红黑树的删除

Posted Lune-Qiu

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红黑树的删除共有12种情况,

设要删除的节点为Z:

1.Z为根  且没有孩子   直接删除,将根赋空

2.Z为根    有一个红孩子(由于第4条性质一定为红孩子) 将孩子颜色->黑,当做新的根,删除节点

3.Z红色   直接删除,判断Z为父亲的左孩子或右孩子 将其赋空  (此节点一定没有孩子,因为2个孩子的已经处理过,一个红孩子(两个红色节点不能相邻),一个黑孩子(到终端节点黑节点数相同))

4.Z为黑色   有一个红孩子   将红孩子->黑,Z的父与Z的子相连,删除Z

5.Z为黑色   没有孩子(由于要删除的是黑节点,整个过程通俗的理解就是想要借一个黑节点;当侄子为红节点则可以变为黑节点,然后借来一个黑节点

  5.1 兄弟为红(初始状态)

    兄是父右,兄->黑,父->红 ,以父为支点左旋   更新兄

      

    

      兄是父左,兄->黑,父->红,以父为支点右旋,更新兄

  5.2兄弟为黑(初始状态或调整状态)

    5.2.1左侄黑,右侄黑

      5.2.1.1父黑:   兄->红,以父亲为当前节点向上调整    ,更新兄 (由于少了一个黑节点,则向上借黑节点)

        初始状态:

             

        调整状态:

             

      5.2.1.2父红:兄->红,父->黑,结束

        初始状态:

          删除Z即可

        调整中:

          

 

     5.2.2左侄子红,右侄子黑

      5.2.2.1兄为父右:左侄子->黑,兄->红,以兄弟为支点右旋  ,更新兄

        初始状态:

          

        调整中:

          

       5.2.2.2兄为父右:兄弟->父亲的颜色,父->黑,左侄->黑,以父亲为节点右旋  结束

    5.2.3右侄红(右侄子红,左侄子黑;或者右侄子红)

      5.2.3.1兄为父右:兄弟->父亲的颜色,父->黑,右侄->黑,以父亲为支点左旋  结束

        初始状态:

         删除Z即可

        调整中:

         

 

       5.2.3.2兄为父左:右侄->黑,兄->红,以兄弟为支点右旋 ,更新兄弟

 

       通过上图,可以看出,5.2.2.1状态的下一个状态是5.2.3.1

                5.2.3.2状态点的下一个状态是5.2.2.2

代码:需要注意的就是:更新兄弟的时候,由于使用的假删除,要特别注意

RBT* Search(RBT* pRBT,int num)
{
    if(pRBT == NULL) return NULL;
    while(pRBT)
    {
        if(pRBT->val == num)
            return pRBT;
        else if(pRBT->val > num)
            pRBT = pRBT->pLeft;
        else
            pRBT = pRBT->pRight;
    }
    return NULL;
}
RBT* GetBrother(RBT* pRBT)
{
    if(pRBT == NULL) return NULL;
    if(pRBT == pRBT->pFather->pLeft)
        return pRBT->pFather->pRight;
    else
        return pRBT->pFather->pLeft;
}
void DelNode(RBT* pRBT,int num)
{
    if(pRBT == NULL) return ;
    RBT* pdel = Search(pRBT,num);//原始要删除的点
    RBT* ptmp = pdel;//真正要删除的点
    if(pdel == NULL) return;
    if(pdel->pLeft && pdel->pRight)
    {
        ptmp = pdel->pLeft;
        while(ptmp->pRight)
        {
            ptmp = ptmp->pRight;
        }
        pdel->val = ptmp->val;
    }
    if(ptmp == rbt)//为根
    {
        //没有孩子
        if(ptmp->pLeft == NULL && ptmp->pRight == NULL)
        {
            free(ptmp);
            ptmp = NULL;
            rbt = NULL;
            return;
        }
        //有一个孩子
        if(ptmp->pLeft != NULL || ptmp->pRight != NULL)
        {
            rbt = ptmp->pLeft ? ptmp->pLeft : ptmp->pRight;
            free(ptmp);
            ptmp = NULL;
            rbt->color = BLACK;
            rbt->pFather = NULL;
            return;
        }
    }


    //红色
    if(ptmp->color == RED)
    {
        if(ptmp->pFather->pLeft == ptmp)
            ptmp->pFather->pLeft = NULL;
        else
            ptmp->pFather->pRight = NULL;
        free(ptmp);
        ptmp = NULL;
        return;
    }
    if(ptmp->color == BLACK)//真正要删除节点为黑
    {
        //有一个红孩子
        if(ptmp->pLeft || ptmp->pRight)
        {
            if(ptmp == ptmp->pFather->pLeft)
            {
                ptmp->pFather->pLeft = ptmp->pLeft ? ptmp->pLeft : ptmp->pRight;
                ptmp->pFather->pLeft->pFather = ptmp->pFather;
                ptmp->pFather->pLeft->color = BLACK;
            }
            else
            {
                ptmp->pFather->pRight = ptmp->pLeft ? ptmp->pLeft : ptmp->pRight;
                ptmp->pFather->pRight->pFather = ptmp->pFather;
                ptmp->pFather->pRight->color = BLACK;
            }
            free(ptmp);
            ptmp = NULL;
            return;
        }
        //没有孩子
        if(ptmp->pLeft == NULL && ptmp->pRight == NULL)
        {
            RBT* pbrother = GetBrother(ptmp);
            RBT* pfather = ptmp->pFather;
       //假删除
if(ptmp == pfather->pLeft) pfather->pLeft = NULL; else pfather->pRight = NULL; pdel = ptmp; while(1) { //兄弟红 if(pbrother != NULL && pbrother->color == RED) { pbrother->color = BLACK; pbrother->pFather->color = RED; if(pbrother == pbrother->pFather->pRight) { pbrother = pbrother->pLeft;//更新兄弟,为左侄子 LeftSpin(&ptmp->pFather); continue; } if(pbrother == pbrother->pFather->pLeft) { pbrother = pbrother->pRight;//更新兄弟为右侄子 RightSpin(&ptmp->pFather); continue; } } //兄弟黑 if(pbrother->color == BLACK) { //两个侄子黑或者没有侄子 if((pbrother->pLeft && pbrother->pLeft->color == BLACK && pbrother->pRight && pbrother->pRight->color == BLACK)|| (pbrother->pLeft == NULL && pbrother->pRight == NULL)) { if(pbrother->pFather->color == RED) { pbrother->pFather->color = BLACK; pbrother->color = RED; break; } if(pbrother->pFather->color == BLACK) { pbrother->color = RED; ptmp = ptmp->pFather; if(ptmp->pFather == NULL) break; pbrother = GetBrother(ptmp); continue; } } //左侄子为红,右侄子为黑 if(pbrother->pLeft && pbrother->pLeft->color == RED && (pbrother->pRight == NULL || pbrother->pRight->color == BLACK) ) { //兄为父右 if(pbrother == pbrother->pFather->pRight) { pbrother->pLeft->color = BLACK; pbrother->color = RED; RightSpin(&pbrother); pbrother = pbrother->pFather;//由于要以兄弟节点右旋,所以旋转完再更新 continue; } //兄为父左 if(pbrother == pbrother->pFather->pLeft) { pbrother->color = pbrother->pFather->color; pbrother->pLeft->color = BLACK; pbrother->pFather->color = BLACK; RightSpin(&ptmp->pFather); break; } } //右侄子为红 if(pbrother->pRight && pbrother->pRight->color == RED) { //兄为父右 if(pbrother == pbrother->pFather->pRight) { pbrother->pRight->color = BLACK; pbrother->color = pbrother->pFather->color; pbrother->pFather->color = BLACK; LeftSpin(&ptmp->pFather); break; } //兄为父左 if(pbrother == pbrother->pFather->pLeft) { pbrother->pRight->color = BLACK; pbrother->color = RED; LeftSpin(&pbrother); pbrother = pbrother->pFather;//兄弟更新 continue; } } } } } } free(pdel); pdel = NULL; }

    这篇博客是有史以来写的最认真的一个了,希望下次看的时候一下就能看懂,也希望能对看到这篇博客的人有一些帮助~

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