<数据结构>-树

正文

• 二叉树
  定义 : 其中每个几点都不能有多余两个的儿子

public class BinaryNode<AnyType> {    public BinaryNode(AnyType element) {        this(element, null, null);    }    public BinaryNode(AnyType element, BinaryNode left, BinaryNode right) {        this.element = element;        this.left = left;        this.right = right;    }    AnyType element;    BinaryNode left;    BinaryNode right;}

• 二叉查找树
  定义 : 一种特殊的二叉树 , 其中每个几点都不能有多余两个的儿子.

public class BinarySearchTree<AnyType extends Comparable<? super AnyType>> {    public static class BinaryNode<AnyType> {        public BinaryNode(AnyType element) {            this(element, null, null);        }        public BinaryNode(AnyType element, BinaryNode left, BinaryNode right) {            this.element = element;            this.left = left;            this.right = right;        }        AnyType element;        BinaryNode left;        BinaryNode right;    }    private BinaryNode<AnyType> root;    public BinarySearchTree() {        root = null;    }    public void makeEmpty() {        root = null;    }    public boolean isEmpty() {        return root == null;    }    public boolean contains(AnyType x) {        return contains(x, root);    }    public AnyType findMin() {        if (isEmpty()) {            throw new BufferUnderflowException();        }        return findMin(root).element;    }    public AnyType findMax() {        if (isEmpty()) {            throw new BufferUnderflowException();        }        return findMax(root).element;    }    public void insert(AnyType x) {        root = insert(x , root);    }    public void remove(AnyType x) {        root = remove(x , root);    }    private boolean contains(AnyType x , BinaryNode<AnyType> t ) {        if (t == null) {            return false;        }        int compareResult = x.compareTo(t.element);        if (compareResult < 0) {            return contains(x, t.left);        } else {            return compareResult <= 0 || contains(x, t.right);        }    }    private BinaryNode<AnyType> findMin(BinaryNode<AnyType> t) {        if (t == null) {            return null;        } else if (t.left == null) {            return t;        }        return findMin(t.left);    }    private BinaryNode<AnyType> findMax(BinaryNode<AnyType> t) {        if (t != null) {            while(t.right != null) {                t = t.right;            }        }        return t;    }    private BinaryNode<AnyType> insert(AnyType x , BinaryNode<AnyType> t) {        if (t == null) {            return new BinaryNode<AnyType>(x , null , null);        }        int compareResult = x.compareTo(t.element);        if (compareResult < 0) {            t.left = insert(x , t.left);        } else if (compareResult > 0) {            t.right = insert(x , t.right);        }        return t;    }    private BinaryNode<AnyType> remove(AnyType x , BinaryNode<AnyType> t) {        if (t == null) {            return t;        }        int compareResult = x.compareTo(t.element);        if (compareResult < 0) {            t.left = remove(x , t.left);        } else if (compareResult > 0) {            t.right = remove(x , t.right);        } else if (t.left != null && t.right != null) {            t.element = (AnyType) findMin(t.right).element;            t.right = remove(t.element , t.right);        } else {            t = (t.left != null) ? t.left : t.right;        }        return t;    }    public void printTree() {        if (isEmpty()) {            System.out.print("Empty Tree");        } else {            printTree(root);        }    }    private void printTree(BinaryNode<AnyType> t) {        if (t != null) {            printTree(t.left);            System.out.print(t.element);            printTree(t.right);        }    }    private int height(BinaryNode<AnyType> t) {        if (t == null) {            return -1;        } else {            return 1 + Math.max(height(t.left) , height(t.right));        }    }}

• AVL树
  定义 : 带有平衡条件的二叉查找树

public class AvlNode<AnyType> {    public AvlNode(AnyType element) {        this(element, null, null);    }    public AvlNode(AnyType element, AvlNode<AnyType> left, AvlNode<AnyType> right) {        this.element = element;        this.left = left;        this.right = right;        this.height = 0;    }    AnyType element;    AvlNode<AnyType> left;    AvlNode<AnyType> right;    int height;    private int height(AvlNode<AnyType> t) {        return t == null ? -1 : t.height;    }    private AvlNode<AnyType> insert(AnyType x, AvlNode<AnyType> t) {        if (t == null) {            return new AvlNode<AnyType>(x, null, null);        }        int compareResult = compare(x, t.element);        if (compareResult < 0) {            t.left = insert(x, t.left);            if (height(t.left) - height(t.right) == 2) {                if (compare(x, t.left.element) < 0) {                    t = rotateWithLeftChild(t);                } else {                    t = doubleWithLeftChild(t);                }            }        } else if (compareResult > 0) {            t.right = insert(x, t.right);            if (height(t.right) - height(t.left) == 2) {                if (compare(x, t.right.element) < 0) {                    t = rotateWithRightChild(t);                } else {                    t = doubleWithRightChild(t);                }            }        } else {            t.height = Math.max(height(t.left), height(t.right)) + 1;        }        return t;    }    private AvlNode<AnyType> rotateWithLeftChild(AvlNode<AnyType> k2) {        AvlNode<AnyType> k1 = k2.left;        k2.left = k1.right;        k1.right = k2;        k2.height =  Math.max(height(k2.left), height(k2.right)) + 1;        k1.height =  Math.max(height(k1.left), k2.height) + 1;        return k1;    }    private AvlNode<AnyType> doubleWithLeftChild(AvlNode<AnyType> k3) {        k3.left = rotateWithRightChild(k3.left);        return rotateWithLeftChild(k3);    }}

标准库的集合与映射

• ArrayList和LinkedList查找效率很低.
• ArrayList和LinkedList的区别 :
  
  1. ArrayList提供了List ADT可增长数组的实现,使用ArrayList的优点在于,对get和set的调用花费常数时间.其缺点是新项的插入和现有项的删除代价昂贵.
  2. LinkedList提供了List ADT双向链表的实现.新项的插入和现有项的删除均开销很小,缺点是不易做索引,对get的调用是昂贵的.
• Set接口代表不重复元素的Collection. 有序状态的Set实现是TreeSet.
• Map是一个接口,代表由关键字以及它们的值组成的一些项的集合.有序状态map的实现是TreeMap.