Given a Binary Tree, the task is to print all prime levels of this tree.
Any level of a Binary tree is said to be a prime level, if all nodes of this level are prime.
Examples:
Input:
1
/ \
15 13
/ / \
11 7 29
\ /
2 3
Output: 11 7 29
2 3
Explanation:
Third and Fourth levels are prime levels.
Input:
7
/ \
23 41
/ \ \
31 16 3
/ \ \ /
2 5 17 11
/
23
Output: 7
23 41
2 5 17 11
23
Explanation:
First, Second, Fourth and
Fifth levels are prime levels.
Approach: In order to check if a level is Prime level or not,
- We first need to make a level order traversal of the binary tree to get the node values of each level.
- Here a Queue data structure is used to store the levels of the tree while doing the level order traversal.
- Then for each level, check if it is a prime level or not.
Below is the implementation of the above approach:
C++
// C++ program for printing a prime// levels of binary Tree#include <bits/stdc++.h>using namespace std;// A Tree nodestruct Node { int key; struct Node *left, *right;};// Utility function to create a new nodeNode* newNode(int key){ Node* temp = new Node; temp->key = key; temp->left = temp->right = NULL; return (temp);}// Function to check whether node// Value is prime or notbool isPrime(int n){ if (n == 1) return false; // Iterate from 2 to sqrt(n) for (int i = 2; i * i <= n; i++) { // If it has a factor if (n % i == 0) { return false; } } return true;}// Function to print a Prime levelvoid printLevel(struct Node* queue[], int index, int size){ for (int i = index; i < size; i++) { cout << queue[i]->key << " "; } cout << endl;}// Function to check whether given level is// prime level or notbool isLevelPrime(struct Node* queue[], int index, int size){ for (int i = index; i < size; i++) { // Check value of node is // pPrime or not if (!isPrime(queue[index++]->key)) { return false; } } // Return true if for loop // iIterate completely return true;}// Utility function to get Prime// Level of a given Binary treevoid findPrimeLevels(struct Node* node, struct Node* queue[], int index, int size){ // Print root node value, if Prime if (isPrime(queue[index]->key)) { cout << queue[index]->key << endl; } // Run while loop while (index < size) { int curr_size = size; // Run inner while loop while (index < curr_size) { struct Node* temp = queue[index]; // Push left child in a queue if (temp->left != NULL) queue[size++] = temp->left; // Push right child in a queue if (temp->right != NULL) queue[size++] = temp->right; // Increment index index++; } // If condition to check, level is // prime or not if (isLevelPrime( queue, index, size - 1)) { // Function call to print // prime level printLevel(queue, index, size); } }}// Function to find total no of nodes// In a given binary treeint findSize(struct Node* node){ // Base condition if (node == NULL) return 0; return 1 + findSize(node->left) + findSize(node->right);}// Function to find Prime levels// In a given binary treevoid printPrimeLevels(struct Node* node){ int t_size = findSize(node); // Create queue struct Node* queue[t_size]; // Push root node in a queue queue[0] = node; // Function call findPrimeLevels(node, queue, 0, 1);}// Driver Codeint main(){ /* 10 / \ 13 11 / \ 19 23 / \ / \ 21 29 43 15 / 7 */ // Create Binary Tree as shown Node* root = newNode(10); root->left = newNode(13); root->right = newNode(11); root->right->left = newNode(19); root->right->right = newNode(23); root->right->left->left = newNode(21); root->right->left->right = newNode(29); root->right->right->left = newNode(43); root->right->right->right = newNode(15); root->right->right->right->left = newNode(7); // Print Prime Levels printPrimeLevels(root); return 0;} |
Java
// Java program for the above approachpublic class Main{ // A Tree node static class Node { public int key; public Node left, right; public Node(int key) { this.key = key; left = right = null; } } // Utility function to create a new node static Node newNode(int key) { Node temp = new Node(key); return temp; } // Function to check whether node // Value is prime or not static boolean isPrime(int n) { if (n == 1) return false; // Iterate from 2 to sqrt(n) for(int i = 2; i * i <= n; i++) { // If it has a factor if (n % i == 0) { return false; } } return true; } // Function to print a Prime level static void printLevel(Node[] queue, int index, int size) { for(int i = index; i < size; i++) { System.out.print(queue[i].key + " "); } System.out.println(); } // Function to check whether given level is // prime level or not static boolean isLevelPrime(Node[] queue, int index, int size) { for(int i = index; i < size; i++) { // Check value of node is // pPrime or not if (!isPrime(queue[index++].key)) { return false; } } // Return true if for loop // iIterate completely return true; } // Utility function to get Prime // Level of a given Binary tree static void findPrimeLevels(Node node, Node[] queue, int index, int size) { // Print root node value, if Prime if (isPrime(queue[index].key)) { System.out.println(queue[index].key); } // Run while loop while (index < size) { int curr_size = size; // Run inner while loop while (index < curr_size) { Node temp = queue[index]; // Push left child in a queue if (temp.left != null) queue[size++] = temp.left; // Push right child in a queue if (temp.right != null) queue[size++] = temp.right; // Increment index index++; } // If condition to check, level is // prime or not if (isLevelPrime(queue, index, size - 1)) { // Function call to print // prime level printLevel(queue, index, size); } } } // Function to find total no of nodes // In a given binary tree static int findSize(Node node) { // Base condition if (node == null) return 0; return 1 + findSize(node.left) + findSize(node.right); } // Function to find Prime levels // In a given binary tree static void printPrimeLevels(Node node) { int t_size = findSize(node); // Create queue Node[] queue = new Node[t_size]; for(int i = 0; i < t_size; i++) { queue[i] = new Node(0); } // Push root node in a queue queue[0] = node; // Function call findPrimeLevels(node, queue, 0, 1); } public static void main(String[] args) { /* 10 / \ 13 11 / \ 19 23 / \ / \ 21 29 43 15 / 7 */ // Create Binary Tree as shown Node root = newNode(10); root.left = newNode(13); root.right = newNode(11); root.right.left = newNode(19); root.right.right = newNode(23); root.right.left.left = newNode(21); root.right.left.right = newNode(29); root.right.right.left = newNode(43); root.right.right.right = newNode(15); root.right.right.right.left = newNode(7); // Print Prime Levels printPrimeLevels(root); }}// This code is contributed by suresh07. |
Python3
# Python3 program for printing a prime# levels of binary Tree # A Tree nodeclass Node: def __init__(self, key): self.key = key self.left = None self.right = None # function to create a # new nodedef newNode(key): temp = Node(key); return temp; # Function to check whether # node Value is prime or notdef isPrime(n): if (n == 1): return False; i = 2 # Iterate from 2 # to sqrt(n) while(i * i <= n): # If it has a factor if (n % i == 0): return False; i += 1 return True;# Function to print a # Prime leveldef printLevel(queue, index, size): for i in range(index, size): print(queue[i].key, end = ' ') print() # Function to check whether # given level is prime level # or notdef isLevelPrime(queue, index, size): for i in range(index, size): # Check value of node is # pPrime or not if (not isPrime(queue[index].key)): index += 1 return False; # Return true if for loop # iIterate completely return True; # Utility function to get Prime# Level of a given Binary treedef findPrimeLevels(node, queue, index, size): # Print root node value, if Prime if (isPrime(queue[index].key)): print(queue[index].key) # Run while loop while (index < size): curr_size = size; # Run inner while loop while (index < curr_size): temp = queue[index]; # Push left child in a queue if (temp.left != None): queue[size] = temp.left; size+=1 # Push right child in a queue if (temp.right != None): queue[size] = temp.right; size+=1 # Increment index index+=1; # If condition to check, level # is prime or not if (isLevelPrime(queue, index, size - 1)): # Function call to print # prime level printLevel(queue, index, size); # Function to find total no # of nodes In a given binary# treedef findSize(node): # Base condition if (node == None): return 0; return (1 + findSize(node.left) + findSize(node.right)); # Function to find Prime levels# In a given binary treedef printPrimeLevels(node): t_size = findSize(node); # Create queue queue=[0 for i in range(t_size)] # Push root node in a queue queue[0] = node; # Function call findPrimeLevels(node, queue, 0, 1); # Driver code if __name__ == "__main__": ''' 10 / \ 13 11 / \ 19 23 / \ / \ 21 29 43 15 / 7 ''' # Create Binary Tree as shown root = newNode(10); root.left = newNode(13); root.right = newNode(11); root.right.left = newNode(19); root.right.right = newNode(23); root.right.left.left = newNode(21); root.right.left.right = newNode(29); root.right.right.left = newNode(43); root.right.right.right = newNode(15); root.right.right.right.left = newNode(7); # Print Prime Levels printPrimeLevels(root);# This code is contributed by Rutvik_56 |
C#
// C# program for printing a prime// levels of binary Treeusing System;using System.Collections.Generic;class GFG { // A Tree node class Node { public int key; public Node left, right; public Node(int key) { this.key = key; left = right = null; } } // Utility function to create a new node static Node newNode(int key) { Node temp = new Node(key); return temp; } // Function to check whether node // Value is prime or not static bool isPrime(int n) { if (n == 1) return false; // Iterate from 2 to sqrt(n) for(int i = 2; i * i <= n; i++) { // If it has a factor if (n % i == 0) { return false; } } return true; } // Function to print a Prime level static void printLevel(Node[] queue, int index, int size) { for(int i = index; i < size; i++) { Console.Write(queue[i].key + " "); } Console.WriteLine(); } // Function to check whether given level is // prime level or not static bool isLevelPrime(Node[] queue, int index, int size) { for(int i = index; i < size; i++) { // Check value of node is // pPrime or not if (!isPrime(queue[index++].key)) { return false; } } // Return true if for loop // iIterate completely return true; } // Utility function to get Prime // Level of a given Binary tree static void findPrimeLevels(Node node, Node[] queue, int index, int size) { // Print root node value, if Prime if (isPrime(queue[index].key)) { Console.WriteLine(queue[index].key); } // Run while loop while (index < size) { int curr_size = size; // Run inner while loop while (index < curr_size) { Node temp = queue[index]; // Push left child in a queue if (temp.left != null) queue[size++] = temp.left; // Push right child in a queue if (temp.right != null) queue[size++] = temp.right; // Increment index index++; } // If condition to check, level is // prime or not if (isLevelPrime(queue, index, size - 1)) { // Function call to print // prime level printLevel(queue, index, size); } } } // Function to find total no of nodes // In a given binary tree static int findSize(Node node) { // Base condition if (node == null) return 0; return 1 + findSize(node.left) + findSize(node.right); } // Function to find Prime levels // In a given binary tree static void printPrimeLevels(Node node) { int t_size = findSize(node); // Create queue Node[] queue = new Node[t_size]; for(int i = 0; i < t_size; i++) { queue[i] = new Node(0); } // Push root node in a queue queue[0] = node; // Function call findPrimeLevels(node, queue, 0, 1); } static void Main() { /* 10 / \ 13 11 / \ 19 23 / \ / \ 21 29 43 15 / 7 */ // Create Binary Tree as shown Node root = newNode(10); root.left = newNode(13); root.right = newNode(11); root.right.left = newNode(19); root.right.right = newNode(23); root.right.left.left = newNode(21); root.right.left.right = newNode(29); root.right.right.left = newNode(43); root.right.right.right = newNode(15); root.right.right.right.left = newNode(7); // Print Prime Levels printPrimeLevels(root); }}// This code is contributed by mukesh07. |
Javascript
<script>// Javascript program for printing a// prime levels of binary Tree// A Tree nodeclass Node{ constructor(key) { this.left = null; this.right = null; this.key = key; }}// Utility function to create a new nodefunction newNode(key){ let temp = new Node(key); return (temp);}// Function to check whether node// Value is prime or notfunction isPrime(n){ if (n == 1) return false; // Iterate from 2 to sqrt(n) for(let i = 2; i * i <= n; i++) { // If it has a factor if (n % i == 0) { return false; } } return true;}// Function to print a Prime levelfunction printLevel(queue, index, size){ for(let i = index; i < size; i++) { document.write(queue[i].key + " "); } document.write("</br>");}// Function to check whether given level is// prime level or notfunction isLevelPrime(queue, index, size){ for(let i = index; i < size; i++) { // Check value of node is // pPrime or not if (!isPrime(queue[index++].key)) { return false; } } // Return true if for loop // iIterate completely return true;}// Utility function to get Prime// Level of a given Binary treefunction findPrimeLevels(node, queue, index, size){ // Print root node value, if Prime if (isPrime(queue[index].key)) { document.write(queue[index].key + "</br>"); } // Run while loop while (index < size) { let curr_size = size; // Run inner while loop while (index < curr_size) { let temp = queue[index]; // Push left child in a queue if (temp.left != null) queue[size++] = temp.left; // Push right child in a queue if (temp.right != null) queue[size++] = temp.right; // Increment index index++; } // If condition to check, level is // prime or not if (isLevelPrime(queue, index, size - 1)) { // Function call to print // prime level printLevel(queue, index, size); } }}// Function to find total no of nodes// In a given binary treefunction findSize(node){ // Base condition if (node == null) return 0; return 1 + findSize(node.left) + findSize(node.right);}// Function to find Prime levels// In a given binary treefunction printPrimeLevels(node){ let t_size = findSize(node); // Create queue let queue = new Array(t_size); for(let i = 0; i < t_size; i++) { queue[i] = new Node(); } // Push root node in a queue queue[0] = node; // Function call findPrimeLevels(node, queue, 0, 1);}// Driver code/* 10 / \ 13 11 / \ 19 23 / \ / \ 21 29 43 15 / 7 */// Create Binary Tree as shownlet root = newNode(10);root.left = newNode(13);root.right = newNode(11);root.right.left = newNode(19);root.right.right = newNode(23);root.right.left.left = newNode(21);root.right.left.right = newNode(29);root.right.right.left = newNode(43);root.right.right.right = newNode(15);root.right.right.right.left = newNode(7);// Print Prime LevelsprintPrimeLevels(root);// This code is contributed by mukesh07</script> |
Output:
13 11 19 23 7
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