二叉排序树，也叫搜索树、查找树，是一种有顺序的二叉树，或者是一颗空树，或者是一颗。
它有以下特点：
1、若左子树不为空，那么左子树上面的所有节点的关键字值都比根节点的关键字值小
2、若右子树不为空，那么右子树上面的所有节点的关键字值都比根节点的关键字值大
3、左右子树都为二叉树
4、没有重复值（这一点在实际中可以忽略）
应用场景
在大数据中，越来越广泛的频繁使用二叉树，解决各种大数据查询的问题。在jdk1.8+版本中的大量的数据结构，都换成树来处理，而且树在大数据里，性能是做好的。它的作用就是快速查找。时间复杂度介于O(log₂n)到O(n)之间，数据量越大，越接近于O(log₂n)，性能越优。
代码实践
1、使用孩子双亲法表示法来定义树
public class Node<T extends Comparable> {
T data;
Node<T> leftChild;
Node<T> rightChild;
Node<T> parent;
public Node(T data) {
this.data = data;
leftChild = null;
rightChild = null;
parent = null;
}
}
2、首先实现新增的方法，在树的叶子节点添加一个节点
/**
* 新增一个节点
*
* @param data
* @return
*/
public Node put(T data) {
Node<T> newNode = new Node(data);
if (root == null) {
root = newNode;
return newNode;
}
Node<T> parent = null;
Node<T> node = root;
while (node != null) {
parent = node;
if (node.data.compareTo(data) > 0) {//小于跟节点就往左查询
node = node.leftChild;
} else if (node.data.compareTo(data) < 0) {//大于跟节点就往右查询
node = node.rightChild;
} else {//是重复值 就不理会了
return node;
}
}
if (parent.data.compareTo(data) > 0) {
parent.leftChild = newNode;
} else {
parent.rightChild = newNode;
}
newNode.parent = parent;
size++;
return newNode;
}
3、查找节点
public Node get(T data) {
if (root == null) {
return null;
}
Node<T> node = root;
while (node != null) {
if (node.data.compareTo(data) > 0) {
node = node.leftChild;
} else if (node.data.compareTo(data) < 0) {
node = node.rightChild;
} else {
return node;
}
}
return null;
}
4、遍历树，采用中序遍历。
/**
* 中序遍历
*
* @param node
*/
public void middleOrderTraseval(Node<T> node) {
if (node == null) {
return;
}
middleOrderTraseval(node.leftChild);
System.out.print(node.data + " ");
middleOrderTraseval(node.rightChild);
}
5、删除节点（难点）分四种情况
1. 要删除node是叶子节点
if (left == null && right == null) {
if (parent == null) {
root = null;
} else {
if (parent.leftChild == node) {
parent.leftChild = null;
} else {
parent.rightChild = null;
}
node.parent = null;
}
}
2. 要删除node节点只有左节点
else if (left != null && right == null) {
if (parent == null) {
root = left;
} else {
if (parent.leftChild == node) {
parent.leftChild = left;
} else {
parent.rightChild = left;
}
}
left.parent = parent;
node.leftChild = null;
node.parent = null;
}
3. 要删除node节点只有右节点
else if (left == null && right != null) {
if (parent == null) {
root = right;
} else {
if (parent.leftChild == node) {
parent.leftChild = right;
} else {
parent.rightChild = right;
}
}
right.parent = parent;
node.rightChild = null;
node.parent = null;
}
4. 要删除node节点左右节点都有
else if (left != null && right != null) {
Node<T> leftMinNode = getLeftMinNode(right);
// 1. 把右节点最小的节点接上node的左节点
leftMinNode.leftChild = left;
left.parent = leftMinNode;
// 2. 如果右节点最小的节点，如果有右节点，则把右节点接上父节点
Node<T> leftMinNodeParent = leftMinNode.parent;
if (leftMinNode.rightChild != null) {
if (leftMinNodeParent != node) {
leftMinNodeParent.leftChild = leftMinNode.rightChild;
leftMinNode.rightChild.parent = leftMinNodeParent;
}
} else {
//没有右节点，则要把最小节点的父节点的左节点赋空
leftMinNodeParent.leftChild = null;
}
// 3. 把右节点最小节点接上node的右节点上
if (leftMinNode != right) {
leftMinNode.rightChild = right;
}
right.parent = leftMinNode;
// 4. 接上node的父节点
if (parent == null) {
root = leftMinNode;
} else {
if (parent.leftChild == node) {
parent.leftChild = leftMinNode;
} else {
parent.rightChild = leftMinNode;
}
}
leftMinNode.parent = parent;
node.leftChild = null;
node.rightChild = null;
node.parent = null;
}
6、完整代码
public class SearchBinaryTree<T extends Comparable> {
//二叉树跟节点
private Node<T> root;
//二叉树大小
private int size;
/**
* 新增一个节点
*
* @param data
* @return
*/
public Node put(T data) {
Node<T> newNode = new Node(data);
if (root == null) {
root = newNode;
return newNode;
}
Node<T> parent = null;
Node<T> node = root;
while (node != null) {
parent = node;
if (node.data.compareTo(data) > 0) {//小于跟节点就往左查询
node = node.leftChild;
} else if (node.data.compareTo(data) < 0) {//大于跟节点就往右查询
node = node.rightChild;
} else {//是重复值 就不理会了
return node;
}
}
if (parent.data.compareTo(data) > 0) {
parent.leftChild = newNode;
} else {
parent.rightChild = newNode;
}
newNode.parent = parent;
size++;
return newNode;
}
public int getSize() {
return size;
}
public Node get(T data) {
if (root == null) {
return null;
}
Node<T> node = root;
while (node != null) {
if (node.data.compareTo(data) > 0) {
node = node.leftChild;
} else if (node.data.compareTo(data) < 0) {
node = node.rightChild;
} else {
return node;
}
}
return null;
}
public void middleOrderTraseval() {
middleOrderTraseval(root);
}
/**
* 中序遍历
*
* @param node
*/
public void middleOrderTraseval(Node<T> node) {
if (node == null) {
return;
}
middleOrderTraseval(node.leftChild);
System.out.print(node.data + " ");
middleOrderTraseval(node.rightChild);
}
public void deleteNode(Node<T> node) {
if (node == null) {
return;
}
Node<T> left = node.leftChild;
Node<T> right = node.rightChild;
Node<T> parent = node.parent;
//第一种情况：node是叶子节点
if (left == null && right == null) {
if (parent == null) {
root = null;
} else {
if (parent.leftChild == node) {
parent.leftChild = null;
} else {
parent.rightChild = null;
}
node.parent = null;
}
}
//第二种情况：node只有左节点，没有右节点的情况
else if (left != null && right == null) {
if (parent == null) {
root = left;
} else {
if (parent.leftChild == node) {
parent.leftChild = left;
} else {
parent.rightChild = left;
}
}
left.parent = parent;
node.leftChild = null;
node.parent = null;
}
//第三种情况：node只有右节点，没有左节点的情况
else if (left == null && right != null) {
if (parent == null) {
root = right;
} else {
if (parent.leftChild == node) {
parent.leftChild = right;
} else {
parent.rightChild = right;
}
}
right.parent = parent;
node.rightChild = null;
node.parent = null;
}
//第四种情况：node左右节点都有的情况
else if (left != null && right != null) {
Node<T> leftMinNode = getLeftMinNode(right);
// 1. 把右节点最小的节点接上node的左节点
leftMinNode.leftChild = left;
left.parent = leftMinNode;
// 2. 如果右节点最小的节点，如果有右节点，则把右节点接上父节点
Node<T> leftMinNodeParent = leftMinNode.parent;
if (leftMinNode.rightChild != null) {
if (leftMinNodeParent != node) {
leftMinNodeParent.leftChild = leftMinNode.rightChild;
leftMinNode.rightChild.parent = leftMinNodeParent;
}
} else {
//没有右节点，则要把最小节点的父节点的左节点赋空
leftMinNodeParent.leftChild = null;
}
// 3. 把右节点最小节点接上node的右节点上
if (leftMinNode != right) {
leftMinNode.rightChild = right;
}
right.parent = leftMinNode;
// 4. 接上node的父节点
if (parent == null) {
root = leftMinNode;
} else {
if (parent.leftChild == node) {
parent.leftChild = leftMinNode;
} else {
parent.rightChild = leftMinNode;
}
}
leftMinNode.parent = parent;
node.leftChild = null;
node.rightChild = null;
node.parent = null;
}
size--;
}
/**
* 获取当前节点的左边最小的值，也就是最左边的节点
*
* @param node
* @return
*/
public Node<T> getLeftMinNode(Node<T> node) {
if (node == null) {
return null;
}
Node currentRoot = node;
while (currentRoot.leftChild != null) {
currentRoot = currentRoot.leftChild;
}
return currentRoot;
}
/**
* 使用孩子双亲法表示法来定义树（实际双向链表）
* @param <T> 对象
*/
public class Node<T extends Comparable> {
T data;
Node<T> leftChild;
Node<T> rightChild;
Node<T> parent;
public Node(T data) {
this.data = data;
leftChild = null;
rightChild = null;
parent = null;
}
}
}
7、测试
@Test
public void testBinarySortTree(){
BinarySortTree<Integer> tree = new BinarySortTree();
//5 2 7 3 4 1 6
int[] array=new int[]{5,2,7,3,4,1,8,6,9};
for (int i = 0; i < array.length; i++) {
int i1 = array[i];
tree.put(i1);
}
tree.middleOrderTraseval();
System.out.println();
//删除单个
tree.deleteNode(tree.get(7));
tree.middleOrderTraseval();
System.out.println();
for (int i : array) {
tree.middleOrderTraseval();
System.out.println("------------------------------");
tree.deleteNode(tree.get(i));
}
System.out.println();
for (int i = 0; i < array.length; i++) {
tree.put(array[i]);
}
tree.middleOrderTraseval();
}
8、测试结果
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 8 9
1 2 3 4 5 6 8 9 ------------------------------
1 2 3 4 6 8 9 ------------------------------
1 3 4 6 8 9 ------------------------------
1 3 4 6 8 9 ------------------------------
1 4 6 8 9 ------------------------------
1 6 8 9 ------------------------------
6 8 9 ------------------------------
6 9 ------------------------------
9 ------------------------------
1 2 3 4 5 6 7 8 9
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