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~