8
    3    9   
  2   6    10
1    4  7 
      5

上面是1到10的二叉排序樹。
如何實現二叉排序樹的節點刪除呢？假設我們刪除結點6，先尋找前驅結點或者後繼節點，6的前驅結點是5，後繼是7，想象一下刪除了結點6後，樹該怎麼變化？其實只要將6改成5，再將5的節點刪除就OK了。

注意前驅或後繼的度為1或者0。

（PS:這是從計蒜客學來的，不是打廣告，侵權則刪）

#include <iostream>
#include <cstdlib>

using namespace std;

class Node
{
public
 
:
    int data;
    Node *lchild, *rchild, *father;
    Node(int _data, Node*_father=NULL){
        data = _data;
        lchild = NULL;
        rchild = NULL;
        father = _father;
    }
    ~Node(){
        if(lchild != NULL)
            delete lchild;
        if(rchild != NULL)
            delete rchild;
    }
    void
 
 myInsert(int value){
        if(data == value)
            return;
        else if(value < data){
            if(lchild == NULL)
                lchild = new Node(value, this);
            else
                lchild->myInsert(value);
        }
        else{
            if(rchild == NULL)
                rchild =
 
 new Node(value, this);
            else
                rchild->myInsert(value);
        }
    }

    Node *mySearch(int value){
        if(data == value)
            return this;
        else if(value < data){
            if(lchild == NULL)
                return NULL;
            else
                lchild->mySearch(value);
        }
        else{
            if(rchild == NULL)
                return NULL;
            else
                rchild->mySearch(value);
        }
    }
    /*尋找前驅*/
    Node *predecessor(){
        Node *temp = lchild;
        while(temp!=NULL && temp->rchild!=NULL){
            temp = temp->rchild;
        }
        return temp;
    }
    /*尋找後繼*/
    Node *successor(){
        Node *temp = rchild;
        while(temp!=NULL && temp->lchild!=NULL){
            temp = temp->lchild;
        }
        return temp;
    }

    /*刪除度為1或0的結點*/
    void removeNode(Node *nodeOfdelete){
        /*注意一定要將temp初始化為NULL*/
        Node *temp = NULL;
        if(nodeOfdelete->lchild != NULL){
            temp = nodeOfdelete->lchild;
            /*更新當前結點的子結點的父節點*/
            temp->father = nodeOfdelete->father;
            /*注意一定要將要刪除節點的lchild和rchild置為NULL，注意Node類的解構函式*/
            nodeOfdelete->lchild = NULL;
        }
        if(nodeOfdelete->rchild != NULL){
            temp = nodeOfdelete->rchild;
            temp->father = nodeOfdelete->father;
            nodeOfdelete->rchild = NULL;
        }
        /*上面兩個if只有一個成立，下面if對應的也只有一個成立*/
        if(nodeOfdelete->father->lchild == nodeOfdelete)
            nodeOfdelete->father->lchild = temp;
        if(nodeOfdelete->father->rchild == nodeOfdelete)
            nodeOfdelete->father->rchild = temp;
        delete nodeOfdelete;
    }

    bool deleteNode(int value){
        Node *currentNode, *nodeOfdelete;
        currentNode = mySearch(value);
        if(currentNode == NULL)
            return false;
        /*尋找前驅*/
        if(currentNode->lchild != NULL)
            nodeOfdelete = currentNode->predecessor();
        /*或尋找後繼*/
        else if(currentNode->rchild != NULL)
            nodeOfdelete = currentNode->successor();
        /*要刪除的結點是葉子結點*/
        else
            nodeOfdelete = currentNode;
        /*更改結點的data值*/
        currentNode->data = nodeOfdelete->data;
        /*因為前驅和後繼都是度為1的結點，如果不是前驅和後繼那一定是葉子結點了，所以可以用remove函式進行刪除*/
        removeNode(nodeOfdelete);
        return true;
    }

    void inOrder(){
        if(lchild != NULL)
            lchild->inOrder();
        cout<<data<<" ";
        if(rchild != NULL)
            rchild->inOrder();
    }

};

class BinaryTree
{
private:
    Node *root;
public:
    BinaryTree(){
        root = NULL;
    }
    ~BinaryTree(){
        if(root != NULL)
            delete root;
    }
    void myInsert(int value){
        if(root == NULL)
            root = new Node(value);
        else
            root->myInsert(value);
    }
    void mySearch(int value){
        if(root->mySearch(value) != NULL)
            cout << "存在" <<endl;
        else
            cout << "不存在" << endl;
    }
    void deleteNode(int value){
        if(root->deleteNode(value))
            cout << "刪除成功" <<endl;
        else
            cout << "刪除失敗" <<endl;
    }
    void inOrder(){
        if(root != NULL)
            root->inOrder();
    }
};

int main(){
    BinaryTree binarytree;
    int arr[] = {-111, 0, 22, 4, 3, 8, -2, -11, 123, 2333, 44, 9, 100};

    for(int i=0; i<13; i++)
        binarytree.myInsert(arr[i]);
    binarytree.inOrder();
    cout<<endl;


    binarytree.mySearch(2333);
    binarytree.mySearch(-2333);

    binarytree.deleteNode(100);
    binarytree.inOrder();
    cout<<endl;


    system("pause");
    return 0;
}

如有疑問或錯誤，歡迎提出，謝謝