Level order traversal in spiral form

Write a function to print spiral order traversal of a tree. For below tree, function should print 1, 2, 3, 4, 5, 6, 7. Method 1 (Recursive)
This problem can be seen as an extension of the level order traversal post.
To print the nodes in spiral order, nodes at different levels should be printed in alternating order. An additional Boolean variable ltr is used to change printing order of levels. If ltr is 1 then printGivenLevel() prints nodes from left to right else from right to left. Value of ltr is flipped in each iteration to change the order.

Function to print level order traversal of tree

printSpiral(tree)
bool ltr = 0;
for d = 1 to height(tree)
printGivenLevel(tree, d, ltr);
ltr ~= ltr /*flip ltr*/

Function to print all nodes at a given level

printGivenLevel(tree, level, ltr)
if tree is NULL then return;
if level is 1, then
print(tree->data);
else if level greater than 1, then
if(ltr)
printGivenLevel(tree->left, level-1, ltr);
printGivenLevel(tree->right, level-1, ltr);
else
printGivenLevel(tree->right, level-1, ltr);
printGivenLevel(tree->left, level-1, ltr);

Following is the implementation of above algorithm.

C

 // C program for recursive level order traversal in spiral form #include #include #include    /* A binary tree node has data, pointer to left child    and a pointer to right child */ struct node {     int data;     struct node* left;     struct node* right; };    /* Function protoypes */ void printGivenLevel(struct node* root, int level, int ltr); int height(struct node* node); struct node* newNode(int data);    /* Function to print spiral traversal of a tree*/ void printSpiral(struct node* root) {     int h = height(root);     int i;        /*ltr -> Left to Right. If this variable is set,       then the given level is traversed from left to right. */     bool ltr = false;     for (i = 1; i <= h; i++) {         printGivenLevel(root, i, ltr);            /*Revert ltr to traverse next level in opposite order*/         ltr = !ltr;     } }    /* Print nodes at a given level */ void printGivenLevel(struct node* root, int level, int ltr) {     if (root == NULL)         return;     if (level == 1)         printf("%d ", root->data);     else if (level > 1) {         if (ltr) {             printGivenLevel(root->left, level - 1, ltr);             printGivenLevel(root->right, level - 1, ltr);         }         else {             printGivenLevel(root->right, level - 1, ltr);             printGivenLevel(root->left, level - 1, ltr);         }     } }    /* Compute the "height" of a tree -- the number of     nodes along the longest path from the root node     down to the farthest leaf node.*/ int height(struct node* node) {     if (node == NULL)         return 0;     else {         /* compute the height of each subtree */         int lheight = height(node->left);         int rheight = height(node->right);            /* use the larger one */         if (lheight > rheight)             return (lheight + 1);         else             return (rheight + 1);     } }    /* Helper function that allocates a new node with the    given data and NULL left and right pointers. */ struct node* newNode(int data) {     struct node* node = (struct node*)         malloc(sizeof(struct node));     node->data = data;     node->left = NULL;     node->right = NULL;        return (node); }    /* Driver program to test above functions*/ int main() {     struct node* root = newNode(1);     root->left = newNode(2);     root->right = newNode(3);     root->left->left = newNode(7);     root->left->right = newNode(6);     root->right->left = newNode(5);     root->right->right = newNode(4);     printf("Spiral Order traversal of binary tree is ");     printSpiral(root);        return 0; }

Java

 // Java program for recursive level order traversal in spiral form    /* A binary tree node has data, pointer to left child     and a pointer to right child */ class Node {     int data;     Node left, right;        public Node(int d)     {         data = d;         left = right = null;     } }    class BinaryTree {     Node root;        // Function to print the spiral traversal of tree     void printSpiral(Node node)     {         int h = height(node);         int i;            /* ltr -> left to right. If this variable is set then the            given label is traversed from left to right */         boolean ltr = false;         for (i = 1; i <= h; i++) {             printGivenLevel(node, i, ltr);                /*Revert ltr to traverse next level in opposite order*/             ltr = !ltr;         }     }        /* Compute the "height" of a tree -- the number of     nodes along the longest path from the root node     down to the farthest leaf node.*/     int height(Node node)     {         if (node == null)             return 0;         else {                /* compute the height of each subtree */             int lheight = height(node.left);             int rheight = height(node.right);                /* use the larger one */             if (lheight > rheight)                 return (lheight + 1);             else                 return (rheight + 1);         }     }        /* Print nodes at a given level */     void printGivenLevel(Node node, int level, boolean ltr)     {         if (node == null)             return;         if (level == 1)             System.out.print(node.data + " ");         else if (level > 1) {             if (ltr != false) {                 printGivenLevel(node.left, level - 1, ltr);                 printGivenLevel(node.right, level - 1, ltr);             }             else {                 printGivenLevel(node.right, level - 1, ltr);                 printGivenLevel(node.left, level - 1, ltr);             }         }     }     /* Driver program to test the above functions */     public static void main(String[] args)     {         BinaryTree tree = new BinaryTree();         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(7);         tree.root.left.right = new Node(6);         tree.root.right.left = new Node(5);         tree.root.right.right = new Node(4);         System.out.println("Spiral order traversal of Binary Tree is ");         tree.printSpiral(tree.root);     } }    // This code has been contributed by Mayank Jaiswal(mayank_24)

Python3

 # Python3 program for recursive level order # traversal in spiral form     class newNode:         # Construct to create a newNode      def __init__(self, key):          self.data = key          self.left = None         self.right = None    """ Function to print spiral traversal of a tree""" def printSpiral(root):        h = height(root)             """ltr Left to Right. If this variable      is set, then the given level is traversed     from left to right. """     ltr = False     for i in range(1, h + 1):                printGivenLevel(root, i, ltr)             """Revert ltr to traverse next level            in opposite order"""         ltr = not ltr         """ Print nodes at a given level """ def printGivenLevel(root, level, ltr):        if(root == None):         return     if(level == 1):         print(root.data, end = " ")      elif (level > 1):                if(ltr):             printGivenLevel(root.left, level - 1, ltr)              printGivenLevel(root.right, level - 1, ltr)                     else:             printGivenLevel(root.right, level - 1, ltr)              printGivenLevel(root.left, level - 1, ltr)             """ Compute the "height" of a tree -- the number of      nodes along the longest path from the root node      down to the farthest leaf node.""" def height(node):        if (node == None):         return 0     else:                """ compute the height of each subtree """         lheight = height(node.left)          rheight = height(node.right)             """ use the larger one """         if (lheight > rheight):             return(lheight + 1)          else:             return(rheight + 1)         # Driver Code if __name__ == '__main__':     root = newNode(1)      root.left = newNode(2)      root.right = newNode(3)      root.left.left = newNode(7)      root.left.right = newNode(6)      root.right.left = newNode(5)      root.right.right = newNode(4)      print("Spiral Order traversal of binary tree is")      printSpiral(root)         # This code is contributed # by SHUBHAMSINGH10

C#

 // C# program for recursive level // order traversal in spiral form using System;    /* A binary tree node has data,  pointer to left child and a  pointer to right child */ public class Node {     public int data;     public Node left, right;        public Node(int d)     {         data = d;         left = right = null;     } }    class GFG {     public Node root;        // Function to print the spiral     // traversal of tree     public virtual void printSpiral(Node node)     {         int h = height(node);         int i;            /* ltr -> left to right. If this          variable is set then the given         label is traversed from left to right */         bool ltr = false;         for (i = 1; i <= h; i++) {             printGivenLevel(node, i, ltr);                /*Revert ltr to traverse next                level in opposite order*/             ltr = !ltr;         }     }        /* Compute the "height" of a tree -- the     number of nodes along the longest path      from the root node down to the farthest      leaf node.*/     public virtual int height(Node node)     {         if (node == null) {             return 0;         }         else {                /* compute the height of each subtree */             int lheight = height(node.left);             int rheight = height(node.right);                /* use the larger one */             if (lheight > rheight) {                 return (lheight + 1);             }             else {                 return (rheight + 1);             }         }     }        /* Print nodes at a given level */     public virtual void printGivenLevel(Node node,                                         int level,                                         bool ltr)     {         if (node == null) {             return;         }         if (level == 1) {             Console.Write(node.data + " ");         }         else if (level > 1) {             if (ltr != false) {                 printGivenLevel(node.left, level - 1, ltr);                 printGivenLevel(node.right, level - 1, ltr);             }             else {                 printGivenLevel(node.right, level - 1, ltr);                 printGivenLevel(node.left, level - 1, ltr);             }         }     }        // Driver Code     public static void Main(string[] args)     {         GFG tree = new GFG();         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(7);         tree.root.left.right = new Node(6);         tree.root.right.left = new Node(5);         tree.root.right.right = new Node(4);         Console.WriteLine("Spiral order traversal "                           + "of Binary Tree is ");         tree.printSpiral(tree.root);     } }    // This code is contributed by Shrikant13

Output:

Spiral Order traversal of binary tree is
1 2 3 4 5 6 7

Time Complexity: Worst case time complexity of the above method is O(n^2). Worst case occurs in case of skewed trees.

Method 2 (Iterative)
We can print spiral order traversal in O(n) time and O(n) extra space. The idea is to use two stacks. We can use one stack for printing from left to right and other stack for printing from right to left. In every iteration, we have nodes of one level in one of the stacks. We print the nodes, and push nodes of next level in other stack.

C++

 // C++ implementation of a O(n) time method for spiral order traversal #include #include using namespace std;    // Binary Tree node struct node {     int data;     struct node *left, *right; };    void printSpiral(struct node* root) {     if (root == NULL)         return; // NULL check        // Create two stacks to store alternate levels     stack s1; // For levels to be printed from right to left     stack s2; // For levels to be printed from left to right        // Push first level to first stack 's1'     s1.push(root);        // Keep printing while any of the stacks has some nodes     while (!s1.empty() || !s2.empty()) {         // Print nodes of current level from s1 and push nodes of         // next level to s2         while (!s1.empty()) {             struct node* temp = s1.top();             s1.pop();             cout << temp->data << " ";                // Note that is right is pushed before left             if (temp->right)                 s2.push(temp->right);             if (temp->left)                 s2.push(temp->left);         }            // Print nodes of current level from s2 and push nodes of         // next level to s1         while (!s2.empty()) {             struct node* temp = s2.top();             s2.pop();             cout << temp->data << " ";                // Note that is left is pushed before right             if (temp->left)                 s1.push(temp->left);             if (temp->right)                 s1.push(temp->right);         }     } }    // A utility function to create a new node struct node* newNode(int data) {     struct node* node = new struct node;     node->data = data;     node->left = NULL;     node->right = NULL;        return (node); }    int main() {     struct node* root = newNode(1);     root->left = newNode(2);     root->right = newNode(3);     root->left->left = newNode(7);     root->left->right = newNode(6);     root->right->left = newNode(5);     root->right->right = newNode(4);     cout << "Spiral Order traversal of binary tree is ";     printSpiral(root);        return 0; }

Java

 // Java implementation of an O(n) approach of level order // traversal in spiral form    import java.util.*;    // A Binary Tree node class Node {     int data;     Node left, right;        public Node(int item)     {         data = item;         left = right = null;     } }    class BinaryTree {        static Node root;        void printSpiral(Node node)     {         if (node == null)             return; // NULL check            // Create two stacks to store alternate levels         // For levels to be printed from right to left         Stack s1 = new Stack();          // For levels to be printed from left to right         Stack s2 = new Stack();             // Push first level to first stack 's1'         s1.push(node);            // Keep printing while any of the stacks has some nodes         while (!s1.empty() || !s2.empty()) {             // Print nodes of current level from s1 and push nodes of             // next level to s2             while (!s1.empty()) {                 Node temp = s1.peek();                 s1.pop();                 System.out.print(temp.data + " ");                    // Note that is right is pushed before left                 if (temp.right != null)                     s2.push(temp.right);                    if (temp.left != null)                     s2.push(temp.left);             }                // Print nodes of current level from s2 and push nodes of             // next level to s1             while (!s2.empty()) {                 Node temp = s2.peek();                 s2.pop();                 System.out.print(temp.data + " ");                    // Note that is left is pushed before right                 if (temp.left != null)                     s1.push(temp.left);                 if (temp.right != null)                     s1.push(temp.right);             }         }     }        public static void main(String[] args)     {         BinaryTree tree = new BinaryTree();         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(7);         tree.root.left.right = new Node(6);         tree.root.right.left = new Node(5);         tree.root.right.right = new Node(4);         System.out.println("Spiral Order traversal of Binary Tree is ");         tree.printSpiral(root);     } }    // This code has been contributed by Mayank Jaiswal(mayank_24)

Python3

 # Python3 implementation of a O(n) time  # method for spiral order traversal     # A class to create a new node  class newNode:     def __init__(self, data):         self.data = data          self.left = None         self.right = None    def printSpiral(root):     if (root == None):         return # None check         # Create two stacks to store      # alternate levels      s1 = [] # For levels to be printed              # from right to left      s2 = [] # For levels to be printed              # from left to right         # append first level to first stack 's1'      s1.append(root)         # Keep printing while any of the      # stacks has some nodes      while not len(s1) == 0 or not len(s2) == 0:                    # Print nodes of current level from s1          # and append nodes of next level to s2          while not len(s1) == 0:             temp = s1[-1]              s1.pop()              print(temp.data, end = " ")                 # Note that is right is appended             # before left              if (temp.right):                  s2.append(temp.right)              if (temp.left):                 s2.append(temp.left)            # Print nodes of current level from s2          # and append nodes of next level to s1          while (not len(s2) == 0):             temp = s2[-1]              s2.pop()              print(temp.data, end = " ")                 # Note that is left is appended             # before right              if (temp.left):                 s1.append(temp.left)              if (temp.right):                  s1.append(temp.right)    # Driver Code if __name__ == '__main__':     root = newNode(1)      root.left = newNode(2)      root.right = newNode(3)      root.left.left = newNode(7)      root.left.right = newNode(6)      root.right.left = newNode(5)      root.right.right = newNode(4)      print("Spiral Order traversal of",                     "binary tree is ")      printSpiral(root)    # This code is contributed by PranchalK

C#

 // C# implementation of an O(n) approach of // level order traversal in spiral form using System; using System.Collections.Generic;    // A Binary Tree node public class Node {     public int data;     public Node left, right;        public Node(int item)     {         data = item;         left = right = null;     } }    public class BinaryTree {     public static Node root;        public virtual void printSpiral(Node node)     {         if (node == null) {             return; // NULL check         }            // Create two stacks to store alternate levels         Stack s1 = new Stack(); // For levels to be printed         // from right to left         Stack s2 = new Stack(); // For levels to be printed         // from left to right            // Push first level to first stack 's1'         s1.Push(node);            // Keep printing while any of the         // stacks has some nodes         while (s1.Count > 0 || s2.Count > 0) {             // Print nodes of current level from             // s1 and push nodes of next level to s2             while (s1.Count > 0) {                 Node temp = s1.Peek();                 s1.Pop();                 Console.Write(temp.data + " ");                    // Note that is right is pushed before left                 if (temp.right != null) {                     s2.Push(temp.right);                 }                    if (temp.left != null) {                     s2.Push(temp.left);                 }             }                // Print nodes of current level from s2             // and push nodes of next level to s1             while (s2.Count > 0) {                 Node temp = s2.Peek();                 s2.Pop();                 Console.Write(temp.data + " ");                    // Note that is left is pushed before right                 if (temp.left != null) {                     s1.Push(temp.left);                 }                 if (temp.right != null) {                     s1.Push(temp.right);                 }             }         }     }        // Driver Code     public static void Main(string[] args)     {         BinaryTree tree = new BinaryTree();         BinaryTree.root = new Node(1);         BinaryTree.root.left = new Node(2);         BinaryTree.root.right = new Node(3);         BinaryTree.root.left.left = new Node(7);         BinaryTree.root.left.right = new Node(6);         BinaryTree.root.right.left = new Node(5);         BinaryTree.root.right.right = new Node(4);         Console.WriteLine("Spiral Order traversal of Binary Tree is ");         tree.printSpiral(root);     } }    // This code is contributed by Shrikant13

Output:

Spiral Order traversal of binary tree is
1 2 3 4 5 6 7