Level order traversal in spiral form

• Difficulty Level : Medium
• Last Updated : 12 Oct, 2021

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#includeusing namespace std; // A binary tree node has data,// pointer to left child and a// pointer to right childstruct node{    int data;    struct node* left;    struct node* right;}; // Function prototypesvoid 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 treevoid 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 levelvoid printGivenLevel(struct node* root,                     int level, int ltr){    if (root == NULL)        return;    if (level == 1)        cout << 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){    node* newnode = new node();    newnode->data = data;    newnode->left = NULL;    newnode->right = NULL;     return (newnode);} // Driver codeint 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 \n");                printSpiral(root);     return 0;} // This code is contributed by samrat2825

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 prototypes */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 \n");    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 Codeif __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 formusing System; /* A binary tree node has data,pointer to left child and apointer 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

Javascript


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 nodestruct 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 nodestruct 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 \n";    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 nodeclass 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 nodeclass 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 Codeif __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 formusing System;using System.Collections.Generic; // A Binary Tree nodepublic 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

Javascript


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

Method 3(Iterative, using Doubly Ended Queue)

The idea is to use a deque. While travelling left to right we can poll and print the elements from the front and insert their children(left child first followed by the right child) at the back. While travelling right to left we can poll and print the elements from the back and insert their children(right child first followed by the left child) at the front of the deque.

Java

 /*package whatever //do not write package name here */ import java.io.*;import java.util.ArrayDeque;import java.util.Deque; class GFG {     //Defining Node class  static class Node {     int key;    Node left;    Node right;     public Node(int key) {        this.key = key;    }}     //Class to construct the tree  static class MyTree {     public MyTree(){};     public Node root; }     //Function that prints the tree in spiral fashion  public static void spiralPrint(Node root){         //Declare a deque        Deque dq = new ArrayDeque<>();                 //Insert the root of the tree into the deque        dq.offer(root);                 //Create a  variable that will switch in each iteration        boolean reverse = true;         //Start iteration        while (!dq.isEmpty()){                           //Save the size of the deque here itself, as in further steps the size              //of deque will frequently change            int n = dq.size();                           //If we are printing left to right            if(!reverse){                             //Iterate from left to right                for (int i =0; i < n; i++){                                           //Insert the child from the back of the deque                  //Left child first                    if (dq.peekFirst().left  != null)                        dq.offerLast(dq.peekFirst().left);                                       if (dq.peekFirst().right != null)                        dq.offerLast(dq.peekFirst().right);                                     //Print the current processed element                    System.out.print(dq.pollFirst().key + "  ");                                                      }                //Switch reverse for next traversal                reverse = !reverse;                           }else{               //If we are printing right to left              //Iterate the deque in reverse order and insert the children              //from the front                while (n-- >0){                    //Insert the child in the front of the deque                    //Right child first                    if (dq.peekLast().right != null)                        dq.offerFirst(dq.peekLast().right);                                       if (dq.peekLast().left != null)                        dq.offerFirst(dq.peekLast().left);                   //Print the current processed element                    System.out.print(dq.pollLast().key + "  ");                 }                //Switch reverse for next traversal                reverse = !reverse;                             }        }    }          public static void main (String[] args) {        MyTree mt = new MyTree();        mt.root = new Node(1);        mt.root.left = new Node(2);        mt.root.right = new Node(3);        mt.root.left.left = new Node(7);        mt.root.left.right = new Node(6);        mt.root.right.left = new Node(5);        mt.root.right.right = new Node(4);                System.out.println("Spiral Order Traversal Of The Tree Is :");        spiralPrint(mt.root);    }} //This code has been contributed by Abhishek Kumar Sah(kumarabhisheksah98)
Output
Spiral Order Traversal Of The Tree Is :
1  2  3  4  5  6  7

Time Complexity: O(N)
Auxiliary Space: O(N)