Maximize count of set bits in a root to leaf path in a binary tree

Given a binary tree, the task is to find the total count of set bits in the node values of all the root to leaf paths and print the maximum among them.

Examples:

Input:

Output: 12
Explanation:
Path 1: 15(1111)->3(0011)->5(0101) = 8
Path 2: 15(1111)->3(0011)->1(0001) = 7
Path 3: 15(01111)->7(00111)->31(11111) = 12 (maximum)
Path 4: 15(1111)->7(0111)->9(1001) = 9
Therefore, the maximum count of set bits obtained in a path is 12.

Input:

Output: 13
Explanation:
Path 1: 31(11111)->3(00011)->7(00111) = 10
Path 2: 31(11111)->3(00011)->1(00001) = 8
Path 3: 31(11111)->15(01111)->5(00101) = 11
Path 4: 31(11111)->15(01111)->23(10111) = 13 (maximum)
Therefore, the maximum count of set bits obtained in a path is 13.

Approach: 
Follow the steps below to solve the problem:

• Traverse each node recursively, starting from the root node
• Calculate the number of set bits in the value of the current node.
• Update the maximum count of set bits(stored in a variable, say maxm).
• Traverse its left and right subtree.
• After complete traversal of all the nodes of the tree, print the final value of maxm as the answer.

Below is the implementation of the above approach:

C++

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
int maxm = 0;

// Node structure
struct Node {
    int val;

    // Pointers to left
    // and right child
    Node *left, *right;

    // Initialize constructor
    Node(int x)
    {
        val = x;
        left = NULL;
        right = NULL;
    }
};

// Function to find the maximum
// count of setbits in a root to leaf
void maxm_setbits(Node* root, int ans)
{
    // Check if root is not null
    if (!root)
        return;

    if (root->left == NULL
        && root->right == NULL) {

        ans += __builtin_popcount(root->val);

        // Update the maximum count
        // of setbits
        maxm = max(ans, maxm);

        return;
    }

    // Traverse left of binary tree
    maxm_setbits(root->left,
                ans + __builtin_popcount(
                        root->val));

    // Traverse right of the binary tree
    maxm_setbits(root->right,
                ans + __builtin_popcount(
                        root->val));
}

// Driver Code
int main()
{
    Node* root = new Node(15);
    root->left = new Node(3);
    root->right = new Node(7);
    root->left->left = new Node(5);
    root->left->right = new Node(1);
    root->right->left = new Node(31);
    root->right->right = new Node(9);

    maxm_setbits(root, 0);

    cout << maxm << endl;

    return 0;
}

Java

// Java Program to implement
// the above approach
import java.util.*;
class GFG{

static int maxm = 0;

// Node structure
static class Node
{
    int val;

    // Pointers to left
    // and right child
    Node left, right;

    // Initialize constructor
    Node(int x)
    {
        val = x;
        left = null;
        right = null;
    }
};

// Function to find the maximum
// count of setbits in a root to leaf
static void maxm_setbits(Node root, int ans)
{
    // Check if root is not null
    if (root == null)
        return;

    if (root.left == null &&
        root.right == null)
    {
        ans += Integer.bitCount(root.val);

        // Update the maximum count
        // of setbits
        maxm = Math.max(ans, maxm);

        return;
    }

    // Traverse left of binary tree
    maxm_setbits(root.left,
                ans + Integer.bitCount(
                        root.val));

    // Traverse right of the binary tree
    maxm_setbits(root.right,
                ans + Integer.bitCount(
                        root.val));
}

// Driver Code
public static void main(String[] args)
{
    Node root = new Node(15);
    root.left = new Node(3);
    root.right = new Node(7);
    root.left.left = new Node(5);
    root.left.right = new Node(1);
    root.right.left = new Node(31);
    root.right.right = new Node(9);

    maxm_setbits(root, 0);

    System.out.print(maxm +"\n");

}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program to implement
# the above approach
maxm = 0

# Node class
class Node:

    # Initialise constructor
    def __init__(self, x):

        self.val = x
        self.left = None
        self.right = None

# Function to count the number of 1 in number
def count_1(n):

    count = 0
    while (n):
        count += n & 1
        n >>= 1

    return count

# Function to find the maximum
# count of setbits in a root to leaf
def maxm_setbits(root, ans):

    global maxm

    # Check if root is null
    if not root:
        return

    if (root.left == None and
        root.right == None):
        ans += count_1(root.val)

        # Update the maximum count
        # of setbits
        maxm = max(ans, maxm)
        return

    # Traverse left of binary tree
    maxm_setbits(root.left,
                 ans + count_1(root.val))

    # Traverse right of the binary tree
    maxm_setbits(root.right,
                 ans + count_1(root.val))

# Driver code
root = Node(15)
root.left = Node(3)
root.right = Node(7)
root.left.left = Node(5)
root.left.right = Node(1)
root.right.left = Node(31)
root.right.right = Node(9)

maxm_setbits(root, 0)

print(maxm)

# This code is contributed by Stuti Pathak

C#

// C# program for the above approach
using System;
class GFG{

// Function to Sort a Bitonic array
// in constant space
static void sortArr(int []a, int n)
{
    int i, k;

    // Initialise the value of k
    k = (int)(Math.Log(n) / Math.Log(2));
    k = (int) Math.Pow(2, k);

    // In each iteration compare elements
    // k distance apart and swap if
    // they are not in order
    while (k > 0)
    {
        for(i = 0; i + k < n; i++)
            if (a[i] > a[i + k])
            {
                int tmp = a[i];
                a[i] = a[i + k];
                a[i + k] = tmp;
            }

        // k is reduced to half
        // after every iteration
        k = k / 2;
    }

    // Print the array elements
    for(i = 0; i < n; i++)
    {
        Console.Write(a[i] + " ");
    }
}

// Driver code
public static void Main(String[] args)
{

    // Given array []arr
    int []arr = { 5, 20, 30, 40, 36,
                  33, 25, 15, 10 };
    int n = arr.Length;

    // Function call
    sortArr(arr, n);
}
}

// This code is contributed by gauravrajput1

Javascript

<script>

// JavaScript Program to implement
// the above approach
let maxm = 0;

// Node structure
class Node
{

    // Initialize constructor
    constructor(x)
    {
        this.val = x;
        this.left = null;
        this.right = null;
    }
}

var root;

// Function to find the maximum
// count of setbits in a root to leaf
function maxm_setbits(root, ans)
{

    // Check if root is not null
    if (!root)
        return;

    if (root.left == null &&
        root.right == null)
    {

        ans += (root.val).toString(2).split('').filter(
          y => y == '1').length;

        // Update the maximum count
        // of setbits
        maxm = Math.max(ans, maxm);

        return;
    }

    // Traverse left of binary tree
    maxm_setbits(root.left,
    ans + (root.val).toString(2).split('').filter(
     y => y == '1').length);

    // Traverse right of the binary tree
    maxm_setbits(root.right,
    ans + (root.val).toString(2).split('').filter(
      y => y == '1').length);
}

// Driver Code
root = new Node(15);
root.left = new Node(3);
root.right = new Node(7);
root.left.left = new Node(5);
root.left.right = new Node(1);
root.right.left = new Node(31);
root.right.right = new Node(9);

maxm_setbits(root, 0);

document.write(maxm);

// This code is contributed by Dharanendra L V.

</script>

Output:

12

Time Complexity: O(N), where N denotes the number of nodes. 
Auxiliary Space: O(1)