二叉树：每个节点至多有两个子节点

二叉查找树的特点：对于每一个节点X,左子树中所有项的值小于X中的值，而它的右子树种所有项的值大于X中的值。

二叉查找树是特殊的二叉树

以下用代码实现

type binarySearchTree struct {
	value       int
	left,right *binarySearchTree
}


//初始化并添加根节点的值
func NewBinarySearchTree(rootValue int) *binarySearchTree {
	return &binarySearchTree{value:rootValue}
}


//添加元素
func (t *binarySearchTree) Insert(value int) *binarySearchTree {
	if t == nil {
		t = NewBinarySearchTree(value)
		return t
	}
	if value < t.value {
		t.left = t.left.Insert(value)
	}else {
		t.right = t.right.Insert(value)
	}
	return t
}

//是否包含某一个元素
func (t *binarySearchTree)Contains(value int)  bool{
	if t == nil {
		return false
	}
	v :=  t.compareTo(value)

	if v < 0 {
		return t.left.Contains(value)
	}else if v > 0 {
		return t.right.Contains(value)
	}else {
		return true
	}
}

func  (t *binarySearchTree)compareTo(value int)  int {
	return value-t.value
}

//移除元素
func (t *binarySearchTree) Remove(value int) *binarySearchTree {
	if t == nil {
		return t
	}
	compareResult := t.compareTo(value)
	if compareResult <0 {
		t.left = t.left.Remove(value)
	}else if compareResult > 0 {
		t.right = t.right.Remove(value)
	}else if t.left != nil && t.right != nil {
		t.value = t.right.FindMin()
		t.right = t.right.Remove(t.value)
	}else if t.left != nil {
		t = t.left
	}else {
		t  = t.right
	}
	return t
}

//查找最大值
func (t *binarySearchTree) FindMax() int {
	if t ==  nil {
		fmt.Println("tree is empty")
		return -1
	}
	if t.right == nil {
		return t.value
	}else {
		return t.right.FindMax()
	}
	//也可以用下面的方法
	//return t.FindMaxNode().value
}

//查找最大的节点
func (t *binarySearchTree) FindMaxNode() *binarySearchTree {
	if  t != nil {
		for t.right != nil {
			t = t.right
		}
	}
	return t
}

//查找最小值
func (t *binarySearchTree) FindMin() int {
	if t ==  nil {
		fmt.Println("tree is empty")
		return -1
	}
	if t.left == nil {
		return t.value
	}else {
		return t.left.FindMin()
	}
	//也可以直接用下面的方法
	//return t.FindMinNode().value
}

//查找最小的节点
func (t *binarySearchTree) FindMinNode() *binarySearchTree {
	if t != nil {
		for t.left != nil {
			t = t.left
		}
	}

	return t
}


//获取树种所有的元素值（并按从小到大排序）
func (t *binarySearchTree) GetAll() []int {
	values := []int{}
	return appendValues(values,t)
}


func appendValues(values []int, t *binarySearchTree) []int {
	if t != nil {
		values = appendValues(values,t.left)
		values = append(values,t.value)
		values = appendValues(values,t.right)
	}
	return values
}



func main() {
	binaryTree := NewBinarySearchTree(50)
	binaryTree.Insert(20)
	binaryTree.Insert(10)
	binaryTree.Insert(100)
	binaryTree.Insert(60)
	binaryTree.Insert(70)
	binaryTree.Insert(5)
	binaryTree.Insert(35)
	binaryTree.Insert(40)
	fmt.Println(binaryTree.GetAll())

	fmt.Println(binaryTree.Contains(30))
	fmt.Println(binaryTree.Contains(20))

	fmt.Println(binaryTree.FindMin())
	fmt.Println(binaryTree.FindMinNode().value)

	fmt.Println(binaryTree.FindMax())
	fmt.Println(binaryTree.FindMaxNode().value)

	binaryTree.Remove(20)
	fmt.Println(binaryTree.GetAll())

}