## Thursday, May 5, 2022

### Question 67 : Count subtrees with Sum equal to target in binary tree?

Given a binary tree and an integer. You need to find the number of subtrees having the sum of all of its nodes equal to given Integer, that is, Target sum.

In this post, we will see how to print vertical sum of binary tree nodes in java. Below diagram will show vertical sum for binary tree.

#### Algorithm:

Steps for print vertical sum of binary tree:
• Traverse tree in inorder traversal.
• Create a variable level and initialise it with 0. When you traverse left child, decrease level by 1(level–) and when you traverse right child, increase level by 1(level++).
• We need to maintain TreeMap with key as level and value as node data. If you get same key(level) again, then you need to add current node data to previous stored value to calculate sum.
For example:
TreeMap has entry with (0,40) where 0 is level and 40 is node data. So while traversing, if you encountered node 30 at level 0, so after processing node 30, TreeMap will have entry as (0,70)
• Once TreeMap is populated after iterating all nodes, print the results.

Code for recursion will be:

``````// prints vertical sum of binary tree
public static void printVertivalSumOfBinaryTree(TreeNode startNode,TreeMap<Integer,Integer> treeNodeMap,int level) {
if(startNode==null)
{
return;
}

// Decrease level by 1 when iterating left child
printVertivalSumOfBinaryTree(startNode.left,treeNodeMap,level-1);

if(treeNodeMap.get(level)!=null)
{
Integer sum=treeNodeMap.get(level)+startNode.data;
// Adding current node data to previous stored value to get the sum
treeNodeMap.put(level, sum);
}
else
{

treeNodeMap.put(level, startNode.data);
}
// Increase level by 1 when iterating left child
printVertivalSumOfBinaryTree(startNode.right,treeNodeMap,level+1);

}``````

Please find diagram below which shows level assigned for each binary tree node.

#### Example:

Lets create java program for printing vertical sum in binary tree:

``````import java.util.Map.Entry;
import java.util.TreeMap;

public class BinaryTreeVerticalSumMain {

public static class TreeNode
{
int data;
TreeNode left;
TreeNode right;
TreeNode(int data)
{
this.data=data;
}
}

// prints vertical sum of binary tree
public static void printVertivalSumOfBinaryTree(TreeNode startNode,TreeMap<Integer,Integer> treeNodeMap,int level) {
if(startNode==null)
{
return;
}

// Decrease level by 1 when iterating left child
printVertivalSumOfBinaryTree(startNode.left,treeNodeMap,level-1);

if(treeNodeMap.get(level)!=null)
{
Integer sum=treeNodeMap.get(level)+startNode.data;
// Adding current node data to previous stored value to get the sum
treeNodeMap.put(level, sum);
}
else
{

treeNodeMap.put(level, startNode.data);
}
// Increase level by 1 when iterating left child
printVertivalSumOfBinaryTree(startNode.right,treeNodeMap,level+1);

}
public static void main(String[] args)
{
// Creating a binary tree
TreeNode rootNode=createBinaryTree();
System.out.println("Vertical sum of binary tree will be:");
TreeMap<Integer,Integer> treeNodeMap=new TreeMap<Integer,Integer>();
printVertivalSumOfBinaryTree(rootNode, treeNodeMap, 0);

for(Entry<Integer,Integer> entry:treeNodeMap.entrySet())
System.out.println(entry.getValue());
}

public static TreeNode createBinaryTree()
{

TreeNode rootNode =new TreeNode(40);
TreeNode node20=new TreeNode(20);
TreeNode node10=new TreeNode(10);
TreeNode node30=new TreeNode(30);
TreeNode node60=new TreeNode(60);
TreeNode node50=new TreeNode(50);
TreeNode node70=new TreeNode(70);
TreeNode node55=new TreeNode(55);
TreeNode node5=new TreeNode(5);

rootNode.left=node20;
rootNode.right=node60;

node20.left=node10;
node20.right=node30;

node60.left=node50;
node60.right=node70;
node50.right=node55;
node30.left=node5;
return rootNode;
}
}``````
Run above program and you will get following output:

``````Vertical sum of binary tree will be:
10
25
120
115
70``````

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