Print the nodes of the Binary Tree whose height is a Prime number

Given a binary tree, our task is to print the nodes whose height is a prime number starting from the root node.

Examples:

Input:     
             1
           /   \
          2     3
         /  \
        4    5
Output: 4 5
Explanation:
For this tree: 
Height of Node 1 - 0, 
Height of Node 2 - 1, 
Height of Node 3 - 1, 
Height of Node 4 - 2, 
Height of Node 5 - 2. 
Hence, the nodes whose height
is a prime number are 4, and 5.

Input:     
             1
           /   \
          2     5
         /  \
        3    4
Output: 3 4
Explanation:
For this tree: 
Height of Node 1 - 0, 
Height of Node 2 - 1, 
Height of Node 3 - 2, 
Height of Node 4 - 2, 
Height of Node 5 - 1. 
Hence, the nodes whose height
is a prime number are 3, and 4.

Approach: To solve the problem mentioned above,

  1. We have to perform Depth First Search(DFS) on the tree and for every node, store the height of every node as we move down the tree.
  2. Iterate over the height array of each node and check if it prime or not.
  3. If yes then print the node else ignore it.

Below is the implementation of the above approach:

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// C++ implementation of nodes
// at prime height in the given tree
  
#include <bits/stdc++.h>
using namespace std;
  
#define MAX 100000
  
vector<int> graph[MAX + 1];
  
// To store Prime Numbers
vector<bool> Prime(MAX + 1, true);
  
// To store height of each node
int height[MAX + 1];
  
// Function to find the
// prime numbers till 10^5
void SieveOfEratosthenes()
{
  
    int i, j;
    Prime[0] = Prime[1] = false;
    for (i = 2; i * i <= MAX; i++) {
  
        // Traverse all multiple of i
        // and make it false
        if (Prime[i]) {
  
            for (j = 2 * i; j < MAX; j += i) {
                Prime[j] = false;
            }
        }
    }
}
  
// Function to perform dfs
void dfs(int node, int parent, int h)
{
    // Store the height of node
    height[node] = h;
  
    for (int to : graph[node]) {
        if (to == parent)
            continue;
        dfs(to, node, h + 1);
    }
}
  
// Function to find the nodes
// at prime height
void primeHeightNode(int N)
{
    // To precompute prime number till 10^5
    SieveOfEratosthenes();
  
    for (int i = 1; i <= N; i++) {
        // Check if height[node] is prime
        if (Prime[height[i]]) {
            cout << i << " ";
        }
    }
}
  
// Driver code
int main()
{
    // Number of nodes
    int N = 5;
  
    // Edges of the tree
    graph[1].push_back(2);
    graph[1].push_back(3);
    graph[2].push_back(4);
    graph[2].push_back(5);
  
    dfs(1, 1, 0);
  
    primeHeightNode(N);
  
    return 0;
}

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Output:

4 5

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