Data Modelling & AI Data Structure & Algorithm

Remove nodes from Binary Tree such that sum of all remaining root-to-leaf paths is atleast K

23 June 2025

0

Given a Binary Tree and an integer K, the task is to delete nodes from the given Tree such that the sum of all nodes of all remaining root to leaf paths is at least K.

Examples:

Input: K = 27

Output: 5 4 8 5 6 11
Explanation:
Below are the paths whose sum is less than 27:

5 -> 3 -> 9: Path Sum = 5 + 3 + 9 = 17.

5 -> 4 -> 9: Path Sum = 5 + 4 + 9 = 18.

5 -> 4 -> 8 -> 5 -> 2: Path Sum = 5 + 4 + 8 + 5 + 2 = 24.

Below is the tree after deleting the required nodes that such that sum of all paths is at least 27:

Input: K = 10

Output: 2 1 8 12 14 7 10

Approach: The idea is to use recursion and perform the Postorder Traversal and delete those nodes whose addition to the path sum is less than K. Below are the steps:

Perform the Post Order Traversal on the given Tree and during this traversal pass the sum of all nodes from the root node to each node.
During traversal, if we reach the leaf node then check if the sum of all nodes till that node is less than K?. If found to be true, remove that node by returning the NULL node from that node.
Repeat the above step for every leaf node encounters in the update tree.
After the above steps, print the Preorder Traversal of the modified Tree.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Tree Node Class
struct Node 
{
    int data;
    Node *left;
    Node *right;
 
    Node(int x)
    {
        data = x;
        left = right = NULL;
    }
};
 
// Utility function that deletes nodes
// from the Tree such that every root
// to leaf path sum is at least K
Node *removePathLessThanK(Node *node, int K,
                          int sum)
{
     
    // Base Case
    if (node == NULL) 
    {
        return NULL;
    }
 
    // Recurse to the left
    if (node->left != NULL)
    {
        node->left = removePathLessThanK(
                     node->left, K,
                     sum + node->left->data);
    }
 
    // Recurse to the right
    if (node->right != NULL)
    {
        node->right = removePathLessThanK(
                      node->right, K,
                      sum + node->right->data);
    }
 
    // Check path sum at leaf node
    // is lesser than K, return NULL
    if (node->left == NULL && 
        node->right == NULL && sum < K)
    {
        node = NULL;
        return node;
    }
 
    // Otherwise return the
    // current node as it is
    return node;
}
 
// Function to print the preorder
// traversal of the Tree
void viewTree(Node *node)
{
     
    // If node is not NULL
    if (node != NULL) 
    {
         
        // Print the node
        cout << node->data << " ";
 
        // Left and Right Traversal
        viewTree(node->left);
        viewTree(node->right);
    }
}
 
// Function that deletes the nodes
// from the Tree such that every root
// to leaf path sum is at least K
void removePathLessThanKUtil(Node *node, int K,
                             int sum)
{
     
    // Function Call to delete Nodes
    Node *result = removePathLessThanK(node, K, sum);
     
    // Preorder Traversal of the
    // modified Tree
    viewTree(result);
}
 
// Driver Code
int main()
{
     
    // Given sum K
    int K = 27;
 
    // Given Binary Tree
    Node *root = NULL;
    root = new Node(5);
    root->right = new Node(3);
    root->left = new Node(4);
    root->left->left = new Node(9);
    root->right->right = new Node(9);
    root->left->right = new Node(8);
    root->left->right->right = new Node(11);
    root->left->right->left = new Node(5);
    root->left->right->left->left = new Node(6);
    root->left->right->left->right = new Node(2);
    root->right->right->right = new Node(4);
 
    // Function Call
    removePathLessThanKUtil(root, K, root->data);
}
 
// This code is contributed by mohit kumar 29

Java

// Java program for the above approach
 
import java.io.*;
import java.util.*;
 
// Tree Node Class
class Node {
    int data;
    Node left;
    Node right;
}
 
class path {
 
    // Function to insert node in the
    // given Binary Tree
    public Node insert(int val)
    {
        Node n = new Node();
        n.data = val;
        n.left = null;
        n.right = null;
        return n;
    }
 
    // Utility function that deletes nodes
    // from the Tree such that every root
    // to leaf path sum is at least K
    public Node removePathLessThanK(
        Node node, int K, int sum)
    {
        // Base Case
        if (node == null) {
            return null;
        }
 
        // Recurse to the left
        if (node.left != null) {
            node.left
                = removePathLessThanK(
                    node.left, K,
                    sum + node.left.data);
        }
 
        // Recurse to the right
        if (node.right != null) {
            node.right
                = removePathLessThanK(
                    node.right, K,
                    sum + node.right.data);
        }
 
        // Check path sum at leaf node
        // is lesser than K, return NULL
        if (node.left == null
            && node.right == null
            && sum < K) {
            node = null;
            return node;
        }
 
        // Otherwise return the
        // current node as it is
        return node;
    }
 
    // Function to print the preorder
    // traversal of the Tree
    public void viewTree(Node node)
    {
        // If node is not NULL
        if (node != null) {
 
            // Print the node
            System.out.print(node.data + " ");
 
            // Left and Right Traversal
            viewTree(node.left);
            viewTree(node.right);
        }
    }
 
    // Function that deletes the nodes
    // from the Tree such that every root
    // to leaf path sum is at least K
    public void removePathLessThanKUtil(
        Node node, int K, int sum)
    {
        // Function Call to delete Nodes
        Node result = removePathLessThanK(
            node, K, sum);
 
        // Preorder Traversal of the
        // modified Tree
        viewTree(result);
    }
}
 
// Driver Code
class GFG {
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given sum K
        int K = 27;
 
        // Object of class path
        path b = new path();
 
        // Given Binary Tree
        Node root = null;
        root = b.insert(5);
        root.right = b.insert(3);
        root.left = b.insert(4);
        root.left.left = b.insert(9);
        root.right.right = b.insert(9);
        root.left.right = b.insert(8);
        root.left.right.right = b.insert(11);
        root.left.right.left = b.insert(5);
        root.left.right.left.left = b.insert(6);
        root.left.right.left.right = b.insert(2);
        root.right.right.right = b.insert(4);
 
        // Function Call
        b.removePathLessThanKUtil(
            root, K, root.data);
    }
}

Python3

# Python3 program for the above approach
 
# Tree Node Class
class newNode:
     
    def __init__(self, x):
         
        self.data = x
        self.left = None
        self.right = None
 
# Utility function that deletes nodes
# from the Tree such that every root
# to leaf path sum is at least K
def removePathLessThanK(node, K, sum):
     
    # Base Case
    if (node == None):
        return None
 
    # Recurse to the left
    if (node.left != None):
        node.left = removePathLessThanK(
                    node.left, K, 
                    sum + node.left.data)
 
    # Recurse to the right
    if (node.right != None):
        node.right = removePathLessThanK(
                     node.right, K,
                     sum + node.right.data)
 
    # Check path sum at leaf node
    # is lesser than K, return None
    if (node.left == None and
       node.right == None and sum < K):
        node = None
        return node
 
    # Otherwise return the
    # current node as it is
    return node
 
# Function to print the preorder
# traversal of the Tree
def viewTree(node):
     
    # If node is not None
    if (node != None):
         
        # Print the node
        print(node.data, end = " ")
 
        # Left and Right Traversal
        viewTree(node.left)
        viewTree(node.right)
 
# Function that deletes the nodes
# from the Tree such that every root
# to leaf path sum is at least K
def removePathLessThanKUtil(node, K, sum):
     
    # Function Call to delete Nodes
    result = removePathLessThanK(node, K, sum)
     
    # Preorder Traversal of the
    # modified Tree
    viewTree(result)
 
# Driver Code
if __name__ == '__main__':
     
    # Given sum K
    K = 27
 
    # Given Binary Tree
    root = None
    root = newNode(5)
    root.right = newNode(3)
    root.left = newNode(4)
    root.left.left = newNode(9)
    root.right.right = newNode(9)
    root.left.right = newNode(8)
    root.left.right.right = newNode(11)
    root.left.right.left = newNode(5)
    root.left.right.left.left = newNode(6)
    root.left.right.left.right = newNode(2)
    root.right.right.right = newNode(4)
 
    # Function Call
    removePathLessThanKUtil(root, K, root.data)
 
# This code is contributed by SURENDRA_GANGWAR

C#

// C# program for the above approach
using System;
 
// Tree Node Class
public class Node 
{
    public int data;
    public Node left;
    public Node right;
}
 
class path{
 
// Function to insert node in the
// given Binary Tree
public Node insert(int val)
{
    Node n = new Node();
    n.data = val;
    n.left = null;
    n.right = null;
    return n;
}
 
// Utility function that deletes nodes
// from the Tree such that every root
// to leaf path sum is at least K
public Node removePathLessThanK(Node node, 
                                int K, int sum)
{
     
    // Base Case
    if (node == null)
    {
        return null;
    }
 
    // Recurse to the left
    if (node.left != null)
    {
        node.left = removePathLessThanK(
                    node.left, K,
                    sum + node.left.data);
    }
 
    // Recurse to the right
    if (node.right != null)
    {
        node.right = removePathLessThanK(
                     node.right, K,
                     sum + node.right.data);
    }
 
    // Check path sum at leaf node
    // is lesser than K, return NULL
    if (node.left == null && 
       node.right == null && sum < K)
    {
        node = null;
        return node;
    }
 
    // Otherwise return the
    // current node as it is
    return node;
}
 
// Function to print the preorder
// traversal of the Tree
public void viewTree(Node node)
{
     
    // If node is not NULL
    if (node != null)
    {
         
        // Print the node
        Console.Write(node.data + " ");
 
        // Left and Right Traversal
        viewTree(node.left);
        viewTree(node.right);
    }
}
 
// Function that deletes the nodes
// from the Tree such that every root
// to leaf path sum is at least K
public void removePathLessThanKUtil(Node node, 
                                    int K, int sum)
{
     
    // Function Call to delete Nodes
    Node result = removePathLessThanK(
        node, K, sum);
 
    // Preorder Traversal of the
    // modified Tree
    viewTree(result);
}
}
 
// Driver Code
class GFG{
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given sum K
    int K = 27;
 
    // Object of class path
    path b = new path();
 
    // Given Binary Tree
    Node root = null;
    root = b.insert(5);
    root.right = b.insert(3);
    root.left = b.insert(4);
    root.left.left = b.insert(9);
    root.right.right = b.insert(9);
    root.left.right = b.insert(8);
    root.left.right.right = b.insert(11);
    root.left.right.left = b.insert(5);
    root.left.right.left.left = b.insert(6);
    root.left.right.left.right = b.insert(2);
    root.right.right.right = b.insert(4);
 
    // Function Call
    b.removePathLessThanKUtil(
        root, K, root.data);
}
}
 
// This code is contributed by Princi Singh

Javascript

<script>
 
// Javascript program for the above approach
 
// Tree Node Class
class Node
{
    constructor(val) 
    {
        this.left = null;
        this.right = null;
        this.data = val;
    }
}
 
// Function to insert node in the
// given Binary Tree
function insert(val)
{
    let n = new Node(val);
    return n;
}
 
// Utility function that deletes nodes
// from the Tree such that every root
// to leaf path sum is at least K
function removePathLessThanK(node, K, sum)
{
     
    // Base Case
    if (node == null) 
    {
        return null;
    }
 
    // Recurse to the left
    if (node.left != null) 
    {
        node.left = removePathLessThanK(
                    node.left, K,
                    sum + node.left.data);
    }
 
    // Recurse to the right
    if (node.right != null) 
    {
        node.right = removePathLessThanK(
                     node.right, K,
                     sum + node.right.data);
    }
 
    // Check path sum at leaf node
    // is lesser than K, return NULL
    if (node.left == null &&
        node.right == null && 
        sum < K) 
    {
        node = null;
        return node;
    }
 
    // Otherwise return the
    // current node as it is
    return node;
}
 
// Function to print the preorder
// traversal of the Tree
function viewTree(node)
{
     
    // If node is not NULL
    if (node != null) 
    {
         
        // Print the node
        document.write(node.data + " ");
 
        // Left and Right Traversal
        viewTree(node.left);
        viewTree(node.right);
    }
}
 
// Function that deletes the nodes
// from the Tree such that every root
// to leaf path sum is at least K
function removePathLessThanKUtil(node, K, sum)
{
     
    // Function Call to delete Nodes
    let result = removePathLessThanK(node, K, sum);
 
    // Preorder Traversal of the
    // modified Tree
    viewTree(result);
}
 
// Driver code
 
// Given sum K
let K = 27;
 
// Given Binary Tree
let root = null;
root = insert(5);
root.right = insert(3);
root.left = insert(4);
root.left.left = insert(9);
root.right.right = insert(9);
root.left.right = insert(8);
root.left.right.right = insert(11);
root.left.right.left = insert(5);
root.left.right.left.left = insert(6);
root.left.right.left.right = insert(2);
root.right.right.right = insert(4);
 
// Function Call
removePathLessThanKUtil(root, K, root.data);
 
// This code is contributed by suresh07
 
</script>

Output:

5 4 8 5 6 11

Time Complexity: O(N), where N is the number of nodes in the given Tree.
Auxiliary Space: O(N)

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Remove nodes from Binary Tree such that sum of all remaining root-to-leaf paths is atleast K

C++

Java

Python3

C#

Javascript

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