赫夫曼树

带权路径最短的树，
构建赫夫曼树的思路

1. 排序，将最小与次小转为节点，并根据权生成父节点，将父节点加入到结合，
2. 移除最小与次小元素，再次排序，重复1
3. 直到集合只有一个元素

public class HuffmanTree {
    
    public static void main(String[] args) {
        int[] array = {13, 7, 8, 3, 29, 6, 1};
        List<Node> list = new ArrayList<>();
        Node node = null;
        for (int i = 0; i < array.length; i++) {
            list.add(new Node(array[i]));
        }
        HuffmanTree ht = new HuffmanTree();
        Node root = ht.createHuffman(list);
        ht.preOrder(root);
    }


    public Node createHuffman(List<Node> list) {

        if (list.size() <= 1) {
            return list.get(0);
        }
        Collections.sort(list);
        Node node1 = list.get(0);
        Node node2 = list.get(1);
        Node parent = new Node(node1.value + node2.value);
        parent.left = node1;
        parent.right = node2;
        list.set(0, parent);
        list.remove(1);
        return createHuffman(list);
    }

    public void preOrder(Node node) {
        node.preOrder(node);
    }
}

class Node implements Comparable<Node> {

    public int value;
    public Node left;
    public Node right;
    public Node(int value) {
        this.value = value;
    }
    @Override
    public String toString() {
        final StringBuilder sb = new StringBuilder("Node{");
        sb.append("value=").append(value);
        sb.append('}');
        return sb.toString();
    }
    
    @Override
    public int compareTo(Node o) {
        return this.value - o.value;
    }
    public void preOrder(Node node) {
        System.out.println(node);
        if (node.left != null) {
            preOrder(node.left);
        }
        if (node.right != null) {
            preOrder(node.right);
        }
    }
}