最优二叉树也称哈夫曼树，讲的直白点就是每个结点都带权值，我们让大的值离根近、小的值离根远，实现整体权值（带权路径长度）最小化。

哈夫曼算法的思想我认为就是上面讲的，而它的算法实现思路是这样的：
从根结点中抽出权值最小的两个（涉及排序，但是我这个实现代码没做严格的排序，只有比较）合并出新的根结点重新加入排序（被抽出来的两个自然是变成非根结点了啊），就这样循环下去，直到合并完成，我们得到一颗最优二叉树——哈夫曼树。

说明：
（1）哈夫曼树有n个叶子结点，则我们可以推出其有n-1个分支结点。因此我在定义名为huffmanTree的HuffmanNode类型数组时定义长度为2*n-1。
（2）这里排序相关没有做得很好，只是为了实现而实现，以后慢慢完善。
（3）理论上讲哈夫曼树应该是不仅仅局限于数值，能compare就行，但这里只用int表示。

下面是代码：

首先定义哈夫曼树结点

public class HuffmanNode { private int weight = -1; private int parent = -1; private int left = -1; private int right = -1; public HuffmanNode(int weight) { super(); this.weight = weight; } public HuffmanNode(int weight, int left, int right) { super(); this.weight = weight; this.left = left; this.right = right; } public int getWeight() { return weight; } public void setWeight(int weight) { this.weight = weight; } public int getParent() { return parent; } public void setParent(int parent) { this.parent = parent; } public int getLeft() { return left; } public void setLeft(int left) { this.left = left; } public int getRight() { return right; } public void setRight(int right) { this.right = right; } @Override public String toString() { return "HuffmanNode [weight=" + weight + ", parent=" + parent + "," + " left=" + left + ", right=" + right + "]"; }}

定义一下哈夫曼树的异常类

public class TreeException extends RuntimeException { private static final long serialVersionUID = 1L; public TreeException() {} public TreeException(String message) { super(message); }}

编码实现（做的处理不是那么高效）

public class HuffmanTree { protected HuffmanNode[] huffmanTree; public HuffmanTree(int[] leafs) { //异常条件判断 if (leafs.length <= 1) { throw new TreeException("叶子结点个数小于2，无法构建哈夫曼树"); } //初始化储存空间 huffmanTree = new HuffmanNode[leafs.length*2-1]; //构造n棵只含根结点的二叉树 for (int i = 0; i < leafs.length; i++) { HuffmanNode node = new HuffmanNode(leafs[i]); huffmanTree[i] = node; } //构造哈夫曼树的选取与合并 for (int i = leafs.length; i < huffmanTree.length; i++) { //获取权值最小的结点下标 int miniNum_1 = selectMiniNum1(); //获取权值次小的结点下标 int miniNum_2 = selectMiniNum2(); if (miniNum_1 == -1 || miniNum_2 == -1) { return; } //两个权值最小的结点合并为新节点 HuffmanNode node = new HuffmanNode(huffmanTree[miniNum_1].getWeight() + huffmanTree[miniNum_2].getWeight(), miniNum_1, miniNum_2); huffmanTree[i] = node; huffmanTree[miniNum_1].setParent(i); huffmanTree[miniNum_2].setParent(i); } } /** * 获取权值最小的结点下标 * @return */ private int selectMiniNum1() { //最小值 int min = -1; //最小值下标 int index = -1; //是否完成最小值初始化 boolean flag = false; //遍历一遍 for (int i = 0; i < huffmanTree.length; i++) { //排空、只看根结点，否则跳过 if (huffmanTree[i] == null || huffmanTree[i].getParent() != -1) { continue; } else if (!flag) { //没初始化先初始化然后跳过 //初始化 min = huffmanTree[i].getWeight(); index = i; //以后不再初始化min flag = true; //跳过本次循环 continue; } int tempWeight = huffmanTree[i].getWeight(); //低效比较 if (tempWeight < min) { min = tempWeight; index = i; } } return index; } /** * 获取权值次小的结点下标 * @return */ private int selectMiniNum2() { //次小值 int min = -1; //是否完成次小值初始化 boolean flag = false; //最小值下标（调用上面的方法） int index = selectMiniNum1(); //最小值都不存在，则次小值也不存在 if (index == -1) { return -1; } //次小值下标 int index2 = -1; //遍历一遍 for (int i = 0; i < huffmanTree.length; i++) { //最小值不要、排空、只看根结点，否则跳过 if (index == i || huffmanTree[i] == null || huffmanTree[i].getParent() != -1) { continue; } else if (!flag) { //没初始化先初始化然后跳过 //初始化 min = huffmanTree[i].getWeight(); index2 = i; //以后不再初始化min flag = true; //跳过本次循环 continue; } int tempWeight = huffmanTree[i].getWeight(); //低效比较 if (tempWeight < min) { min = tempWeight; index2 = i; } } return index2; }}

测试类1

public class HuffmanTreeTester { public static void main(String[] args) { int[] leafs = {1, 3, 5, 6, 2, 22, 77, 4, 9}; HuffmanTree tree = new HuffmanTree(leafs); HuffmanNode[] nodeList = tree.huffmanTree; for (HuffmanNode node : nodeList) { System.out.println(node); } }}

测试结果1

HuffmanNode [weight=1, parent=9, left=-1, right=-1]
HuffmanNode [weight=3, parent=10, left=-1, right=-1]
HuffmanNode [weight=5, parent=11, left=-1, right=-1]
HuffmanNode [weight=6, parent=12, left=-1, right=-1]
HuffmanNode [weight=2, parent=9, left=-1, right=-1]
HuffmanNode [weight=22, parent=15, left=-1, right=-1]
HuffmanNode [weight=77, parent=16, left=-1, right=-1]
HuffmanNode [weight=4, parent=11, left=-1, right=-1]
HuffmanNode [weight=9, parent=13, left=-1, right=-1]
HuffmanNode [weight=3, parent=10, left=0, right=4]
HuffmanNode [weight=6, parent=12, left=1, right=9]
HuffmanNode [weight=9, parent=13, left=7, right=2]
HuffmanNode [weight=12, parent=14, left=3, right=10]
HuffmanNode [weight=18, parent=14, left=8, right=11]
HuffmanNode [weight=30, parent=15, left=12, right=13]
HuffmanNode [weight=52, parent=16, left=5, right=14]
HuffmanNode [weight=129, parent=-1, left=15, right=6]

图形表示：

测试类2

public class HuffmanTreeTester { public static void main(String[] args) { int[] leafs = {2, 4, 5, 3}; HuffmanTree tree = new HuffmanTree(leafs); HuffmanNode[] nodeList = tree.huffmanTree; for (HuffmanNode node : nodeList) { System.out.println(node); } }}

测试结果2

HuffmanNode [weight=2, parent=4, left=-1, right=-1]
HuffmanNode [weight=4, parent=5, left=-1, right=-1]
HuffmanNode [weight=5, parent=5, left=-1, right=-1]
HuffmanNode [weight=3, parent=4, left=-1, right=-1]
HuffmanNode [weight=5, parent=6, left=0, right=3]
HuffmanNode [weight=9, parent=6, left=1, right=2]
HuffmanNode [weight=14, parent=-1, left=4, right=5]

图形表示：

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