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
Approach:
- Create an array inorder[] and store the inorder traversal of the given binary search tree.
- Since the inorder traversal of the binary search tree is sorted in ascending, initialise i = 0 and j = n – 1.
- Print inorder[i] and update i = i + 1.
- Print inorder[j] and update j = j – 1.
- 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 <iostream>using namespace std;// Structure of each node of BSTstruct node { int key; struct node *left, *right;};// A utility function to create a new BST nodenode* 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 treeint 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 BSTvoid 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 BSTvoid 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 codeint 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;} |
Java
// Java implementation of the approachclass GFG{// Structure of each node of BSTstatic class node { int key; node left, right;};static int index;// A utility function to create a new BST nodestatic 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 */static node insert(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 treestatic 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 BSTstatic void printMinMaxOrderUtil(node root, int inOrder[]){ // Base condition if (root == null) { return; } // Left recursive call printMinMaxOrderUtil(root.left, inOrder); // Store elements in inorder array inOrder[index++] = root.key; // Right recursive call printMinMaxOrderUtil(root.right, inOrder);}// Function to print the// Min max order of BSTstatic 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 = new int[numNode + 1]; // Function call for printing // element in min max order printMinMaxOrderUtil(root, inOrder); int i = 0; index--; // While loop for printing elements // In front last order while (i < index) { System.out.print(inOrder[i++] + " " + inOrder[index--] + " "); } if (i == index) { System.out.println(inOrder[i]); }}// Driver codepublic static void main(String[] args) { 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);}}// This code is contributed by 29AjayKumar |
Python3
# Python3 implementation of the approach# Structure of each node of BSTclass 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[0]] = root.val index[0] += 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 = [0] * (numNode + 1) index = 0 # Function call for printing # element in min max order ref = [index] printMinMaxOrderUtil(root, inOrder, ref) index = ref[0] 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 Coderoot = 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 |
C#
// C# implementation of the approachusing System;class GFG{// Structure of each node of BSTclass node { public int key; public node left, right;};static int index;// A utility function to create a new BST nodestatic 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 */static node insert(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 treestatic 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 BSTstatic void printMinMaxOrderUtil(node root, int []inOrder){ // Base condition if (root == null) { return; } // Left recursive call printMinMaxOrderUtil(root.left, inOrder); // Store elements in inorder array inOrder[index++] = root.key; // Right recursive call printMinMaxOrderUtil(root.right, inOrder);}// Function to print the// Min max order of BSTstatic 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 = new int[numNode + 1]; // Function call for printing // element in min max order printMinMaxOrderUtil(root, inOrder); int i = 0; index--; // While loop for printing elements // In front last order while (i < index) { Console.Write(inOrder[i++] + " " + inOrder[index--] + " "); } if (i == index) { Console.WriteLine(inOrder[i]); }}// Driver codepublic static void Main(String[] args) { 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);}}// This code is contributed by PrinciRaj1992 |
Javascript
<script>// Javascript implementation of the approach// Structure of each node of BSTclass node { constructor() { this.key = 0; this.left = null; this.right = null; }};var index = 0;// A utility function to create a new BST nodefunction newNode(item){ var 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 function insert(node, 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 treefunction sizeOfTree(root){ if (root == null) { return 0; } // Calculate left size recursively var left = sizeOfTree(root.left); // Calculate right size recursively var right = sizeOfTree(root.right); // Return total size recursively return (left + right + 1);}// Utility function to print the// Min max order of BSTfunction printMinMaxOrderUtil(root, inOrder){ // Base condition if (root == null) { return; } // Left recursive call printMinMaxOrderUtil(root.left, inOrder); // Store elements in inorder array inOrder[index++] = root.key; // Right recursive call printMinMaxOrderUtil(root.right, inOrder);}// Function to print the// Min max order of BSTfunction printMinMaxOrder(root){ // Store the size of BST var numNode = sizeOfTree(root); // Take auxiliary array for storing // The inorder traversal of BST var inOrder = Array(numNode+1); // Function call for printing // element in min max order printMinMaxOrderUtil(root, inOrder); var i = 0; index--; // While loop for printing elements // In front last order while (i < index) { document.write(inOrder[i++] + " " + inOrder[index--] + " "); } if (i == index) { document.write(inOrder[i]); }}// Driver codevar 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);// This code is contributed by noob2000</script> |
Output:
20 80 30 70 40 60 50
Time Complexity: O(N)
Auxiliary Space: O(N)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
