# Find the node whose sum with X has maximum set bits

Given a tree, and the weights of all the nodes and an integer **x**, the task is to find a node **i** such that **weight[i] + x** has the maximum set bits. If two or more nodes have the same count of set bits when added with **x** then find the one with the minimum value.

**Examples:**

Input:

x = 15

Output:4

Node 1: setbits(5 + 15) = 2

Node 2: setbits(10 + 15) = 3

Node 3: setbits(11 + 15) = 3

Node 4: setbits(8 + 15) = 4

Node 5: setbits(6 + 15) = 3

**Approach:** Perform dfs on the tree and keep track of the node whose sum with **x** has maximum set bits. If two or more nodes have equal count of set bits then choose the one with the minimum number.

Below is the implementation of the above approach:

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `maximum = INT_MIN, x, ans = INT_MAX; ` ` ` `vector<` `int` `> graph[100]; ` `vector<` `int` `> weight(100); ` ` ` `// Function to perform dfs to find ` `// the maximum set bits value ` `void` `dfs(` `int` `node, ` `int` `parent) ` `{ ` ` ` `// If current set bits value is greater than ` ` ` `// the current maximum ` ` ` `int` `a = __builtin_popcount(weight[node] + x); ` ` ` `if` `(maximum < a) { ` ` ` `maximum = a; ` ` ` `ans = node; ` ` ` `} ` ` ` ` ` `// If count is equal to the maximum ` ` ` `// then choose the node with minimum value ` ` ` `else` `if` `(maximum == a) ` ` ` `ans = min(ans, node); ` ` ` ` ` `for` `(` `int` `to : graph[node]) { ` ` ` `if` `(to == parent) ` ` ` `continue` `; ` ` ` `dfs(to, node); ` ` ` `} ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `x = 15; ` ` ` ` ` `// Weights of the node ` ` ` `weight[1] = 5; ` ` ` `weight[2] = 10; ` ` ` `weight[3] = 11; ` ` ` `weight[4] = 8; ` ` ` `weight[5] = 6; ` ` ` ` ` `// Edges of the tree ` ` ` `graph[1].push_back(2); ` ` ` `graph[2].push_back(3); ` ` ` `graph[2].push_back(4); ` ` ` `graph[1].push_back(5); ` ` ` ` ` `dfs(1, 1); ` ` ` ` ` `cout << ans; ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

4

## Recommended Posts:

- Find the node whose sum with X has minimum set bits
- Find the node whose xor with x gives maximum value
- Find element with the maximum set bits in an array
- Find the node whose absolute difference with X gives maximum value
- Find the maximum node at a given level in a binary tree
- Find the node with maximum value in a Binary Search Tree
- Print the number of set bits in each node of a Binary Tree
- Minimum cost path from source node to destination node via an intermediate node
- Node having maximum sum of immediate children and itself in n-ary tree
- Get maximum left node in binary tree
- Maximum difference between node and its ancestor in Binary Tree
- Iterative Segment Tree (Range Maximum Query with Node Update)
- Minimum and maximum node that lies in the path connecting two nodes in a Binary Tree
- Find next right node of a given key
- Find next right node of a given key | Set 2

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.