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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]
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