java代码实现线索化构造一棵中序线索二叉树,并在其中实现调用求结点的前驱结点算法,按中根次序遍历一颗中序线索二叉树,按后根次序遍历中序线索二叉树,插入、删除操作,并实例化该类
时间: 2024-03-17 17:47:48 浏览: 58
好的,我会尽力回答你的问题。首先,我们需要了解中序线索二叉树的概念。中序线索二叉树是一种特殊的二叉树,它的每个节点除了有左右子树指针之外,还有一个标志位,用来表示该节点的前驱或后继节点是否为实际的左右子树指针。这样,我们就可以在不使用递归或栈的情况下,以 O(1) 的时间复杂度访问二叉树的前驱或后继节点。
接下来,让我们看一下如何实现线索化构造一棵中序线索二叉树。这里我提供一份 Java 代码,供您参考:
```java
class ThreadedBinaryTreeNode {
public int data;
public ThreadedBinaryTreeNode left;
public ThreadedBinaryTreeNode right;
public boolean isLeftThreaded;
public boolean isRightThreaded;
public ThreadedBinaryTreeNode(int data) {
this.data = data;
this.left = null;
this.right = null;
this.isLeftThreaded = false;
this.isRightThreaded = false;
}
}
class ThreadedBinaryTree {
private ThreadedBinaryTreeNode root;
public ThreadedBinaryTree() {
this.root = null;
}
public void insert(int data) {
ThreadedBinaryTreeNode newNode = new ThreadedBinaryTreeNode(data);
if (root == null) {
root = newNode;
return;
}
ThreadedBinaryTreeNode current = root;
ThreadedBinaryTreeNode parent = null;
while (true) {
parent = current;
if (data < current.data) {
if (current.isLeftThreaded) {
break;
}
current = current.left;
} else {
if (current.isRightThreaded) {
break;
}
current = current.right;
}
}
if (data < parent.data) {
newNode.left = parent.left;
newNode.right = parent;
parent.isLeftThreaded = false;
parent.left = newNode;
} else {
newNode.right = parent.right;
newNode.left = parent;
parent.isRightThreaded = false;
parent.right = newNode;
}
}
public ThreadedBinaryTreeNode getInorderSuccessor(ThreadedBinaryTreeNode node) {
if (node.isRightThreaded) {
return node.right;
}
node = node.right;
while (!node.isLeftThreaded) {
node = node.left;
}
return node;
}
public ThreadedBinaryTreeNode getInorderPredecessor(ThreadedBinaryTreeNode node) {
if (node.isLeftThreaded) {
return node.left;
}
node = node.left;
while (!node.isRightThreaded) {
node = node.right;
}
return node;
}
public void inorderTraversal() {
ThreadedBinaryTreeNode current = root;
while (current != null) {
while (!current.isLeftThreaded) {
current = current.left;
}
System.out.print(current.data + " ");
while (current.isRightThreaded) {
current = current.right;
if (current == null) {
return;
}
System.out.print(current.data + " ");
}
current = current.right;
}
}
public void postorderTraversal() {
ThreadedBinaryTreeNode current = root;
ThreadedBinaryTreeNode lastVisited = null;
while (current != null) {
while (!current.isLeftThreaded) {
current = current.left;
}
while (current != null && (current.isRightThreaded || current.right == lastVisited)) {
System.out.print(current.data + " ");
lastVisited = current;
current = current.right;
}
if (current != null) {
current = current.right;
}
}
}
public void delete(int data) {
ThreadedBinaryTreeNode current = root;
ThreadedBinaryTreeNode parent = null;
while (current != null && current.data != data) {
parent = current;
if (data < current.data) {
current = current.left;
} else {
current = current.right;
}
}
if (current == null) {
return;
}
if (current.isLeftThreaded && current.isRightThreaded) {
if (parent == null) {
root = null;
} else if (current == parent.left) {
parent.isLeftThreaded = true;
parent.left = current.left;
parent.left.right = parent;
} else {
parent.isRightThreaded = true;
parent.right = current.right;
parent.right.left = parent;
}
} else if (current.isLeftThreaded) {
if (parent == null) {
root = current.right;
} else if (current == parent.left) {
parent.left = current.right;
ThreadedBinaryTreeNode predecessor = getInorderPredecessor(current);
predecessor.left = current.left;
parent.isLeftThreaded = true;
} else {
parent.right = current.right;
ThreadedBinaryTreeNode predecessor = getInorderPredecessor(current);
predecessor.left = current.left;
parent.isRightThreaded = true;
}
} else if (current.isRightThreaded) {
if (parent == null) {
root = current.left;
} else if (current == parent.left) {
parent.left = current.left;
ThreadedBinaryTreeNode successor = getInorderSuccessor(current);
successor.right = current.right;
parent.isLeftThreaded = true;
} else {
parent.right = current.left;
ThreadedBinaryTreeNode successor = getInorderSuccessor(current);
successor.right = current.right;
parent.isRightThreaded = true;
}
} else {
ThreadedBinaryTreeNode predecessor = getInorderPredecessor(current);
int temp = predecessor.data;
delete(predecessor.data);
current.data = temp;
}
}
}
public class ThreadedBinaryTreeExample {
public static void main(String[] args) {
ThreadedBinaryTree tree = new ThreadedBinaryTree();
tree.insert(5);
tree.insert(2);
tree.insert(8);
tree.insert(1);
tree.insert(3);
tree.insert(7);
tree.insert(9);
System.out.println("Inorder traversal:");
tree.inorderTraversal();
System.out.println();
System.out.println("Postorder traversal:");
tree.postorderTraversal();
System.out.println();
tree.delete(2);
System.out.println("Inorder traversal after deleting 2:");
tree.inorderTraversal();
System.out.println();
tree.delete(5);
System.out.println("Inorder traversal after deleting 5:");
tree.inorderTraversal();
System.out.println();
}
}
```
在上面的代码中,我们定义了两个类 `ThreadedBinaryTreeNode` 和 `ThreadedBinaryTree`。`ThreadedBinaryTreeNode` 表示中序线索二叉树的节点,其中包含了节点的值、左右子树指针、以及标志位 `isLeftThreaded` 和 `isRightThreaded`。`isLeftThreaded` 和 `isRightThreaded` 分别表示左右子树指针是否为实际的左右子树指针。
`ThreadedBinaryTree` 表示中序线索二叉树,其中包含了根节点 `root`,以及插入、删除、中序遍历、后序遍历等方法。其中,插入方法是标准的二叉搜索树插入方法,而线索化构造则是在插入节点时进行的。具体来说,我们在插入一个节点时,顺便将其前驱和后继节点的指针进行线索化,从而将二叉树转换为中序线索二叉树。
为了实现求某个节点的前驱节点,我们可以从其右子树开始,一直沿着左子树指针查找,直到遇到一个左子树指针为线索的节点为止。同理,求后继节点则是从其左子树开始,一直沿着右子树指针查找,直到遇到一个右子树指针为线索的节点为止。
中序遍历一颗中序线索二叉树可以通过一个简单的循环实现,具体来说,我们从根节点开始,一直沿着左子树指针查找,直到遇到一个左子树指针为线索的节点为止,然后输出该节点的值,并继续沿着右子树指针查找,直到遇到一个右子树指针为线索的节点为止,然后跳转到该右子树指针指向的节点,重复以上步骤,直到遍历完整棵树。
后序遍历一颗中序线索二叉树可以通过一个类似于中序遍历的循环实现,具体来说,我们从根节点开始,一直沿着左子树指针查找,直到遇到一个左子树指针为线索的节点为止,然后沿着右子树指针查找,直到遇到一个右子树指针为线索的节点为止,输出该节点的值,并将其作为 `lastVisited`,然后跳转到该右子树指针指向的节点,重复以上步骤,直到遍历完整棵树。
最后,我们实例化了 `ThreadedBinaryTree` 类,并进行了插入、删除、中序遍历、后序遍历等操作,以便您更好地理解该类的用法。
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