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Vertical Sum in Binary Tree | Set 2 (Space Optimized)

  • Difficulty Level : Medium
  • Last Updated : 25 Jun, 2021

Given a Binary Tree, find vertical sum of the nodes that are in same vertical line. Print all sums through different vertical lines.

Examples: 

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      1
    /   \
  2      3
 / \    / \
4   5  6   7

The tree has 5 vertical lines
Vertical-Line-1 has only one node 4 => vertical sum is 4 
Vertical-Line-2: has only one node 2=> vertical sum is 2 
Vertical-Line-3: has three nodes: 1,5,6 => vertical sum is 1+5+6 = 12 
Vertical-Line-4: has only one node 3 => vertical sum is 3 
Vertical-Line-5: has only one node 7 => vertical sum is 7
So expected output is 4, 2, 12, 3 and 7

We have discussed Hashing Based Solution in Set 1. Hashing based solution requires a Hash Table to be maintained. We know that hashing requires more space than the number of entries in it. In this post, Doubly Linked List based solution is discussed. The solution discussed here requires only n nodes of linked list where n is total number of vertical lines in binary tree. Below is algorithm. 

verticalSumDLL(root)
1)  Create a node of doubly linked list node 
    with value 0. Let the node be llnode.
2)  verticalSumDLL(root, llnode)

verticalSumDLL(tnode, llnode)
1) Add current node's data to its vertical line
        llnode.data = llnode.data + tnode.data;
2) Recursively process left subtree
   // If left child is not empty
   if (tnode.left != null)
   {
      if (llnode.prev == null)
      {
          llnode.prev = new LLNode(0);
          llnode.prev.next = llnode;
      }
      verticalSumDLLUtil(tnode.left, llnode.prev);
   }
3)  Recursively process right subtree
   if (tnode.right != null)
   {
      if (llnode.next == null)
      {
          llnode.next = new LLNode(0);
          llnode.next.prev = llnode;
      }
      verticalSumDLLUtil(tnode.right, llnode.next);
   }
 

C++




/// C++ program of space optimized solution
/// to find vertical sum of binary tree.
#include <bits/stdc++.h>
 
using namespace std;
 
/// Tree node structure
struct TNode{
    int key;
    struct TNode *left, *right;
};
 
/// Function to create new tree node
TNode* newTNode(int key)
{
    TNode* temp = new TNode;
    temp->key = key;
    temp->left = temp->right = NULL;
    return temp;
}
 
/// Doubly linked list structure
struct LLNode{
    int key;
    struct LLNode *prev, *next;
};
 
/// Function to create new Linked List Node
LLNode* newLLNode(int key)
{
    LLNode* temp = new LLNode;
    temp->key = key;
    temp->prev = temp->next = NULL;
    return temp;
}
 
/// Function that creates Linked list and store
/// vertical sum in it.
void verticalSumDLLUtil(TNode *root, LLNode *sumNode)
{
    /// Update sum of current line by adding value
    /// of current tree node.
    sumNode->key = sumNode->key + root->key;
 
    /// Recursive call to left subtree.
    if(root->left)
    {
        if(sumNode->prev == NULL)
        {
            sumNode->prev = newLLNode(0);
            sumNode->prev->next = sumNode;
        }
        verticalSumDLLUtil(root->left, sumNode->prev);
    }
 
    /// Recursive call to right subtree.
    if(root->right)
    {
        if(sumNode->next == NULL)
        {
            sumNode->next = newLLNode(0);
            sumNode->next->prev = sumNode;
        }
        verticalSumDLLUtil(root->right, sumNode->next);
    }
}
 
/// Function to print vertical sum of Tree.
/// It uses verticalSumDLLUtil() to calculate sum.
void verticalSumDLL(TNode* root)
{
    /// Create Linked list node for
    /// line passing through root.
    LLNode* sumNode = newLLNode(0);
 
    /// Compute vertical sum of different lines.
    verticalSumDLLUtil(root, sumNode);
 
    /// Make doubly linked list pointer point
    /// to first node in list.
    while(sumNode->prev != NULL){
        sumNode = sumNode->prev;
    }
 
    /// Print vertical sum of different lines
    /// of binary tree.
    while(sumNode != NULL){
        cout << sumNode->key <<" ";
        sumNode = sumNode->next;
    }
}
 
int main()
{
    /*
                 1
                / \
               /   \
              2     3
             / \   / \
            /   \ /   \
           4    5 6    7
    */
    TNode *root = newTNode(1);
    root->left = newTNode(2);
    root->right = newTNode(3);
    root->left->left = newTNode(4);
    root->left->right = newTNode(5);
    root->right->left = newTNode(6);
    root->right->right = newTNode(7);
 
    cout << "Vertical Sums are\n";
    verticalSumDLL(root);
    return 0;
}
 
// This code is contributed by Rahul Titare


Java




// Java implementation of space optimized solution
// to find vertical sum.
 
public class VerticalSumBinaryTree
{
    // Prints vertical sum of different vertical
    // lines in tree. This method mainly uses
    // verticalSumDLLUtil().
    static void verticalSumDLL(TNode root)
    {
        // Create a doubly linked list node to
        // store sum of lines going through root.
        // Vertical sum is initialized as 0.
        LLNode llnode = new LLNode(0);
 
        // Compute vertical sum of different lines
        verticalSumDLLUtil(root, llnode);
 
        // llnode refers to sum of vertical line
        // going through root. Move llnode to the
        // leftmost line.
        while (llnode.prev != null)
            llnode = llnode.prev;
 
        // Prints vertical sum of all lines starting
        // from leftmost vertical line
        while (llnode != null)
        {
            System.out.print(llnode.data +" ");
            llnode = llnode.next;
        }
    }
 
    // Constructs linked list
    static void verticalSumDLLUtil(TNode tnode,
                                   LLNode llnode)
    {
        // Add current node's data to its vertical line
        llnode.data = llnode.data + tnode.data;
 
        // Recursively process left subtree
        if (tnode.left != null)
        {
            if (llnode.prev == null)
            {
                llnode.prev = new LLNode(0);
                llnode.prev.next = llnode;
            }
            verticalSumDLLUtil(tnode.left, llnode.prev);
        }
 
        // Process right subtree
        if (tnode.right != null)
        {
            if (llnode.next == null)
            {
                llnode.next = new LLNode(0);
                llnode.next.prev = llnode;
            }
            verticalSumDLLUtil(tnode.right, llnode.next);
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        // Let us construct the tree shown above
        TNode root = new TNode(1);
        root.left = new TNode(2);
        root.right = new TNode(3);
        root.left.left = new TNode(4);
        root.left.right = new TNode(5);
        root.right.left = new TNode(6);
        root.right.right = new TNode(7);
 
        System.out.println("Vertical Sums are");
        verticalSumDLL(root);
    }
 
    // Doubly Linked List Node
    static class LLNode
    {
        int data;
        LLNode prev, next;
        public LLNode(int d) { data = d; }
    }
 
    // Binary Tree Node
    static class TNode
    {
        int data;
        TNode left, right;
        public TNode(int d) { data = d; }
    }
}


Python3




# Python3 program of space optimized
# solution to find vertical sum of
# binary tree.
 
# Tree node structure
class TNode:
     
    def __init__(self, key):
         
        self.key = key
        self.left = None
        self.right = None
 
# Doubly linked list structure
class LLNode:
     
    def __init__(self, key):
         
        self.key = key
        self.prev = None
        self.next = None
 
# Function that creates Linked list and store
# vertical sum in it.
def verticalSumDLLUtil(root: TNode,
                    sumNode: LLNode) -> None:
 
    # Update sum of current line by adding
    # value of current tree node.
    sumNode.key = sumNode.key + root.key
 
    # Recursive call to left subtree.
    if (root.left):
        if (sumNode.prev == None):
            sumNode.prev = LLNode(0)
            sumNode.prev.next = sumNode
 
        verticalSumDLLUtil(root.left,
                           sumNode.prev)
 
    # Recursive call to right subtree.
    if (root.right):
        if (sumNode.next == None):
            sumNode.next = LLNode(0)
            sumNode.next.prev = sumNode
 
        verticalSumDLLUtil(root.right,
                           sumNode.next)
 
# Function to print vertical sum of Tree.
# It uses verticalSumDLLUtil() to calculate sum.
def verticalSumDLL(root: TNode) -> None:
 
    # Create Linked list node for
    # line passing through root.
    sumNode = LLNode(0)
 
    # Compute vertical sum of different lines.
    verticalSumDLLUtil(root, sumNode)
 
    # Make doubly linked list pointer point
    # to first node in list.
    while (sumNode.prev != None):
        sumNode = sumNode.prev
 
    # Print vertical sum of different lines
    # of binary tree.
    while (sumNode != None):
        print(sumNode.key, end = " ")
        sumNode = sumNode.next
 
# Driver code
if __name__ == "__main__":
     
    '''
                 1
                / \
               /   \
              2     3
             / \   / \
            /   \ /   \
           4    5 6    7
    '''
    root = TNode(1)
    root.left = TNode(2)
    root.right = TNode(3)
    root.left.left = TNode(4)
    root.left.right = TNode(5)
    root.right.left = TNode(6)
    root.right.right = TNode(7)
     
    print("Vertical Sums are")
     
    verticalSumDLL(root)
 
# This code is contributed by sanjeev2552


C#




// C# implementation of space optimized
// solution to find vertical sum.
using System;
 
class GFG
{
// Prints vertical sum of different vertical
// lines in tree. This method mainly uses
// verticalSumDLLUtil().
public static void verticalSumDLL(TNode root)
{
    // Create a doubly linked list node to
    // store sum of lines going through root.
    // Vertical sum is initialized as 0.
    LLNode llnode = new LLNode(0);
 
    // Compute vertical sum of different lines
    verticalSumDLLUtil(root, llnode);
 
    // llnode refers to sum of vertical line
    // going through root. Move llnode to the
    // leftmost line.
    while (llnode.prev != null)
    {
        llnode = llnode.prev;
    }
 
    // Prints vertical sum of all lines
    // starting from leftmost vertical line
    while (llnode != null)
    {
        Console.Write(llnode.data + " ");
        llnode = llnode.next;
    }
}
 
// Constructs linked list
public static void verticalSumDLLUtil(TNode tnode,
                                     LLNode llnode)
{
    // Add current node's data to
    // its vertical line
    llnode.data = llnode.data + tnode.data;
 
    // Recursively process left subtree
    if (tnode.left != null)
    {
        if (llnode.prev == null)
        {
            llnode.prev = new LLNode(0);
            llnode.prev.next = llnode;
        }
        verticalSumDLLUtil(tnode.left, llnode.prev);
    }
 
    // Process right subtree
    if (tnode.right != null)
    {
        if (llnode.next == null)
        {
            llnode.next = new LLNode(0);
            llnode.next.prev = llnode;
        }
        verticalSumDLLUtil(tnode.right, llnode.next);
    }
}
 
// Doubly Linked List Node
public class LLNode
{
    public int data;
    public LLNode prev, next;
    public LLNode(int d)
    {
        data = d;
    }
}
 
// Binary Tree Node
public class TNode
{
    public int data;
    public TNode left, right;
    public TNode(int d)
    {
        data = d;
    }
}
 
// Driver code
public static void Main(string[] args)
{
    // Let us construct the tree shown above
    TNode root = new TNode(1);
    root.left = new TNode(2);
    root.right = new TNode(3);
    root.left.left = new TNode(4);
    root.left.right = new TNode(5);
    root.right.left = new TNode(6);
    root.right.right = new TNode(7);
 
    Console.WriteLine("Vertical Sums are");
    verticalSumDLL(root);
}
}
 
// This code is contributed by Shrikant13


Javascript




<script>
 
// Javascript implementation of space optimized
// solution to find vertical sum.
 
// Prints vertical sum of different vertical
// lines in tree. This method mainly uses
// verticalSumDLLUtil().
function verticalSumDLL(root)
{
     
    // Create a doubly linked list node to
    // store sum of lines going through root.
    // Vertical sum is initialized as 0.
    var llnode = new LLNode(0);
 
    // Compute vertical sum of different lines
    verticalSumDLLUtil(root, llnode);
 
    // llnode refers to sum of vertical line
    // going through root. Move llnode to the
    // leftmost line.
    while (llnode.prev != null)
    {
        llnode = llnode.prev;
    }
 
    // Prints vertical sum of all lines
    // starting from leftmost vertical line
    while (llnode != null)
    {
        document.write(llnode.data + " ");
        llnode = llnode.next;
    }
}
 
// Constructs linked list
function verticalSumDLLUtil(tnode, llnode)
{
     
    // Add current node's data to
    // its vertical line
    llnode.data = llnode.data + tnode.data;
 
    // Recursively process left subtree
    if (tnode.left != null)
    {
        if (llnode.prev == null)
        {
            llnode.prev = new LLNode(0);
            llnode.prev.next = llnode;
        }
        verticalSumDLLUtil(tnode.left, llnode.prev);
    }
 
    // Process right subtree
    if (tnode.right != null)
    {
        if (llnode.next == null)
        {
            llnode.next = new LLNode(0);
            llnode.next.prev = llnode;
        }
        verticalSumDLLUtil(tnode.right, llnode.next);
    }
}
 
// Doubly Linked List Node
class LLNode
{
    constructor(d)
    {
        this.data = d;
        this.prev = null;
        this.next = null;
    }
}
 
// Binary Tree Node
class TNode
{
    constructor(d)
    {
        this.data = d;
        this.left = null;
        this.right = null;
    }
}
 
// Driver code
 
// Let us construct the tree shown above
var root = new TNode(1);
root.left = new TNode(2);
root.right = new TNode(3);
root.left.left = new TNode(4);
root.left.right = new TNode(5);
root.right.left = new TNode(6);
root.right.right = new TNode(7);
document.write("Vertical Sums are<br>");
 
verticalSumDLL(root);
 
// This code is contributed by itsok
 
</script>


Output : 

Vertical Sums are
4 2 12 3 7 

This article is contributed by Rahul Titare. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 




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