Dado un árbol binario, encuentra su densidad haciendo un recorrido.
La densidad del árbol binario se define como:
Density of Binary Tree = Size / Height
Ejemplos :
Input :
Root of following tree
10
/ \
20 30
Output : 1.5
Height of given tree = 2
Size of given tree = 3
Input :
Root of the following tree
10
/
20
/
30
Output : 1
Height of given tree = 3
Size of given tree = 3
El tamaño y la altura del árbol se pueden encontrar en un solo recorrido utilizando el recorrido de orden de nivel .
Para calcular la altura del árbol binario, la idea es usar un puntero «NULO» como separador entre dos niveles. Cada vez que se produce «NULL» durante el recorrido, se incrementa la altura.
Para calcular el tamaño del árbol binario, incremente el contador para cada nuevo Node encontrado durante el recorrido del orden de niveles.
Finalmente, use la fórmula anterior para calcular la densidad del árbol binario.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
// A binary tree node
struct Node {
int data;
Node *left, *right;
};
// Helper function to allocates a new node
Node* newNode(int data)
{
Node* node = new Node;
node->data = data;
node->left = node->right = NULL;
return node;
}
// Function to calculate density of Binary Tree
float density(Node* root)
{
queue<Node*> q;
// push root to queue first
q.push(root);
// push NULL as a separator
q.push(NULL);
int height = 1, size = 0;
while (!q.empty()) {
Node* t = q.front();
q.pop();
if (t)
size++;
else {
// If after popping NULL queue is
// empty then get out of loop i.e
// stop the level order traversal.
if (q.empty())
break;
q.push(NULL);
height++;
continue;
}
// if t has left child
// then push it to queue
if (t->left) {
q.push(t->left);
}
// if t has right child
// then push it to queue
if (t->right) {
q.push(t->right);
}
}
return (float)size / height;
}
// Driver code
int main()
{
Node* root = newNode(1);
root->left = newNode(2);
root->right = newNode(3);
cout << density(root) << endl;
return 0;
}
Java
// Java implementation of the above approach
import java.util.*;
class Solution
{
// A binary tree node
static class Node
{
int data;
Node left, right;
}
// Helper function to allocates a new node
static Node newNode(int data)
{
Node node = new Node();
node.data = data;
node.left = node.right = null;
return node;
}
// Function to calculate density of Binary Tree
static float density(Node root)
{
Queue<Node> q = new LinkedList<Node>();
// add root to queue first
q.add(root);
// add null as a separator
q.add(null);
int height = 1, size = 0;
while (q.size() > 0)
{
Node t = q.peek();
q.remove();
if (t != null)
size++;
else
{
// If after removeping null queue is
// empty then get out of loop i.e
// stop the level order traversal.
if (q.size() == 0)
break;
q.add(null);
height++;
continue;
}
// if t has left child
// then add it to queue
if (t.left !=null)
{
q.add(t.left);
}
// if t has right child
// then add it to queue
if (t.right != null)
{
q.add(t.right);
}
}
return ((float)size )/ height;
}
// Driver code
public static void main(String args[])
{
Node root = newNode(1);
root.left = newNode(2);
root.right = newNode(3);
System.out.println(density(root));
}
}
// This code is contributed by Arnab Kundu
Python3
# Python implementation of the above approach # Linked List node class Node: def __init__(self, data): self.data = data self.left = None self.right = None # Helper function to allocates a new node def newNode( data) : node = Node(0) node.data = data node.left = node.right = None return node # Function to calculate density of Binary Tree def density(root) : q = [] # append root to queue first q.append(root) # append None as a separator q.append(None) height = 1 size = 0 while (len(q) > 0): t = q[0] q.pop(0) if (t != None): size = size + 1 else: # If after removeping None queue is # empty then get out of loop i.e # stop the level order traversal. if (len(q) == 0): break q.append(None) height = height + 1 continue # if t has left child # then append it to queue if (t.left != None) : q.append(t.left) # if t has right child # then append it to queue if (t.right != None): q.append(t.right) return (size ) / height # Driver code root = newNode(1) root.left = newNode(2) root.right = newNode(3) print(density(root)) # This code is contributed by Arnab Kundu
C#
// C# implementation of the above approach
using System;
using System.Collections.Generic;
class GFG
{
// A binary tree node
public class Node
{
public int data;
public Node left, right;
}
// Helper function to allocates a new node
static Node newNode(int data)
{
Node node = new Node();
node.data = data;
node.left = node.right = null;
return node;
}
// Function to calculate density of Binary Tree
static float density(Node root)
{
Queue<Node> q = new Queue<Node>();
// add root to queue first
q.Enqueue(root);
// add null as a separator
q.Enqueue(null);
int height = 1, size = 0;
while (q.Count > 0)
{
Node t = q.Peek();
q.Dequeue();
if (t != null)
size++;
else
{
// If after removeping null queue is
// empty then get out of loop i.e
// stop the level order traversal.
if (q.Count == 0)
break;
q.Enqueue(null);
height++;
continue;
}
// if t has left child
// then add it to queue
if (t.left !=null)
{
q.Enqueue(t.left);
}
// if t has right child
// then add it to queue
if (t.right != null)
{
q.Enqueue(t.right);
}
}
return ((float)size ) / height;
}
// Driver code
public static void Main(String []args)
{
Node root = newNode(1);
root.left = newNode(2);
root.right = newNode(3);
Console.WriteLine(density(root));
}
}
// This code is contributed by PrinciRaj1992
Javascript
<script>
// Javascript implementation of the above approach
// A binary tree node
class Node
{
constructor()
{
this.data = 0;
this.left = null;
this.right = null;
}
}
// Helper function to allocates a new node
function newNode(data)
{
var node = new Node();
node.data = data;
node.left = node.right = null;
return node;
}
// Function to calculate density of Binary Tree
function density(root)
{
var q = [];
// Add root to queue first
q.push(root);
// Add null as a separator
q.push(null);
var height = 1, size = 0;
while (q.length > 0)
{
var t = q[0];
q.shift();
if (t != null)
size++;
else
{
// If after removeping null queue is
// empty then get out of loop i.e
// stop the level order traversal.
if (q.length == 0)
break;
q.push(null);
height++;
continue;
}
// If t has left child
// then add it to queue
if (t.left != null)
{
q.push(t.left);
}
// If t has right child
// then add it to queue
if (t.right != null)
{
q.push(t.right);
}
}
return(size) / height;
}
// Driver code
var root = newNode(1);
root.left = newNode(2);
root.right = newNode(3);
document.write(density(root));
// This code is contributed by noob2000
</script>
Producción:
1.5
Complejidad de tiempo : O(N)