Factor Tree of a given Number
Factor Tree is an intuitive method to understand the factors of a number. It shows how all the factors are been derived from the number. It is a special diagram where you find the factors of a number, then the factors of those numbers, etc until you can’t factor anymore. The ends are all the prime factors of the original number.
Example:
Input : v = 48
Output : Root of below tree
48
/\
2 24
/\
2 12
/\
2 6
/\
2 3
The factor tree is created recursively. A binary tree is used.
- We start with a number and find the minimum divisor possible.
- Then, we divide the parent number by the minimum divisor.
- We store both the divisor and quotient as two children of the parent number.
- Both the children are sent into function recursively.
- If a divisor less than half the number is not found, two children are stored as NULL.
CPP
// C++ program to construct Factor Tree for// a given number#include<bits/stdc++.h>using namespace std;// Tree nodestruct Node{ struct Node *left, *right; int key;};// Utility function to create a new tree NodeNode* newNode(int key){ Node* temp = new Node; temp->key = key; temp->left = temp->right = NULL; return temp;}// Constructs factor tree for given value and stores// root of tree at given reference.void createFactorTree(struct Node **node_ref, int v){ (*node_ref) = newNode(v); // the number is factorized for (int i = 2 ; i < v/2 ; i++) { if (v % i != 0) continue; // If we found a factor, we construct left // and right subtrees and return. Since we // traverse factors starting from smaller // to greater, left child will always have // smaller factor createFactorTree(&((*node_ref)->left), i); createFactorTree(&((*node_ref)->right), v/i); return; }}// Iterative method to find the height of Binary Treevoid printLevelOrder(Node *root){ // Base Case if (root == NULL) return; queue<Node *> q; q.push(root); while (q.empty() == false) { // Print front of queue and remove // it from queue Node *node = q.front(); cout << node->key << " "; q.pop(); if (node->left != NULL) q.push(node->left); if (node->right != NULL) q.push(node->right); }}// driver programint main(){ int val = 48;// sample value struct Node *root = NULL; createFactorTree(&root, val); cout << "Level order traversal of " "constructed factor tree"; printLevelOrder(root); return 0;} |
Java
// Java program to conFactor Tree for// a given numberimport java.util.*;class GFG{ // Tree node static class Node { Node left, right; int key; }; static Node root; // Utility function to create a new tree Node static Node newNode(int key) { Node temp = new Node(); temp.key = key; temp.left = temp.right = null; return temp; } // Constructs factor tree for given value and stores // root of tree at given reference. static Node createFactorTree(Node node_ref, int v) { (node_ref) = newNode(v); // the number is factorized for (int i = 2 ; i < v/2 ; i++) { if (v % i != 0) continue; // If we found a factor, we conleft // and right subtrees and return. Since we // traverse factors starting from smaller // to greater, left child will always have // smaller factor node_ref.left = createFactorTree(((node_ref).left), i); node_ref.right = createFactorTree(((node_ref).right), v/i); return node_ref; } return node_ref; } // Iterative method to find the height of Binary Tree static void printLevelOrder(Node root) { // Base Case if (root == null) return; Queue<Node > q = new LinkedList<>(); q.add(root); while (q.isEmpty() == false) { // Print front of queue and remove // it from queue Node node = q.peek(); System.out.print(node.key + " "); q.remove(); if (node.left != null) q.add(node.left); if (node.right != null) q.add(node.right); } } // Driver program public static void main(String[] args) { int val = 48;// sample value root = null; root = createFactorTree(root, val); System.out.println("Level order traversal of "+ "constructed factor tree"); printLevelOrder(root); }}// This code is contributed by Rajput-Ji |
C#
// C# program to conFactor Tree for// a given numberusing System;using System.Collections.Generic;public class GFG{ // Tree node public class Node { public Node left, right; public int key; }; static Node root; // Utility function to create a new tree Node static Node newNode(int key) { Node temp = new Node(); temp.key = key; temp.left = temp.right = null; return temp; } // Constructs factor tree for given value and stores // root of tree at given reference. static Node createFactorTree(Node node_ref, int v) { (node_ref) = newNode(v); // the number is factorized for (int i = 2 ; i < v/2 ; i++) { if (v % i != 0) continue; // If we found a factor, we conleft // and right subtrees and return. Since we // traverse factors starting from smaller // to greater, left child will always have // smaller factor node_ref.left = createFactorTree(((node_ref).left), i); node_ref.right = createFactorTree(((node_ref).right), v/i); return node_ref; } return node_ref; } // Iterative method to find the height of Binary Tree static void printLevelOrder(Node root) { // Base Case if (root == null) return; Queue<Node > q = new Queue<Node>(); q.Enqueue(root); while (q.Count != 0) { // Print front of queue and remove // it from queue Node node = q.Peek(); Console.Write(node.key + " "); q.Dequeue(); if (node.left != null) q.Enqueue(node.left); if (node.right != null) q.Enqueue(node.right); } } // Driver program public static void Main(String[] args) { int val = 48;// sample value root = null; root = createFactorTree(root, val); Console.WriteLine("Level order traversal of "+ "constructed factor tree"); printLevelOrder(root); }}// This code is contributed by gauravrajput1 |
Output:
Level order traversal of constructed factor tree 48 2 24 2 12 2 6 2 3
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