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Find the maximum sum leaf to root path in a Binary Tree

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Given a Binary Tree, find the maximum sum path from a leaf to root.

For example, in the following tree, there are three leaf to root paths 8->-2->10, -4->-2->10 and 7->10. The sums of these three paths are 16, 4 and 17 respectively. The maximum of them is 17 and the path for maximum is 7->10.

                  10
/ \
-2 7
/ \
8 -4

Solution

1) First find the leaf node that is on the maximum sum path. In the following code getTargetLeaf() does this by assigning the result to *target_leaf_ref.

2) Once we have the target leaf node, we can print the maximum sum path by traversing the tree. In the following code, printPath() does this. The main function is maxSumPath() that uses above two functions to get the complete solution.

C++

// CPP program to find maximum sum leaf to root
// path in Binary Tree
#include <bits/stdc++.h>
using namespace std;
 
/* A tree node structure */
class node {
public:
    int data;
    node* left;
    node* right;
};
 
// A utility function that prints all nodes
// on the path from root to target_leaf
bool printPath(node* root,
               node* target_leaf)
{
    // base case
    if (root == NULL)
        return false;
 
    // return true if this node is the target_leaf
    // or target leaf is present in one of its
    // descendants
    if (root == target_leaf || printPath(root->left, target_leaf) ||
                               printPath(root->right, target_leaf)) {
        cout << root->data << " ";
        return true;
    }
 
    return false;
}
 
// This function Sets the target_leaf_ref to refer
// the leaf node of the maximum path sum. Also,
// returns the max_sum using max_sum_ref
void getTargetLeaf(node* Node, int* max_sum_ref,
                   int curr_sum, node** target_leaf_ref)
{
    if (Node == NULL)
        return;
 
    // Update current sum to hold sum of nodes on path
    // from root to this node
    curr_sum = curr_sum + Node->data;
 
    // If this is a leaf node and path to this node has
    // maximum sum so far, then make this node target_leaf
    if (Node->left == NULL && Node->right == NULL) {
        if (curr_sum > *max_sum_ref) {
            *max_sum_ref = curr_sum;
            *target_leaf_ref = Node;
        }
    }
 
    // If this is not a leaf node, then recur down
    // to find the target_leaf
    getTargetLeaf(Node->left, max_sum_ref, curr_sum,
                  target_leaf_ref);
    getTargetLeaf(Node->right, max_sum_ref, curr_sum,
                  target_leaf_ref);
}
 
// Returns the maximum sum and prints the nodes on max
// sum path
int maxSumPath(node* Node)
{
    // base case
    if (Node == NULL)
        return 0;
 
    node* target_leaf;
    int max_sum = INT_MIN;
 
    // find the target leaf and maximum sum
    getTargetLeaf(Node, &max_sum, 0, &target_leaf);
 
    // print the path from root to the target leaf
    printPath(Node, target_leaf);
 
    return max_sum; // return maximum sum
}
 
/* Utility function to create a new Binary Tree node */
node* newNode(int data)
{
    node* temp = new node;
    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;
    return temp;
}
 
/* Driver function to test above functions */
int main()
{
    node* root = NULL;
 
    /* Constructing tree given in the above figure */
    root = newNode(10);
    root->left = newNode(-2);
    root->right = newNode(7);
    root->left->left = newNode(8);
    root->left->right = newNode(-4);
 
    cout << "Following are the nodes on the maximum "
            "sum path \n";
    int sum = maxSumPath(root);
    cout << "\nSum of the nodes is " << sum;
    return 0;
}
 
// This code is contributed by rathbhupendra

                    

C

// C program to find maximum sum leaf to root
// path in Binary Tree
#include <limits.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
 
/* A tree node structure */
struct node {
    int data;
    struct node* left;
    struct node* right;
};
 
// A utility function that prints all nodes
// on the path from root to target_leaf
bool printPath(struct node* root,
               struct node* target_leaf)
{
    // base case
    if (root == NULL)
        return false;
 
    // return true if this node is the target_leaf
    // or target leaf is present in one of its
    // descendants
    if (root == target_leaf || printPath(root->left, target_leaf) ||
                               printPath(root->right, target_leaf)) {
        printf("%d ", root->data);
        return true;
    }
 
    return false;
}
 
// This function Sets the target_leaf_ref to refer
// the leaf node of the maximum path sum. Also,
// returns the max_sum using max_sum_ref
void getTargetLeaf(struct node* node, int* max_sum_ref,
                   int curr_sum, struct node** target_leaf_ref)
{
    if (node == NULL)
        return;
 
    // Update current sum to hold sum of nodes on path
    // from root to this node
    curr_sum = curr_sum + node->data;
 
    // If this is a leaf node and path to this node has
    // maximum sum so far, then make this node target_leaf
    if (node->left == NULL && node->right == NULL) {
        if (curr_sum > *max_sum_ref) {
            *max_sum_ref = curr_sum;
            *target_leaf_ref = node;
        }
    }
 
    // If this is not a leaf node, then recur down
    // to find the target_leaf
    getTargetLeaf(node->left, max_sum_ref, curr_sum,
                  target_leaf_ref);
    getTargetLeaf(node->right, max_sum_ref, curr_sum,
                  target_leaf_ref);
}
 
// Returns the maximum sum and prints the nodes on max
// sum path
int maxSumPath(struct node* node)
{
    // base case
    if (node == NULL)
        return 0;
 
    struct node* target_leaf;
    int max_sum = INT_MIN;
 
    // find the target leaf and maximum sum
    getTargetLeaf(node, &max_sum, 0, &target_leaf);
 
    // print the path from root to the target leaf
    printPath(node, target_leaf);
 
    return max_sum; // return maximum sum
}
 
/* Utility function to create a new Binary Tree node */
struct node* newNode(int data)
{
    struct node* temp = (struct node*)malloc(sizeof(struct node));
    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;
    return temp;
}
 
/* Driver function to test above functions */
int main()
{
    struct node* root = NULL;
 
    /* Constructing tree given in the above figure */
    root = newNode(10);
    root->left = newNode(-2);
    root->right = newNode(7);
    root->left->left = newNode(8);
    root->left->right = newNode(-4);
 
    printf("Following are the nodes on the maximum "
           "sum path \n");
    int sum = maxSumPath(root);
    printf("\nSum of the nodes is %d ", sum);
 
    getchar();
    return 0;
}

                    

Java

// Java program to find maximum sum leaf to root
// path in Binary Tree
 
// A Binary Tree node
class Node {
    int data;
    Node left, right;
 
    Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
// A wrapper class is used so that max_no
// can be updated among function calls.
class Maximum {
    int max_no = Integer.MIN_VALUE;
}
 
class BinaryTree {
    Node root;
    Maximum max = new Maximum();
    Node target_leaf = null;
 
    // A utility function that prints all nodes on the
    // path from root to target_leaf
    boolean printPath(Node node, Node target_leaf)
    {
        // base case
        if (node == null)
            return false;
 
        // return true if this node is the target_leaf or
        // target leaf is present in one of its descendants
        if (node == target_leaf || printPath(node.left, target_leaf)
            || printPath(node.right, target_leaf)) {
            System.out.print(node.data + " ");
            return true;
        }
 
        return false;
    }
 
    // This function Sets the target_leaf_ref to refer
    // the leaf node of the maximum path sum. Also,
    // returns the max_sum using max_sum_ref
    void getTargetLeaf(Node node, Maximum max_sum_ref,
                       int curr_sum)
    {
        if (node == null)
            return;
 
        // Update current sum to hold sum of nodes on
        // path from root to this node
        curr_sum = curr_sum + node.data;
 
        // If this is a leaf node and path to this node
        // has maximum sum so far, the n make this node
        // target_leaf
        if (node.left == null && node.right == null) {
            if (curr_sum > max_sum_ref.max_no) {
                max_sum_ref.max_no = curr_sum;
                target_leaf = node;
            }
        }
 
        // If this is not a leaf node, then recur down
        // to find the target_leaf
        getTargetLeaf(node.left, max_sum_ref, curr_sum);
        getTargetLeaf(node.right, max_sum_ref, curr_sum);
    }
 
    // Returns the maximum sum and prints the nodes on
    // max sum path
    int maxSumPath()
    {
        // base case
        if (root == null)
            return 0;
 
        // find the target leaf and maximum sum
        getTargetLeaf(root, max, 0);
 
        // print the path from root to the target leaf
        printPath(root, target_leaf);
        return max.max_no; // return maximum sum
    }
 
    // driver function to test the above functions
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(10);
        tree.root.left = new Node(-2);
        tree.root.right = new Node(7);
        tree.root.left.left = new Node(8);
        tree.root.left.right = new Node(-4);
        System.out.println("Following are the nodes "
                           + "on maximum sum path");
        int sum = tree.maxSumPath();
        System.out.println("");
        System.out.println("Sum of nodes is : " + sum);
    }
}
// This code has been contributed by Mayank Jaiswal

                    

Python3

# Python3 program to find maximum sum leaf to root
# path in Binary Tree
 
# A tree node structure
class node :
    def __init__(self):
        self.data = 0
        self.left = None
        self.right = None
 
# A utility function that prints all nodes
# on the path from root to target_leaf
def printPath( root,target_leaf):
 
    # base case
    if (root == None):
        return False
 
    # return True if this node is the target_leaf
    # or target leaf is present in one of its
    # descendants
    if (root == target_leaf or
        printPath(root.left, target_leaf) or
        printPath(root.right, target_leaf)) :
        print( root.data, end = " ")
        return True
     
    return False
 
max_sum_ref = 0
target_leaf_ref = None
 
# This function Sets the target_leaf_ref to refer
# the leaf node of the maximum path sum. Also,
# returns the max_sum using max_sum_ref
def getTargetLeaf(Node, curr_sum):
     
    global max_sum_ref
    global target_leaf_ref
     
    if (Node == None):
        return
 
    # Update current sum to hold sum of nodes on path
    # from root to this node
    curr_sum = curr_sum + Node.data
 
    # If this is a leaf node and path to this node has
    # maximum sum so far, then make this node target_leaf
    if (Node.left == None and Node.right == None):
        if (curr_sum > max_sum_ref) :
            max_sum_ref = curr_sum
            target_leaf_ref = Node
         
    # If this is not a leaf node, then recur down
    # to find the target_leaf
    getTargetLeaf(Node.left, curr_sum)
    getTargetLeaf(Node.right, curr_sum)
 
# Returns the maximum sum and prints the nodes on max
# sum path
def maxSumPath( Node):
     
    global max_sum_ref
    global target_leaf_ref
     
    # base case
    if (Node == None):
        return 0
 
    target_leaf_ref = None
    max_sum_ref = -32676
 
    # find the target leaf and maximum sum
    getTargetLeaf(Node, 0)
     
    # print the path from root to the target leaf
    printPath(Node, target_leaf_ref);
 
    return max_sum_ref; # return maximum sum
 
# Utility function to create a new Binary Tree node
def newNode(data):
 
    temp = node();
    temp.data = data;
    temp.left = None;
    temp.right = None;
    return temp;
 
# Driver function to test above functions
 
root = None;
 
# Constructing tree given in the above figure
root = newNode(10);
root.left = newNode(-2);
root.right = newNode(7);
root.left.left = newNode(8);
root.left.right = newNode(-4);
 
print( "Following are the nodes on the maximum sum path ");
sum = maxSumPath(root);
print( "\nSum of the nodes is " , sum);
 
# This code is contributed by Arnab Kundu

                    

C#

using System;
 
// C# program to find maximum sum leaf to root
// path in Binary Tree
 
// A Binary Tree node
public class Node {
    public int data;
    public Node left, right;
 
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
// A wrapper class is used so that max_no
// can be updated among function calls.
public class Maximum {
    public int max_no = int.MinValue;
}
 
public class BinaryTree {
    public Node root;
    public Maximum max = new Maximum();
    public Node target_leaf = null;
 
    // A utility function that prints all nodes on the
    // path from root to target_leaf
    public virtual bool printPath(Node node, Node target_leaf)
    {
        // base case
        if (node == null) {
            return false;
        }
 
        // return true if this node is the target_leaf or
        // target leaf is present in one of its descendants
        if (node == target_leaf || printPath(node.left, target_leaf)
            || printPath(node.right, target_leaf)) {
            Console.Write(node.data + " ");
            return true;
        }
 
        return false;
    }
 
    // This function Sets the target_leaf_ref to refer
    // the leaf node of the maximum path sum. Also,
    // returns the max_sum using max_sum_ref
    public virtual void getTargetLeaf(Node node, Maximum max_sum_ref,
                                      int curr_sum)
    {
        if (node == null) {
            return;
        }
 
        // Update current sum to hold sum of nodes on
        // path from root to this node
        curr_sum = curr_sum + node.data;
 
        // If this is a leaf node and path to this node
        // has maximum sum so far, the n make this node
        // target_leaf
        if (node.left == null && node.right == null) {
            if (curr_sum > max_sum_ref.max_no) {
                max_sum_ref.max_no = curr_sum;
                target_leaf = node;
            }
        }
 
        // If this is not a leaf node, then recur down
        // to find the target_leaf
        getTargetLeaf(node.left, max_sum_ref, curr_sum);
        getTargetLeaf(node.right, max_sum_ref, curr_sum);
    }
 
    // Returns the maximum sum and prints the nodes on
    // max sum path
    public virtual int maxSumPath()
    {
        // base case
        if (root == null) {
            return 0;
        }
 
        // find the target leaf and maximum sum
        getTargetLeaf(root, max, 0);
 
        // print the path from root to the target leaf
        printPath(root, target_leaf);
        return max.max_no; // return maximum sum
    }
 
    // driver function to test the above functions
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(10);
        tree.root.left = new Node(-2);
        tree.root.right = new Node(7);
        tree.root.left.left = new Node(8);
        tree.root.left.right = new Node(-4);
        Console.WriteLine("Following are the nodes "
                          + "on maximum sum path");
        int sum = tree.maxSumPath();
        Console.WriteLine("");
        Console.WriteLine("Sum of nodes is : " + sum);
    }
}
 
// This code is contributed by Shrikant13

                    

Javascript

// JavaScript program to find maximum sum leaf to root
// path in Binary Tree
 
// A tree node structure
class Node {
    constructor() {
        this.data = 0;
        this.left = null;
        this.right = null;
    }
}
 
// A utility function that prints all nodes
// on the path from root to target_leaf
function printPath(root, target_leaf) {
    // base case
    if (root === null)
        return false;
 
    // return true if this node is the target_leaf
    // or target leaf is present in one of its
    // descendants
    if (root === target_leaf ||
        printPath(root.left, target_leaf) ||
        printPath(root.right, target_leaf)) {
        process.stdout.write(root.data + " ");
        return true;
    }
     
    return false;
}
 
let max_sum_ref = 0;
let target_leaf_ref = null;
 
// This function Sets the target_leaf_ref to refer
// the leaf node of the maximum path sum. Also,
// returns the max_sum using max_sum_ref
function getTargetLeaf(Node, curr_sum) {
     
    if (Node === null)
        return;
 
    // Update current sum to hold sum of nodes on path
    // from root to this node
    curr_sum = curr_sum + Node.data;
 
    // If this is a leaf node and path to this node has
    // maximum sum so far, then make this node target_leaf
    if (Node.left === null && Node.right === null) {
        if (curr_sum > max_sum_ref) {
            max_sum_ref = curr_sum;
            target_leaf_ref = Node;
        }
    }
     
    // If this is not a leaf node, then recur down
    // to find the target_leaf
    getTargetLeaf(Node.left, curr_sum);
    getTargetLeaf(Node.right, curr_sum);
}
 
// Returns the maximum sum and prints the nodes on max
// sum path
function maxSumPath(Node) {
     
    // base case
    if (Node === null)
        return 0;
 
    target_leaf_ref = null;
    max_sum_ref = -32676;
 
    // find the target leaf and maximum sum
    getTargetLeaf(Node, 0);
     
    // print the path from root to the target leaf
    printPath(Node, target_leaf_ref);
 
    return max_sum_ref; // return maximum sum
}
 
// Utility function to create a new Binary Tree node
function newNode(data) {
 
    let temp = new Node();
    temp.data = data;
    temp.left = null;
    temp.right = null;
    return temp;
}
 
// Driver function to test above functions
 
let root = null;
 
// Constructing tree given in the above figure
root = newNode(10);
root.left = newNode(-2);
root.right = newNode(7);
root.left.left = newNode(8);
root.left.right = newNode(-4);
 
console.log("Following are the nodes on the maximum sum path ");
let sum = maxSumPath(root);
console.log("\nSum of the nodes is ", sum);
 
// This code is contributed by phasing17

                    

Output:

Following are the nodes on the maximum sum path
7 10
Sum of the nodes is 17

Time Complexity:

Time complexity of the above solution is O(n) as it involves tree traversal two times.



Last Updated : 21 Sep, 2023
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