二叉查找树

相关概念

二叉树中每个节点都不能有多于两个的子节点。
二叉树的一个性质是一棵平均二叉树的深度要比节点个数N小得多。
二叉查找树, 其深度的平均值是O(logN)。

二叉查找树的实现

public class BinarySearchTree<T extends Comparable<? super T>> {

    private static class BinaryNode<T>{
        T element;
        BinaryNode<T> left;
        BinaryNode<T> right;

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

    private BinaryNode<T> root;

    public BinarySearchTree() {
        root = null;
    }

    public boolean isEmpty() {
        return root == null;
    }

    public boolean contails(T x) {
        return contails(x, root);
    }

    public void insert(T x) {
            root = insert(x, root);
    }

    public T findMin() {
        return findMin(root).element;
    }

    public T findMax() {
        return findMax(root).element;
    }

    public void remove(T x) {
        root = remove(x, root);
    }

    private  boolean contails(T x,BinaryNode<T> t) {
            //如果t是空集，直接return false
        if (t == null) {
            return false;
        }
        //与当前节点相比较，小于0说明x在当前左子树上，大于0说明x在当前右子树上，等于0说明当前节点就是x
        int compareResult = x.compareTo(t.element);
        if (compareResult < 0) {
            return contails(x, t.left);
        }else if (compareResult > 0) {
            return contails(x, t.right);
        }else {
            return true;
        }
    }

    private BinaryNode<T> insert(T x,BinaryNode<T> t) {
        if (t == null) {
            return new BinaryNode<T>(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);
        }else {

        }
        return t;
    }

    private BinaryNode<T> findMin(BinaryNode<T> t) {
        if (t == null) {
            return null;
        }else if (t.left == null) {
            return t;
        }
        return findMin(t.left);
    }

    private BinaryNode<T> findMax(BinaryNode<T> t) {
        if (t != null) {
            while (t.right != null) {
                t = t.right;
            }
        }
        return t;
    }

    private BinaryNode<T> remove(T x,BinaryNode<T> t) {
        if (t == null) {
            return t;
        }
        //与当前节点相比较，小于0说明x在当前左子树上，大于0说明x在当前右子树上，等于0说明当前节点就是x
        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 = findMin(t.right).element;
            t.right = remove(t.element, t.right);
        }{
            t= (t.left == null) ? t.right : t.left;
        }
        return t;
    }
}