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:

  1. First calculate the width of the given tree.
  2. Create an auxiliary 2D array of order (width*width)
  3. 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.
  4. 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.
    • Then second last row from right to left and so on and repeat the steps until the complete 2-D array is traversed.

Below is the implementation of the above approach:

C++

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// 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

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Python3

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# 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 prthose 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 prthose 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 ramge(k2, width):
  
            # only prthose 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)
      
    # Prthe 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

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Output:

Circular Clockwise Spiral Traversal : 
10, 24, 23, 22, 21, 12, 13, 15, 14,


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