Data Modelling & AI Data Structure & Algorithm

Maximum spiral sum in Binary Tree

23 June 2025

0

Given a binary tree containing n nodes. The problem is to find the maximum sum obtained when the tree is spirally traversed. In spiral traversal one by one all levels are being traversed with the root level traversed from right to left, then next level from left to right, then further next level from right to left and so on.

Example:

Maximum spiral sum = 4 + (-1) + (-2) + 1 + 5 = 7

Approach: Obtain the level order traversal in spiral form of the given binary tree with the help of two stacks and store it in an array. Find the maximum sum sub-array of the array so obtained.

Implementation:

C++

// C++ implementation to find maximum spiral sum
#include <bits/stdc++.h>
 
using namespace std;
 
// structure of a node of binary tree
struct Node {
    int data;
    Node *left, *right;
};
 
// A utility function to create a new node
Node* newNode(int data)
{
    // allocate space
    Node* node = new Node;
 
    // put in the data
    node->data = data;
    node->left = node->right = NULL;
 
    return node;
}
 
// function to find the maximum sum contiguous subarray.
// implements kadane's algorithm
int maxSum(vector<int> arr, int n)
{
    // to store the maximum value that is ending
    // up to the current index
    int max_ending_here = INT_MIN;
 
    // to store the maximum value encountered so far
    int max_so_far = INT_MIN;
 
    // traverse the array elements
    for (int i = 0; i < n; i++) {
 
        // if max_ending_here < 0, then it could
        // not possibly contribute to the maximum 
        // sum further
        if (max_ending_here < 0)
            max_ending_here = arr[i];
 
        // else add the value arr[i] to max_ending_here
        else
            max_ending_here += arr[i];
 
        // update max_so_far
        max_so_far = max(max_so_far, max_ending_here);
    }
 
    // required maximum sum contiguous subarray value
    return max_so_far;
}
 
// function to find maximum spiral sum
int maxSpiralSum(Node* root)
{
    // if tree is empty
    if (root == NULL)
        return 0;
 
    // Create two stacks to store alternate levels
    stack<Node*> s1; // For levels from right to left
    stack<Node*> s2; // For levels from left to right
 
    // vector to store spiral order traversal
    // of the binary tree
    vector<int> arr;
 
    // Push first level to first stack 's1'
    s1.push(root);
 
    // traversing tree in spiral form until 
    // there are elements in any one of the 
    // stacks
    while (!s1.empty() || !s2.empty()) {
 
        // traverse current level from s1 and
        // push nodes of next level to s2
        while (!s1.empty()) {
            Node* temp = s1.top();
            s1.pop();
 
            // push temp-data to 'arr'
            arr.push_back(temp->data);
 
            // Note that right is pushed before left
            if (temp->right)
                s2.push(temp->right);
            if (temp->left)
                s2.push(temp->left);
        }
 
        // traverse current level from s2 and
        // push nodes of next level to s1
        while (!s2.empty()) {
            Node* temp = s2.top();
            s2.pop();
 
            // push temp-data to 'arr'
            arr.push_back(temp->data);
 
            // Note that left is pushed before right
            if (temp->left)
                s1.push(temp->left);
            if (temp->right)
                s1.push(temp->right);
        }
    }
 
    // required maximum spiral sum
    return maxSum(arr, arr.size());
}
 
// Driver program to test above
int main()
{
    Node* root = newNode(-2);
    root->left = newNode(-3);
    root->right = newNode(4);
    root->left->left = newNode(5);
    root->left->right = newNode(1);
    root->right->left = newNode(-2);
    root->right->right = newNode(-1);
    root->left->left->left = newNode(-3);
    root->right->right->right = newNode(2);
 
    cout << "Maximum Spiral Sum = "
         << maxSpiralSum(root);
 
    return 0;
}

Java

// Java implementation to find maximum spiral sum
import java.util.ArrayList;
import java.util.Stack;
public class MaxSpiralSum {
 
    // function to find the maximum sum contiguous subarray. 
    // implements kadane's algorithm 
    static int maxSum(ArrayList<Integer> arr) 
    { 
        // to store the maximum value that is ending 
        // up to the current index 
        int max_ending_here = Integer.MIN_VALUE; 
   
        // to store the maximum value encountered so far 
        int max_so_far = Integer.MIN_VALUE; 
   
        // traverse the array elements 
        for (int i = 0; i < arr.size(); i++) 
        {         
            // if max_ending_here < 0, then it could 
            // not possibly contribute to the maximum  
            // sum further 
            if (max_ending_here < 0) 
                max_ending_here = arr.get(i); 
   
            // else add the value arr[i] to max_ending_here 
            else
                max_ending_here +=arr.get(i); 
   
            // update max_so_far 
            max_so_far = Math.max(max_so_far, max_ending_here); 
        } 
   
        // required maximum sum contiguous subarray value 
        return max_so_far; 
    } 
 
    // Function to find maximum spiral sum 
    public static int maxSpiralSum(Node root) 
    {  
        // if tree is empty 
        if (root == null) 
            return 0; 
   
        // Create two stacks to store alternate levels 
        Stack<Node> s1=new Stack<>();// For levels from right to left 
        Stack<Node> s2=new Stack<>(); // For levels from left to right 
   
        // ArrayList to store spiral order traversal 
        // of the binary tree 
        ArrayList<Integer> arr=new ArrayList<>();
   
        // Push first level to first stack 's1' 
        s1.push(root); 
   
        // traversing tree in spiral form until  
        // there are elements in any one of the  
        // stacks 
        while (!s1.isEmpty() || !s2.isEmpty()) 
        { 
   
            // traverse current level from s1 and 
            // push nodes of next level to s2 
            while (!s1.isEmpty()) 
            { 
                Node temp = s1.pop(); 
   
                // push temp-data to 'arr' 
                arr.add(temp.data); 
   
                // Note that right is pushed before left 
                if (temp.right!=null) 
                    s2.push(temp.right); 
                if (temp.left!=null) 
                    s2.push(temp.left); 
            } 
   
            // traverse current level from s2 and 
            // push nodes of next level to s1 
            while (!s2.isEmpty()) 
            { 
                Node temp = s2.pop(); 
                // push temp-data to 'arr' 
                arr.add(temp.data); 
                // Note that left is pushed before right 
                if (temp.left!=null) 
                    s1.push(temp.left); 
                if (temp.right!=null) 
                    s1.push(temp.right); 
            } 
        } 
   
        // required maximum spiral sum 
        return maxSum(arr); 
    } 
 
 
    public static void main(String args[]) {
        Node root = new Node(-2); 
        root.left = new Node(-3); 
        root.right = new Node(4); 
        root.left.left = new Node(5); 
        root.left.right = new Node(1); 
        root.right.left = new Node(-2); 
        root.right.right = new Node(-1); 
        root.left.left.left = new Node(-3); 
        root.right.right.right = new Node(2); 
        System.out.print("Maximum Spiral Sum = "+maxSpiralSum(root));
    }
}
 
/* A binary tree node has data, pointer to left child 
   and a pointer to right child */
class Node 
{ 
    int data ; 
    Node  left,  right ; 
    Node(int data)
    {
        this.data=data;
        left=right=null;
    }
 
}; 
//This code is contributed by Gaurav Tiwari

Python3

# Python3 Implementation to find the maximum Spiral Sum
 
# Structure of a node in binary tree
class Node:
     
    def __init__(self, data):
         
        self.data = data
        self.left = None
        self.right = None
 
# function to find the maximum sum contiguous subarray
# implementing kadane's algorithm
def maxSum(Arr):
 
    currSum = maxSum = 0
    for element in Arr:
        currSum = max(currSum + element, element)
        maxSum = max(maxSum, currSum)
 
    return maxSum
 
# function to find maximum spiral sum 
def maxSpiralSum(root):
 
    # if tree is empty
    if not root:
        return 0
 
    # create two stacks to stopre alternative levels
    stack_s1 = [] # from levels right to left
    stack_s2 = [] # from levels left to right
 
    # store spiral order traversal in Arr
    Arr = []
    stack_s1.append(root)
 
    # traversing tree in spiral form
    # until there are elements in any one
    # of the stack
    while stack_s1 or stack_s2:
 
        # traverse current level from s1 and
        # push node of next level to s2 
        while stack_s1:
             
            temp = stack_s1.pop()
 
            # append temp-> data to Arr
            Arr.append(temp.data)
 
            if temp.right:
                stack_s2.append(temp.right)
            if temp.left:
                stack_s2.append(temp.left)
 
        # traverse current level from s2 and
        # push node of next level to s1
        while stack_s2:
             
            temp = stack_s2.pop()
 
            # append temp-> data to Arr
            Arr.append(temp.data)
 
            if temp.left:
                stack_s1.append(temp.left)
            if temp.right:
                stack_s1.append(temp.right)
 
    return maxSum(Arr) 
 
# Driver code
if __name__ == "__main__":
 
    root = Node(-2)
    root.left = Node(-3)
    root.right = Node(4)
    root.left.left = Node(5)
    root.left.right = Node(1)
    root.right.left = Node(-2)
    root.right.right = Node(-1)
    root.left.left.left = Node(-3)
    root.right.right.right = Node(2)
 
    print("Maximum Spiral Sum is : ", maxSpiralSum(root))
 
# This code is contributed by
# Mayank Chaudhary (chaudhary_19)

C#

// C# implementation to find maximum spiral sum
using System;
using System.Collections.Generic;
 
public class MaxSpiralSum 
{
 
    // function to find the maximum
    // sum contiguous subarray. 
    // implements kadane's algorithm 
    static int maxSum(List<int> arr) 
    { 
        // to store the maximum value that is ending 
        // up to the current index 
        int max_ending_here = int.MinValue; 
     
        // to store the maximum value encountered so far 
        int max_so_far = int.MinValue; 
     
        // traverse the array elements 
        for (int i = 0; i < arr.Count; i++) 
        {         
            // if max_ending_here < 0, then it could 
            // not possibly contribute to the maximum 
            // sum further 
            if (max_ending_here < 0) 
                max_ending_here = arr[i]; 
     
            // else add the value arr[i]
            // to max_ending_here 
            else
                max_ending_here +=arr[i]; 
     
            // update max_so_far 
            max_so_far = Math.Max(max_so_far, max_ending_here); 
        } 
     
        // required maximum sum
        // contiguous subarray value 
        return max_so_far; 
    } 
 
    // Function to find maximum spiral sum 
    public static int maxSpiralSum(Node root) 
    { 
        // if tree is empty 
        if (root == null) 
            return 0; 
     
        // Create two stacks to store alternate levels 
        Stack<Node> s1 = new Stack<Node>();// For levels from right to left 
        Stack<Node> s2 = new Stack<Node>(); // For levels from left to right 
     
        // ArrayList to store spiral order traversal 
        // of the binary tree 
        List<int> arr=new List<int>();
     
        // Push first level to first stack 's1' 
        s1.Push(root); 
     
        // traversing tree in spiral form until 
        // there are elements in any one of the 
        // stacks 
        while (s1.Count != 0 || s2.Count != 0) 
        { 
     
            // traverse current level from s1 and 
            // push nodes of next level to s2 
            while (s1.Count != 0) 
            { 
                Node temp = s1.Pop(); 
     
                // push temp-data to 'arr' 
                arr.Add(temp.data); 
     
                // Note that right is pushed before left 
                if (temp.right != null) 
                    s2.Push(temp.right); 
                if (temp.left != null) 
                    s2.Push(temp.left); 
            } 
     
            // traverse current level from s2 and 
            // push nodes of next level to s1 
            while (s2.Count != 0) 
            { 
                Node temp = s2.Pop(); 
                 
                // push temp-data to 'arr' 
                arr.Add(temp.data);
                 
                // Note that left is pushed before right 
                if (temp.left != null) 
                    s1.Push(temp.left); 
                if (temp.right != null) 
                    s1.Push(temp.right); 
            } 
        } 
     
        // required maximum spiral sum 
        return maxSum(arr); 
    } 
 
    // Driver code
    public static void Main(String []args)
    {
        Node root = new Node(-2); 
        root.left = new Node(-3); 
        root.right = new Node(4); 
        root.left.left = new Node(5); 
        root.left.right = new Node(1); 
        root.right.left = new Node(-2); 
        root.right.right = new Node(-1); 
        root.left.left.left = new Node(-3); 
        root.right.right.right = new Node(2); 
        Console.Write("Maximum Spiral Sum = " + 
                      maxSpiralSum(root));
    }
}
 
/* 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 data)
    {
        this.data = data;
        left = right = null;
    }
 
};
 
// This code is contributed Rajput-Ji 

Javascript

<script>
 
    // JavaScript implementation to find maximum spiral sum
     
    /* A binary tree node has data, pointer to left child
   and a pointer to right child */
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }
 
    // function to find the maximum sum contiguous subarray.
    // implements kadane's algorithm
    function maxSum(arr)
    {
        // to store the maximum value that is ending
        // up to the current index
        let max_ending_here = Number.MIN_VALUE;
    
        // to store the maximum value encountered so far
        let max_so_far = Number.MIN_VALUE;
    
        // traverse the array elements
        for (let i = 0; i < arr.length; i++)
        {        
            // if max_ending_here < 0, then it could
            // not possibly contribute to the maximum 
            // sum further
            if (max_ending_here < 0)
                max_ending_here = arr[i];
    
            // else add the value arr[i] to max_ending_here
            else
                max_ending_here +=arr[i];
    
            // update max_so_far
            max_so_far = Math.max(max_so_far, max_ending_here);
        }
    
        // required maximum sum contiguous subarray value
        return max_so_far;
    }
  
    // Function to find maximum spiral sum
    function maxSpiralSum(root)
    { 
        // if tree is empty
        if (root == null)
            return 0;
    
        // Create two stacks to store alternate levels
        let s1 = [];// For levels from right to left
        let s2 = []; // For levels from left to right
    
        // ArrayList to store spiral order traversal
        // of the binary tree
        let arr = [];
    
        // Push first level to first stack 's1'
        s1.push(root);
    
        // traversing tree in spiral form until 
        // there are elements in any one of the 
        // stacks
        while (s1.length > 0 || s2.length > 0)
        {
    
            // traverse current level from s1 and
            // push nodes of next level to s2
            while (s1.length > 0)
            {
                let temp = s1.pop();
    
                // push temp-data to 'arr'
                arr.push(temp.data);
    
                // Note that right is pushed before left
                if (temp.right!=null)
                    s2.push(temp.right);
                if (temp.left!=null)
                    s2.push(temp.left);
            }
    
            // traverse current level from s2 and
            // push nodes of next level to s1
            while (s2.length > 0)
            {
                let temp = s2.pop();
                // push temp-data to 'arr'
                arr.push(temp.data);
                // Note that left is pushed before right
                if (temp.left!=null)
                    s1.push(temp.left);
                if (temp.right!=null)
                    s1.push(temp.right);
            }
        }
    
        // required maximum spiral sum
        return maxSum(arr);
    }
     
    let root = new Node(-2);
    root.left = new Node(-3);
    root.right = new Node(4);
    root.left.left = new Node(5);
    root.left.right = new Node(1);
    root.right.left = new Node(-2);
    root.right.right = new Node(-1);
    root.left.left.left = new Node(-3);
    root.right.right.right = new Node(2);
    document.write("Maximum Spiral Sum = "+maxSpiralSum(root));
     
</script>

Output

Maximum Spiral Sum = 7

Time Complexity: O(n).
Auxiliary Space: O(n).

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Maximum spiral sum in Binary Tree

C++

Java

Python3

C#

Javascript

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