3

 # Python3 implementation of the approach    # Structure of each node of BST class Node:      def __init__(self,key):          self.left = None         self.right = None         self.val = key            def insert(root,node):      if root is None:          root = Node(node)      else:          if root.val < node:              if root.right is None:                  root.right = Node(node)              else:                  insert(root.right, node)          else:              if root.left is None:                  root.left = Node(node)              else:                  insert(root.left, node)                     # Function to return the size of the tree  def sizeOfTree(root):         if root == None:         return 0            # Calculate left size recursively      left = sizeOfTree(root.left)        # Calculate right size recursively      right = sizeOfTree(root.right);         # Return total size recursively      return (left + right + 1)     # Utility function to print the  # Min max order of BST  def printMinMaxOrderUtil(root, inOrder, index):         # Base condition      if root == None:          return        # Left recursive call      printMinMaxOrderUtil(root.left, inOrder, index)         # Store elements in inorder array      inOrder[index] = root.val     index += 1        # Right recursive call      printMinMaxOrderUtil(root.right, inOrder, index)     # Function to print the  # Min max order of BST  def printMinMaxOrder(root):             # Store the size of BST      numNode = sizeOfTree(root);         # Take auxiliary array for storing      # The inorder traversal of BST      inOrder =  * (numNode + 1)      index = 0        # Function call for printing      # element in min max order      ref = [index]     printMinMaxOrderUtil(root, inOrder, ref)      index = ref     i = 0;      index -= 1        # While loop for printing elements      # In front last order      while (i < index):                    print (inOrder[i], inOrder[index], end = ' ')          i += 1         index -= 1            if i == index:          print(inOrder[i])         # Driver Code root = Node(50)  insert(root, 30)  insert(root, 20) insert(root, 40)  insert(root, 70)  insert(root, 60)  insert(root, 80)    printMinMaxOrder(root)        # This code is contributed by Sadik Ali

Output:

20 80 30 70 40 60 50

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