目录

树结构及其算法-二叉树节点的删除

C++代码

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树结构及其算法-二叉树节点的删除

二叉树节点的删除操作稍为复杂，可分为以下3种情况。

1. 删除的节点为树叶，只要将其相连的父节点指向NULL即可。
2. 删除的节点只有一棵子树。
3. 删除的节点有两棵子树。要删除节点，方式有两种，虽然结果不同，但是都符合二叉树的特性。

• 找出中序立即先行者（Inorder Immediate Predecessor），就是将要删除节点的左子树中的最大者向上提。简单来说，就是从该节点的左子树往右寻找，直到右指针为NULL，这个节点就是中序立即先行者。
• 找出中序立即后继者（Inorder Immediate Successor），就是把要删除节点的右子树中的最小者向上提。简单来说，就是从该节点的右子树往左寻找，直到左指针为NULL，这个节点就是中序立即后继者。

C++代码

#include<iostream>
using namespace std;struct TreeNode {int data;TreeNode* leftNode;TreeNode* rightNode;TreeNode(int tempData, TreeNode* tempLeftNode = nullptr, TreeNode* tempRightNode = nullptr) {this->data = tempData;this->leftNode = tempLeftNode;this->rightNode = tempRightNode;}
};class Tree {
private:TreeNode* treeNode;
public:Tree() {treeNode = nullptr;}TreeNode* GetTreeNode() {return this->treeNode;}void AddNodeToTree(int* tempData, int tempSize) {for (int i = 0; i < tempSize; i++) {TreeNode* currentNode;TreeNode* newNode;int flag = 0;newNode = new TreeNode(tempData[i]);if (treeNode == nullptr)treeNode = newNode;else {currentNode = treeNode;while (!flag) {if (tempData[i] < currentNode->data) {if (currentNode->leftNode == nullptr) {currentNode->leftNode = newNode;flag = 1;}elsecurrentNode = currentNode->leftNode;}else {if (currentNode->rightNode == nullptr) {currentNode->rightNode = newNode;flag = 1;}elsecurrentNode = currentNode->rightNode;}}}}}void DeleteNodeToTree(TreeNode* tempTree, int tempData) {if (tempTree == nullptr)return;TreeNode* findNode = tempTree;TreeNode* pre = nullptr;while (findNode != nullptr) {if (findNode->data == tempData)break;else if (tempData < findNode->data) {pre = findNode;findNode = findNode->leftNode;}else {pre = findNode;findNode = findNode->rightNode;}}if (findNode == nullptr)return;if (findNode->leftNode == nullptr) {if (findNode == tempTree) {TreeNode* temp = findNode;findNode = findNode->rightNode;free(temp);}TreeNode* temp = findNode;(pre->data < findNode->data ? pre->rightNode : pre->leftNode) = findNode->rightNode;free(temp);temp = nullptr;}else if (findNode->rightNode == nullptr) {if (findNode == tempTree) {TreeNode* temp = findNode;findNode = findNode->leftNode;free(temp);}TreeNode* temp = findNode;(pre->data < findNode->data ? pre->rightNode : pre->leftNode) = findNode->leftNode;free(temp);temp = nullptr;}else {TreeNode* post = findNode;TreeNode* max = findNode->leftNode;while (max->rightNode != nullptr) {post = max;max = max->rightNode;}findNode->data = max->data;if (post == findNode)post->leftNode = max->leftNode;elsepost->rightNode = max->rightNode;free(max);}}void Inorder(TreeNode* tempTree) {if (tempTree != nullptr) {Inorder(tempTree->leftNode);cout << tempTree->data << " ";Inorder(tempTree->rightNode);}}TreeNode* Find(TreeNode* tree, int value) {while (true) {if (tree == nullptr)return nullptr;if (tree->data == value)return tree;else if (tree->data > value)tree = tree->leftNode;elsetree = tree->rightNode;}}
};int main() {int data[]{ 7,4,1,5,16,8,11,12,15,9,2 };cout << "原始数据：" << endl;for (int i = 0; i < 11; i++)cout << data[i] << " ";cout << endl;Tree* tree = new Tree;tree->AddNodeToTree(data, 11);cout << "中序遍历：" << endl;tree->Inorder(tree->GetTreeNode());cout << endl;cout << "请输入要删除的值：";int value;cin >> value;if ((tree->Find(tree->GetTreeNode(), value)) == nullptr)cout << "二叉树中没有此节点了" << endl;else {tree->DeleteNodeToTree(tree->GetTreeNode(), value);cout << "中序遍历：" << endl;tree->Inorder(tree->GetTreeNode());cout << endl;}return 0;
}

输出结果