红黑树

Posted 2020-08-20

弄了很久，学习过程中觉得很难，但学完了，其实感觉也就那样，就是情况多了些。

首先是插入，插入的时候其实也就3种情况，因为只有当插入的节点的父亲是红色的时候，此时红黑树的性质遭到破坏，需要旋转，再分1.叔父节点为红，此时只要改变颜色，但祖父节点颜色的改变可能会破坏红黑树的性质，所以要node = grandparent，继续向上，叔父为黑，这时需要旋转，所以得判断，自身的位置，也就是自己和父亲分别是左孩子还是右孩子，2.如果自身是右，父亲是左，的先把自己也旋转到左，再和自己是左，父亲也是左的情况一起处理，即再进行一次旋转，旋转其实只要是为了满足根节点到叶子节点的黑色节点数这一性质（其实是在减小树的深度），颜色的改变一是配合旋转，二是满足些别的性质，3.自身是左，而父亲是右也就是差不多的了。

另外就是删除，删除就很麻烦一些了，首先是要找到要删除节点的右孩子的最左儿子（左右儿子都存在的情况下）来替代，左儿子不存在直接用右儿子替代，右儿子不存在直接用左儿子替代，都不存在则用空节点替代，另外记录下替代节点的孩子和替代节点的父亲（如果删除节点只有一个孩子，替代节点的孩子就是替代节点），然后把孩子指向父亲，只记一个node是不行的，因为node可能为空，当替代点的颜色是黑色的话，需要另外平衡，平衡中如果替代节点的孩子是红色，直接改成黑色就OK了（因为之前只是少了个黑色节点，而红改黑除了改变黑色节点的个数外是不改变别的性质的），当替代节点孩子是黑色时，再分其兄弟节点的颜色1.兄弟节点是红色，此时改变颜色，单步旋转（因为兄弟节点所在的枝黑色节点只比另一边多一）；然后如果兄弟节点是黑色2.兄弟节点的两个孩子也是黑色或者是空，此时只需改变颜色，但父亲颜色的改变可能会破坏树的性质则node = grandparent，向上继续传，来平衡3.兄弟节点有一个红，此时又得确定位置，父亲是左孩子，而自己是右孩子黑色或空，又得先把黑色的旋转到和父亲相同的相对位置，4然后转到父亲和自己都是左孩子情况，一步旋转。父亲是右孩子的情况也一样。

 

自己写上面的删除和插入的时候自己都感觉晕晕的，感觉了解的还不是很彻底，改天得再写一遍。。。

#include <iostream>
#include <cstdio>
using namespace std;

#define red 0
#define black 1



template <class T>
class  red_black_node
{
    public:
    red_black_node* left;
    red_black_node* right;
    red_black_node* parent;
    T key;
    int color;
    red_black_node(T value):left(NULL),right(NULL),parent(NULL),color(red),key(value){};
    red_black_node(T value,red_black_node* l,red_black_node* r,red_black_node* p):
        left(l),right(r),parent(p),T(value),color(red){};
};



template <class T>
class red_black_tree
{
public:
   red_black_node<T>* mRoot;//根节点
public:
    red_black_tree();
    ~red_black_tree();
    void Destory(red_black_node<T>* Pnode);
    red_black_node<T>* RotateLeft(red_black_node<T>* p,red_black_node<T>* r);
    red_black_node<T>* RotateRight(red_black_node<T>* p,red_black_node<T>* r);
    red_black_node<T>* Insert_into(T k,red_black_node<T>* root);
    void Insert(T k);
    red_black_node<T>* Search(T k,red_black_node<T>* root);
    red_black_node<T>* Insert_balance(red_black_node<T>* node,red_black_node<T>* root);
    void Travel_it(red_black_node<T> *root);
    void Trave();

    red_black_node<T>* Delete_Replace(T k,red_black_node<T>* root);
    void Delete(T k);
    red_black_node<T>* Delete_balance(red_black_node<T>* child,red_black_node<T>* parent,red_black_node<T>* root);
};

//左旋函数，并未改变颜色
template <class T>
red_black_node<T>* red_black_tree<T>::RotateLeft(red_black_node<T>* node,red_black_node<T>* root)
{
    red_black_node<T>* tem = node->left;
    node->left = tem->right;
    tem->right = node;
    tem->parent = node->parent;
    node->parent = tem;
    if(node->left!=NULL)
    node->left->parent = node;

    if(tem->parent==NULL)
    {
        root = tem;
    }
    else
    {
        if(tem->key > tem->parent->key)
        {
            tem->parent->right = tem;
        }
        else
        {
            tem->parent->left = tem;
        }
    }
    return root;
}

//构造函数
template <class T>
red_black_tree<T>::red_black_tree()
{
    mRoot = NULL;
}

//析构函数
template <class T>
red_black_tree<T>::~red_black_tree()
{
    Destory(mRoot);
}


//单步右旋
template <class T>
red_black_node<T>* red_black_tree<T>::RotateRight(red_black_node<T>* node,red_black_node<T>* root)
{

    red_black_node<T>* tem = node->right;
    node->right = tem->left;
    tem->left = node;
    tem->parent = node->parent;
    node->parent = tem;
    if(node->right!=NULL)
    node->right->parent = node;


    if(tem->parent==NULL)
    {
        root = tem;
    }
    else
    {
        if(tem->parent->key > tem->key)
        {
            tem->parent->left = tem;
            //red_black_tree<T>::Travel_it(root);
        }
        else
        {
            tem->parent->right = tem;
        }

    }
    return root;
}

//销毁红黑树
template <class T>
void red_black_tree<T>::Destory(red_black_node<T>* PnodeHeader)
{
    if(PnodeHeader==NULL)
        return ;
    if(PnodeHeader->left!=NULL)
        Destory(PnodeHeader->left);
    if(PnodeHeader->right!=NULL)
        Destory(PnodeHeader->right);
    delete PnodeHeader;
}

template <class T>
void red_black_tree<T>::Insert(T k)
{
   mRoot =  Insert_into(k,mRoot);
}

template <class T>//返回的是自己或者是自己的父亲
red_black_node<T>* red_black_tree<T>::Search(T k,red_black_node<T>* root)
{
    red_black_node<T>* tem = root;
    if(tem==NULL)return NULL;
    while(true)
    {
        if(k<tem->key)
        {
            if(tem->left==NULL)return tem;
            else tem = tem->left;
        }
        else if(k>tem->key)
        {
            if(tem->right==NULL)return tem;
            else tem = tem->right;
        }
        else
        return tem;
    }
}

template <class T>
red_black_node<T>* red_black_tree<T>::Insert_into(T k,red_black_node<T>* root)
{
    red_black_node<T>* node;
    red_black_node<T>* tem = Search(k,root);

    //if(tem->key==k)return root;//重复直接退出
    node = new red_black_node<T>(k);
    node->parent = tem;
    if(tem)
    {
        if(tem->key > k)
        {
            tem->left = node;
        }
        else
        {
            tem->right = node;
        }
    }
    else
    {
        root = node;
    }
    //red_black_tree<T>::Trave();
    return Insert_balance(node,root);
}

template<class T>
red_black_node<T>* red_black_tree<T>::Insert_balance(red_black_node<T>* node,red_black_node<T> *root)
{
    red_black_node<T> *p,*gp,*uncle,*tem;
    while((p=node->parent)&&p->color==red)
    {
        gp = p->parent;
        if(p==gp->left)
        {
            uncle = gp->right;
            if(uncle&&uncle->color==red)//1.父亲节点和叔父节点都为红
            {
                uncle->color = black;//
                p->color = black;
                gp->color = red;
                node = gp;
            }
            else
            {
                if(p->right==node)//2.叔父节点为黑，或者不存在，自己是右孩子，父亲是左孩子
                {
                    root = RotateRight(p,root);

                    tem = p;
                    p = node;
                    node = tem;
                }

                p->color = black;
                gp->color = red;

                root = RotateLeft(gp,root);
            }
        }
        else
        {
            uncle = gp->left;
            if(uncle&&uncle->color==red)
            {
                uncle->color = black;
                p->color = black;
                gp->color = red;
                node = gp;
            }
            else
            {

                    if(p->left==node)
                    {
                        root = RotateLeft(p,root);
                        tem = p;
                        p = node;
                        node = tem;
                    }
                    p->color = black;
                    gp->color = red;
                    root = RotateRight(gp,root);

            }
        }
    }
    root->color = black;
    return root;
}

//打印函数
template <class T>
void red_black_tree<T>::Travel_it(red_black_node<T> *root)
{
    if(root==NULL)return;
    printf("father is:%d",root->key);
     if(root->color==red)printf("(red)");
        else printf("(black)");
    printf(" left:");
    if(root->left==NULL)printf("NULL");
    else
    {
        printf("%d",root->left->key);
        if(root->left->color==red)printf("(red)");
        else printf("(black)");
    }
    printf(" right:");
    if(root->right==NULL)printf("NULL\\n");
    else
    {
        printf("%d",root->right->key);
       if(root->right->color==red)printf("(red)\\n");
        else printf("(black)\\n");
    }
    Travel_it(root->left);
    Travel_it(root->right);
}


template <class T>
void red_black_tree<T>::Trave()
{
    Travel_it(mRoot);
}

template <class T>//左右子树都不空时用右孩子的最左子树来替代，左子树为空，直接用右孩子替代，右子树为空直接用左孩子替代
red_black_node<T>* red_black_tree<T>::Delete_Replace(T k,red_black_node<T>* root)
{
    red_black_node<T> *tem;
    tem = red_black_tree<T>::Search(k,mRoot);
    if(tem==NULL)return mRoot;
    if(tem->key!=k)
    {
        printf("The Key Is Wrong\\r\\n");
        return mRoot;
    }
    red_black_node<T>* aim = tem;
    red_black_node<T>* replace_parent;
    red_black_node<T>* replace_child;
    int color;
    if(tem->left&&tem->right)
    {
        tem = tem->right;
        while(tem->left!=NULL)
        {
            tem = tem->left;
        }
        replace_parent = tem->parent;
         replace_child  = tem->right;
         color = tem->color;
        if(replace_child)
        {
            replace_child->parent = replace_parent;
        }
        if(replace_parent)
        {
            if(tem->key < replace_parent->key)
            {
                replace_parent->left = replace_child;
            }
            else
            {
                replace_parent->right = replace_child;
            }
        }
        else//??
        {
            root = replace_child;
        }
        //??
        if (tem->parent == aim)
        {
            replace_parent = tem;
        }
        tem->parent = aim->parent;

        tem->left = aim->left;

            tem->right = aim->right;
        tem->color = aim->color;

        if(aim->parent)
        {
            if(tem->key < aim->parent->key)
            {
                tem->parent->left = tem;
            }
            else
            {
                tem->parent->right = tem;
            }
        }
        else
        {
            root = tem;
        }
        aim->left->parent = tem;
        if(aim->right)
        {
            aim->right->parent = tem;
        }
    }
    else
    {
        if(!tem->left)
        {
            replace_child = tem->right;
        }
        else if(!tem->right)
        {
            replace_child = tem->left;
        }
        replace_parent = tem->parent;
        color = tem->color;
        if(replace_child)
        {
            replace_child->parent = replace_parent;
        }
        if(replace_parent)
        {
            if(replace_parent->left==tem)
            {
                replace_parent->left = replace_child;
            }
            else
            {
                replace_parent->right = replace_child;
            }
        }
        else
        {
            root = replace_child;
        }
    }
    delete aim;
    if(color==black)
    {
        root = Delete_balance(replace_child,replace_parent,root);
    }
    return root;
}

template <class T>
void red_black_tree<T>::Delete(T k)
{
    mRoot = Delete_Replace(k,mRoot);
}

template <class T>//替代的节点是黑色时的旋转平衡
red_black_node<T>* red_black_tree<T>::Delete_balance(red_black_node<T>* child,red_black_node<T>* parent,red_black_node<T>* root)
{
   red_black_node<T> *other, *o_left, *o_right;
   while((!child||child->color==black)&&child!=root)
   {
       if(parent->left==child)//是左孩子，只能是，之前用删除节点的左孩子替代
       {
           other = parent->right;
           if(other->color==red)
           {
               other->color = black;//兄弟节点是红色
               parent->color = red;
               root = RotateRight(parent,root);//旋转下即可
               other = parent->right;
           }
           //x的兄弟是黑色的，且两个孩子也是黑色的
            if ((!other->left || other->left->color == black) &&
                (!other->right || other->right->color == black))
                {
                    other->color = red;
                    child = parent;
                    parent = child->parent;
                }
                else
                {
                    if(!other->right||other->right->color==black)
                    {
                        if(o_left = other->left)
                        {
                            o_left->color = black;
                        }
                        other->color = black;
                        root = RotateLeft(other,root);
                        other = parent->right;
                    }
                    //x的兄弟是黑色的
                    other->color  = parent->color;
                    parent->color = black;
                    if(other->right)
                    {
                        other->right->color = black;
                    }
                    root = RotateRight(parent,root);
                    child = root;
                    break;
                }
       }
       else
       {
           other = parent->left;
           if(other->color==red)
           {
               other->color  = black;
               parent->color = red;
               root = RotateLeft(parent,root);
               other = parent->left;
           }
           if((!other->left||other->left->color==black)&&(!other->right||other->right->color==black))
              {
                  other->color = red;
                  child = parent;
                  parent = child->parent;
              }
              else
                {
                    if(!other->left||other->left->color==black)
                    {
                        if(o_right = other->right)
                        {
                            o_right->color = black;
                        }
                        other->color = red;
                        root  = RotateRight(other,root);
                        other = parent->left;
                    }
                    other->color = parent->color;
                    parent->color = black;
                    if(other->left)
                    {
                        other->left->color = black;
                    }
                    root = RotateLeft(parent,root);
                    child = root;
                    break;
                }
       }
   }
   if(child)
   {
       child->color = black;
   }
   return root;
}

int main()
{
    int a[] = {15,7,10,9,4,5,8,20,1,6};
    red_black_tree<int>* tree = new red_black_tree<int>();
    red_black_node<int> *root = NULL;

    for(int i=0;i<sizeof(a)/sizeof(int);i++)
    {
       tree->Insert(a[i]);
       //tree->Find_parent();
      // tree->Trave();
      // getchar();
    }
        tree->Trave();
        printf("\\n");
    for(int i=0;i<sizeof(a)/sizeof(int);i++)
    {
        tree->Delete(a[i]);
        tree->Trave();
        getchar();
    }
    return 0;
}

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