Shulou(Shulou.com)06/02 Report--

This article gives you an introduction to Java how to achieve the creation of Huffman tree, the content is very detailed, interested friends can refer to, I hope to help you.

What is a Huffman tree?

Given N weights as N leaf nodes, a binary tree is constructed, and if the weighted path length (WPL) of the tree reaches a minimum, such a binary tree is called an optimal binary tree, also known as a Huffman tree. Huffman tree is the tree with shortest weighted path length, and the nodes with larger weights are closer to the root.

Figure 1 A Huffman tree

1. Path and Path Length

A path between child or grandchild nodes reachable from a node down in a tree is called a path.

For example, the path from the root node to node b in Figure 1 is called a path.

For each node in a path, the path length is incremented by 1. If the number of root nodes is 1, then the path length from root node to Lth node is L-1.

For example, the path length from root node to node c in Figure 1 is 4 - 1 = 3.

2. Weight of nodes and weighted path length

If a node in a tree is assigned a value with some meaning, this value is called the node's weight.

For example, the weights of abcd nodes in Figure 1 are 12, 5, 6, and 21, respectively.

The weighted path length of a node is the product of the path length from the root node to the node and the weight of the node.

For example, the weighted path length of node c in Figure 1 is 3 * 6 = 18.

3. Weighted Path Length of Trees

The weighted path length of a tree is defined as the sum of the weighted path lengths of all leaf nodes, and is denoted as WPL.

For example, WPL =(5 + 6)* 3 + 12 * 2 + 21 = 78

Second, create Huffman tree 1. Graphic creation process

Assuming there are n weights, the Huffman tree constructed has n leaf nodes. If the n weights are w1, w2,..., wn, then the Huffman tree construction rules are:

例如有四个叶子节点 a b c d 权值分别为 12、5、6、21

创建赫夫曼树前森林如下

(1) 将w1、w2、…，wn看成是有n 棵树的森林(每棵树仅有一个结点);

(2) 在森林中选出两个根结点的权值最小的树合并，作为一棵新树的左、右子树，且新树的根结点权值为其左、右子树根结点权值之和;

在森林中取出 b c节点 形成一棵新树M

(3)从森林中删除选取的两棵树，并将新树加入森林;

将新树M添加到森林后 森林如下

(4)重复(2)、(3)步，直到森林中只剩一棵树为止，该树即为所求得的哈夫曼树。

** 4.1重复步骤（2）

在森林中取出权为11的节点以及a节点组成一棵新树N

** 4.2重复步骤（3）

将新树N添加到森林中 森林如下

** 4.3重复步骤（2）

在森林中取出b节点和权为23的节点组成一棵新树S

则新树S就是我们要创建的赫夫曼树

2.代码实现

创建赫夫曼树的过程中，为确保每次从森林中取出的节点为最小值，这里采用快速排序算法，每次取出节点前，将森林中的树按照权值从小到大重新排列一次

节点的结构如下:

class Node implements Comparable { private int element; //节点的权 private Node left; //节点的左子树 private Node right; //节点的右子树 //构造器 public Node(int aElement) { this.element = aElement; } public int getElement() { return element; } public void setElement(int element) { this.element = element; } public Node getLeft() { return left; } public void setLeft(Node left) { this.left = left; } public Node getRight() { return right; } public void setRight(Node right) { this.right = right; } //前序遍历 public void preOrder() { System.out.print(this + " "); if (this.getLeft() != null) { this.getLeft().preOrder(); } if (this.getRight() != null) { this.getRight().preOrder(); } } @Override public String toString() { return element + ""; } @Override public int compareTo(Node o) { return this.getElement() - o.getElement(); //从小大到排序 }}

完整代码如下：

package com.xx.huffmantree;import java.util.*;/** * @author 谢鑫 * @version 1.0 * @date 2021/12/7 16:31 * 赫夫曼树 */public class HuffmanTreeDemo { public static void main(String[] args) { int[] arr = {12, 5, 6, 21}; HuffmanTree huffmanTree = new HuffmanTree(); Node root = huffmanTree.creTree(arr); huffmanTree.preOrder(root); }}class HuffmanTree { public Node creTree(int[] aArr) { List list = new ArrayList(); //用于存放数组元素 //将数组放存放list中 for (int element : aArr) { list.add(new Node(element)); } while (list.size() > 1) { //循环创建树 Collections.sort(list); //从小到大排序 //从list中从小取出两个节点 Node left = list.get(0); Node right = list.get(1); //初始化小树根节点 Node root = new Node(left.getElement() + right.getElement()); //小树根节点为左右子树节点element值的和 //构建小树 root.setLeft(left); root.setRight(right); list.add(root); //将小树根节点再次添加到list中 //移除集合中已经参与构建过树的节点 list.remove(left); list.remove(right);// list.remove(0);// list.remove(0); //取出两个队头元素 也可 } return list.get(0); } //前序遍历 public void preOrder(Node aRoot) { if (aRoot != null) { aRoot.preOrder(); } else { System.out.println("此树为空, 无法完成前序遍历!"); } }}class Node implements Comparable { private int element; //节点的权 private Node left; //节点的左子树 private Node right; //节点的右子树 //构造器 public Node(int aElement) { this.element = aElement; } public int getElement() { return element; } public void setElement(int element) { this.element = element; } public Node getLeft() { return left; } public void setLeft(Node left) { this.left = left; } public Node getRight() { return right; } public void setRight(Node right) { this.right = right; } //前序遍历 public void preOrder() { System.out.print(this + " "); if (this.getLeft() != null) { this.getLeft().preOrder(); } if (this.getRight() != null) { this.getRight().preOrder(); } } @Override public String toString() { return element + ""; } @Override public int compareTo(Node o) { return this.getElement() - o.getElement(); //从小大到排序 }}

最后我们采用前序遍历输出我们创建的赫夫曼树，结果如下

关于Java怎样实现赫夫曼树的创建就分享到这里了，希望以上内容可以对大家有一定的帮助，可以学到更多知识。如果觉得文章不错，可以把它分享出去让更多的人看到。

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.