Java 最优二叉树的哈夫曼算法的简单实现

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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