Clockwise Spiral Traversal of Binary Tree
Given a Binary Tree. The task is to print the circular clockwise spiral order traversal of the given binary tree.
For the above binary tree, the circular clockwise spiral order traversal will be 1, 4, 5, 6, 7, 2, 3.
Examples:
Input :
10
/ \
12 13
/ \
14 15
/ \ / \
21 22 23 24
Output : 10, 24, 23, 22, 21, 12, 13, 15, 14
Approach:
- First, calculate the width of the given tree.
- Create an auxiliary 2D array of order (width*width)
- Do level order traversal of the binary tree and store levels in the newly created 2D matrix one by one in respective rows. That is, store nodes at level 0 at row indexed 0, nodes at level 1 at row indexed 1, and so on.
- Finally, traverse the 2d array in the below fashion:
- Start from the first row from left to right and print elements.
- Then traverse the last row from right to left and print elements.
- Again traverse the second row from left to right and print.
- The second last row from right to left and so on repeats the steps until the complete 2-D array is traversed.
Below is the implementation of the above approach:
C++
// C++ program for Clockwise Spiral Traversal // of Binary Tree #include <bits/stdc++.h> using namespace std; // A Tree node struct Node { int key; struct Node *left, *right; }; // Utility function to create a new node Node* newNode( int key) { Node* temp = new Node; temp->key = key; temp->left = temp->right = NULL; return (temp); } //function to calculate the height of the tree int findHeight( struct Node* node) { //Base condition if (node == NULL) return 0; int leftHeight = findHeight(node->left); int rightHeight = findHeight(node->right); //return maximum of left or right subtree height addition with one return 1+(leftHeight > rightHeight ? leftHeight : rightHeight ); } // Function to find the width of tree void findWidth( struct Node* node, int & maxValue, int & minValue, int hd) { if (node == NULL) return ; if (hd > maxValue) { maxValue = hd; } if (hd < minValue) { minValue = hd; } findWidth(node->left, maxValue, minValue, hd - 1); findWidth(node->right, maxValue, minValue, hd + 1); } // Function to traverse the tree and // store level order traversal in a matrix void BFS( int ** mtrx, struct Node* node) { // Create queue for storing // the addresses of nodes queue< struct Node*> qu; qu.push(node); int i = -1, j = -1; struct Node* poped_node = NULL; while (!qu.empty()) { i++; int qsize = qu.size(); while (qsize--) { j++; poped_node = qu.front(); // Store data of node into the matrix mtrx[i][j] = poped_node->key; qu.pop(); if (poped_node->left != NULL) { qu.push(poped_node->left); } if (poped_node->right != NULL) { qu.push(poped_node->right); } } j = -1; } } // Function for Clockwise Spiral Traversal // of Binary Tree void traverse_matrix( int ** mtrx, int height, int width) { int j = 0, k1 = 0, k2 = 0, k3 = height - 1; int k4 = width - 1; for ( int round = 0; round < height / 2; round++) { for (j = k2; j < width; j++) { // only print those values which // are not MAX_INTEGER if (mtrx[k1][j] != INT_MAX) { cout << mtrx[k1][j] << ", " ; } } k2 = 0; k1++; for (j = k4; j >= 0; j--) { // only print those values which are // not MAX_INTEGER if (mtrx[k3][j] != INT_MAX) { cout << mtrx[k3][j] << ", " ; } } k4 = width - 1; k3--; } // condition (one row may be left traversing) // if number of rows in matrix are odd if (height % 2 != 0) { for (j = k2; j < width; j++) { // only print those values which are // not MAX_INTEGER if (mtrx[k1][j] != INT_MAX) { cout << mtrx[k1][j] << ", " ; } } } } // A utility function to print clockwise // spiral traversal of tree void printPattern( struct Node* node) { // max, min has taken for // calculating width of tree int max_value = INT_MIN; int min_value = INT_MAX; int hd = 0; // calculate the width of a tree findWidth(node, max_value, min_value, hd); int width = max_value + abs (min_value); //calculate the height of the tree int height = findHeight(node); // use double pointer to create 2D array int ** mtrx = new int *[height]; // initialize width for each row of matrix for ( int i = 0; i < height; i++) { mtrx[i] = new int [width]; } // initialize complete matrix with // MAX INTEGER(purpose garbage) for ( int i = 0; i < height; i++) { for ( int j = 0; j < width; j++) { mtrx[i][j] = INT_MAX; } } // Store the BFS traversal of the tree // into the 2-D matrix BFS(mtrx, node); // Print the circular clockwise spiral // traversal of the tree traverse_matrix(mtrx, height, width); // release extra memory // allocated for matrix free (mtrx); } // Driver Code int main() { /* 10 / \ 12 13 / \ 14 15 / \ / \ 21 22 23 24 Let us create Binary Tree as shown in above example */ Node* root = newNode(10); root->left = newNode(12); root->right = newNode(13); root->right->left = newNode(14); root->right->right = newNode(15); root->right->left->left = newNode(21); root->right->left->right = newNode(22); root->right->right->left = newNode(23); root->right->right->right = newNode(24); cout << "Circular Clockwise Spiral Traversal : \n" ; printPattern(root); return 0; } // This code is contributed by MOHAMMAD MUDASSIR |
Java
// Java program for above approach import java.util.*; // A Tree node class Node { int key; Node left, right; Node( int key) { this .key = key; left = right = null ; } } class BinaryTree { // root of the binary tree Node root; // function to calculate the height of the tree int findHeight(Node node) { // Base condition if (node == null ) return 0 ; int leftHeight = findHeight(node.left); int rightHeight = findHeight(node.right); // return maximum of left or right subtree height // addition with one return 1 + (leftHeight > rightHeight ? leftHeight : rightHeight); } // Function to find the width of tree void findWidth(Node node, int [] maxValue, int [] minValue, int hd) { if (node == null ) return ; if (hd > maxValue[ 0 ]) { maxValue[ 0 ] = hd; } if (hd < minValue[ 0 ]) { minValue[ 0 ] = hd; } findWidth(node.left, maxValue, minValue, hd - 1 ); findWidth(node.right, maxValue, minValue, hd + 1 ); } // Function to traverse the tree and // store level order traversal in a matrix void BFS( int [][] mtrx, Node node) { // Create queue for storing // the addresses of nodes Queue<Node> qu = new LinkedList<Node>(); qu.add(node); int i = - 1 , j = - 1 ; Node poped_node; while (!qu.isEmpty()) { i++; int qsize = qu.size(); while (qsize-- > 0 ) { j++; poped_node = qu.remove(); // Store data of node into the matrix mtrx[i][j] = poped_node.key; if (poped_node.left != null ) { qu.add(poped_node.left); } if (poped_node.right != null ) { qu.add(poped_node.right); } } j = - 1 ; } } // Function for Clockwise Spiral Traversal // of Binary Tree void traverse_matrix( int [][] mtrx, int height, int width) { int j = 0 , k1 = 0 , k2 = 0 , k3 = height - 1 ; int k4 = width - 1 ; for ( int round = 0 ; round < height / 2 ; round++) { for (j = k2; j < width; j++) { // only print those values which // are not MAX_INTEGER if (mtrx[k1][j] != Integer.MAX_VALUE) { System.out.print(mtrx[k1][j] + ", " ); } } k2 = 0 ; k1++; for (j = k4; j >= 0 ; j--) { // only print those values which are // not MAX_INTEGER if (mtrx[k3][j] != Integer.MAX_VALUE) { System.out.print(mtrx[k3][j] + ", " ); } } k4 = width - 1 ; k3--; } // condition (one row may be left traversing) // if number of rows in matrix are odd if (height % 2 != 0 ) { for (j = k2; j < width; j++) { // only print those values which are // not MAX_INTEGER if (mtrx[k1][j] != Integer.MAX_VALUE) { System.out.print(mtrx[k1][j] + ", " ); } } } } // A utility function to print clockwise // spiral traversal of tree void printPattern(Node node) { // max, min has taken for // calculating width of tree int [] max_value = new int [ 1 ]; max_value[ 0 ] = Integer.MIN_VALUE; int [] min_value = new int [ 1 ]; min_value[ 0 ] = Integer.MAX_VALUE; int hd = 0 ; // calculate the width of a tree findWidth(node, max_value, min_value, hd); int width = max_value[ 0 ] + Math.abs(min_value[ 0 ]); // calculate the height of the tree int height = findHeight(node); // use double pointer to create 2D array int [][] mtrx = new int [height][width]; // initialize complete matrix with // MAX INTEGER(purpose garbage) for ( int i = 0 ; i < height; i++) { for ( int j = 0 ; j < width; j++) { mtrx[i][j] = Integer.MAX_VALUE; } } // Store the BFS traversal of the tree // into the 2-D matrix BFS(mtrx, node); // Print the circular clockwise spiral // traversal of the tree traverse_matrix(mtrx, height, width); } // Driver Code public static void main(String[] args) { /* 10 / \ 12 13 / \ 14 15 / \ / \ 21 22 23 24 Let us create Binary Tree as shown in above example */ BinaryTree tree = new BinaryTree(); tree.root = new Node( 10 ); tree.root.left = new Node( 12 ); tree.root.right = new Node( 13 ); tree.root.right.left = new Node( 14 ); tree.root.right.right = new Node( 15 ); tree.root.right.left.left = new Node( 21 ); tree.root.right.left.right = new Node( 22 ); tree.root.right.right.left = new Node( 23 ); tree.root.right.right.right = new Node( 24 ); System.out.println( "Circular Clockwise Spiral Traversal : " ); tree.printPattern(tree.root); } } // This code is contributed by adityamaharshi21 |
Python3
# Python3 program for Clockwise Spiral # Traversal of Binary Tree INT_MAX = 2 * * 31 INT_MIN = - 2 * * 31 # Binary tree node class newNode: # Constructor to create a newNode def __init__( self , data): self .key = data self .left = None self .right = None # Function to find the width of tree def findWidth(node, maxValue, minValue, hd): if (node = = None ): return if (hd > maxValue[ 0 ]): maxValue[ 0 ] = hd if (hd < minValue[ 0 ]): minValue[ 0 ] = hd findWidth(node.left, maxValue, minValue, hd - 1 ) findWidth(node.right, maxValue, minValue, hd + 1 ) # Function to traverse the tree and # store level order traversal in a matrix def BFS(mtrx,node): # Create queue for storing # the addresses of nodes qu = [] qu.append(node) i = - 1 j = - 1 poped_node = None while ( len (qu)): i + = 1 qsize = len (qu) while (qsize > 0 ): qsize - = 1 j + = 1 poped_node = qu[ 0 ] # Store data of node into the matrix mtrx[i][j] = poped_node.key qu.pop( 0 ) if (poped_node.left ! = None ): qu.append(poped_node.left) if (poped_node.right ! = None ): qu.append(poped_node.right) j = - 1 # Function for Clockwise Spiral # Traversal of Binary Tree def traverse_matrix(mtrx, width): j = 0 k1 = 0 k2 = 0 k3 = width - 1 k4 = width - 1 for round in range (width / / 2 ): for j in range (k2, width): # only print those values which # are not MAX_INTEGER if (mtrx[k1][j] ! = INT_MAX): print (mtrx[k1][j], ", " , end = "") k2 = 0 k1 + = 1 for j in range (k4, - 1 , - 1 ): # only print those values which are # not MAX_INTEGER if (mtrx[k3][j] ! = INT_MAX): print (mtrx[k3][j], ", " , end = "") k4 = width - 1 k3 - = 1 # condition (one row may be left traversing) # if number of rows in matrix are odd if (width % 2 ! = 0 ): for j in range (k2, width): # only print those values which # are not MAX_INTEGER if (mtrx[k1][j] ! = INT_MAX): print (mtrx[k1][j], ", " , end = "") # A utility function to prclockwise # spiral traversal of tree def printPattern(node): # max, min has taken for # calculating width of tree max_value = [INT_MIN] min_value = [INT_MAX ] hd = 0 # calculate the width of a tree findWidth(node, max_value, min_value, hd) width = max_value[ 0 ] + abs (min_value[ 0 ]) # use double pointer to # create 2D array mtrx = [ 0 ] * width # initialize width for each # row of matrix for i in range (width): mtrx[i] = [ 0 ] * width # initialize complete matrix with # MAX INTEGER(purpose garbage) for i in range (width): for j in range (width): mtrx[i][j] = INT_MAX # Store the BFS traversal of the # tree into the 2-D matrix BFS(mtrx, node) # Print the circular clockwise spiral # traversal of the tree traverse_matrix(mtrx, width) # Driver Code if __name__ = = '__main__' : """ 10 / \ 12 13 / \ 14 15 / \ / \ 21 22 23 24 Let us create Binary Tree as shown in above example """ root = newNode( 10 ) root.left = newNode( 12 ) root.right = newNode( 13 ) root.right.left = newNode( 14 ) root.right.right = newNode( 15 ) root.right.left.left = newNode( 21 ) root.right.left.right = newNode( 22 ) root.right.right.left = newNode( 23 ) root.right.right.right = newNode( 24 ) print ( "Circular Clockwise Spiral Traversal :" ) printPattern(root) # This code is contributed by # SHUBHAMSINGH10 |
C#
using System; using System.Collections.Generic; // A Tree node class Node { public int key; public Node left, right; public Node( int key) { this .key = key; left = right = null ; } } class BinaryTree { // root of the binary tree public Node root; // function to calculate the height of the tree public int findHeight(Node node) { // Base condition if (node == null ) return 0; int leftHeight = findHeight(node.left); int rightHeight = findHeight(node.right); // return maximum of left or right subtree height // addition with one return 1 + (leftHeight > rightHeight ? leftHeight : rightHeight); } // Function to find the width of tree public void findWidth(Node node, int [] maxValue, int [] minValue, int hd) { if (node == null ) return ; if (hd > maxValue[0]) { maxValue[0] = hd; } if (hd < minValue[0]) { minValue[0] = hd; } findWidth(node.left, maxValue, minValue, hd - 1); findWidth(node.right, maxValue, minValue, hd + 1); } // Function to traverse the tree and // store level order traversal in a matrix public void BFS( int [, ] mtrx, Node node) { // Create queue for storing // the addresses of nodes Queue<Node> qu = new Queue<Node>(); qu.Enqueue(node); int i = -1, j = -1; Node poped_node; while (qu.Count != 0) { i++; int qsize = qu.Count; while (qsize-- > 0) { j++; poped_node = qu.Dequeue(); // Store data of node into the matrix mtrx[i, j] = poped_node.key; if (poped_node.left != null ) { qu.Enqueue(poped_node.left); } if (poped_node.right != null ) { qu.Enqueue(poped_node.right); } } j = -1; } } // Function for Clockwise Spiral Traversal // of Binary Tree public void traverse_matrix( int [, ] mtrx, int height, int width) { int j = 0, k1 = 0, k2 = 0, k3 = height - 1; int k4 = width - 1; for ( int round = 0; round < height / 2; round++) { for (j = k2; j < width; j++) { // only print those values which // are not MAX_INTEGER if (mtrx[k1, j] != int .MaxValue) { Console.Write(mtrx[k1, j] + ", " ); } } k2 = 0; k1++; for (j = k4; j >= 0; j--) { // only print those values which are // not MAX_INTEGER if (mtrx[k3, j] != int .MaxValue) { Console.Write(mtrx[k3, j] + ", " ); } } k4 = width - 1; k3--; } // condition (one row may be left traversing) // if number of rows in matrix are odd if (height % 2 != 0) { for (j = k2; j < width; j++) { // only print those values which are // not MAX_INTEGER if (mtrx[k1, j] != int .MaxValue) { Console.Write(mtrx[k1, j] + ", " ); } } } } // A utility function to print clockwise public void print_spiral_traversal(Node node) { int height = findHeight(node); int width = ( int )Math.Pow(2, height - 1); int [, ] mtrx = new int [height, width]; for ( int i = 0; i < height; i++) { for ( int j = 0; j < width; j++) { mtrx[i, j] = int .MaxValue; } } BFS(mtrx, node); traverse_matrix(mtrx, height, width); } // Driver code public static void Main( string [] args) { BinaryTree tree = new BinaryTree(); // Let us create a binary tree shown // in above diagram tree.root = new Node(10); tree.root.left = new Node(12); tree.root.right = new Node(13); tree.root.left.left = new Node(14); tree.root.left.right = new Node(15); tree.root.right.left = new Node(21); tree.root.right.right = new Node(22); tree.root.right.right.left = new Node(23); tree.root.right.right.right = new Node(24); Console.WriteLine( "Circular Clockwise Spiral Traversal : " ); tree.print_spiral_traversal(tree.root); } } |
Javascript
<script> //JavaScript code for the above approach let INT_MAX = Math.pow(2, 31); let INT_MIN = -Math.pow(2, 31); class Node { constructor(data) { this .key = data; this .left = null ; this .right = null ; } } function findWidth(node, maxValue, minValue, hd) { if (!node) return ; if (hd > maxValue[0]) maxValue[0] = hd; if (hd < minValue[0]) minValue[0] = hd; findWidth(node.left, maxValue, minValue, hd - 1); findWidth(node.right, maxValue, minValue, hd + 1); } function BFS(mtrx, node) { let qu = []; qu.push(node); let i = -1; let j = -1; let popedNode = null ; while (qu.length) { i += 1; let qsize = qu.length; while (qsize > 0) { qsize -= 1; j += 1; popedNode = qu[0]; mtrx[i][j] = popedNode.key; qu.shift(); if (popedNode.left) qu.push(popedNode.left); if (popedNode.right) qu.push(popedNode.right); } j = -1; } } function traverseMatrix(mtrx, width) { let j = 0; let k1 = 0; let k2 = 0; let k3 = width - 1; let k4 = width - 1; for (let round = 0; round < width / 2; round++) { for (j = k2; j < width; j++) { if (mtrx[k1][j] !== INT_MAX) document.write(mtrx[k1][j] + ", " ); } k2 = 0; k1 += 1; for (j = k4; j >= 0; j--) { if (mtrx[k3][j] !== INT_MAX) document.write(mtrx[k3][j] + ", " ); } k4 = width - 1; k3 -= 1; } if (width % 2 !== 0) { for (j = k2; j < width; j++) { if (mtrx[k1][j] !== INT_MAX) document.write(mtrx[k1][j] + ", " ); } } } function printPattern(node) { let maxValue = [INT_MIN]; let minValue = [INT_MAX]; let hd = 0; findWidth(node, maxValue, minValue, hd); let width = maxValue[0] + Math.abs(minValue[0]); let mtrx = new Array(width); for (let i = 0; i < width; i++) { mtrx[i] = new Array(width).fill(INT_MAX); } BFS(mtrx, node); traverseMatrix(mtrx, width); } let root = new Node(10); root.left = new Node(12); root.right = new Node(13); root.right.left = new Node(14); root.right.right = new Node(15); root.right.left.left = new Node(21); root.right.left.right = new Node(22); root.right.right.left = new Node(23); root.right.right.right = new Node(24); document.write( "Circular Clockwise Spiral Traversal :" + "<br>" ); printPattern(root); // This code is contributed by Potta Lokesh </script> |
Output:
Circular Clockwise Spiral Traversal : 10, 24, 23, 22, 21, 12, 13, 15, 14,
Time Complexity: O(N), N is the number of nodes.
Auxiliary Space: O(N).