Maximum sum of Non-adjacent nodes

Problem Statement - link #

Given a binary tree with a value associated with each node, we need to choose a subset of these nodes such that sum of chosen nodes is maximum under a constraint that no two chosen node in subset should be directly connected that is, if we have taken a node in our sum then we can’t take its any children or parents in consideration and vice versa.

Your Task: You don’t need to read input or print anything. You just have to complete function getMaxSum() which accepts root node of the tree as parameter and returns the maximum sum as described.

Expected Time Complexity: O(N)
Expected Auxiliary Space: O(h)

Examples #

Example 1:

Input:
     11
    /  \
   1    2
Output: 11
Explanation: The maximum sum is sum of
node 11.

Example 2:

Input:
        1
      /   \
     2     3
    /     /  \
   4     5    6
Output: 16
Explanation: The maximum sum is sum of
nodes 1 4 5 6 , i.e 16. These nodes are
non adjacent.

Constraints #

• 1 <= Number of nodes <= 10^5
• 1 <= value of node <= 10^5

Solutions #

class Solution{
  public:
    pair<int, int> nitish(Node* root){
        if(!root) return {0,0};
        pair<int,int> p1 = nitish(root->left);
        pair<int,int> p2 = nitish(root->right);
        int inc = p1.second + p2.second + root->data;
        int ninc = max(p1.first,p1.second) + max(p2.first,p2.second);
        return {inc,ninc};
        
    }
    //Function to return the maximum sum of non-adjacent nodes.
    int getMaxSum(Node *root) 
    {
        // Add your code here
        pair<int, int> res = nitish(root);
        return max(res.first,res.second);
    }
};