红黑树RBT基本概念与实现

1. 基本概念

RBT的作用与平衡二叉树类似，目的是优化原始BST查找效率低的问题。RBT需成立，要满足如下条件：

树中每个节点有颜色（红或黑）
根节点必须为黑色
NULL值处称为终端节点，我们可以认为是黑色
不允许两个红节点互为父子关系
从任意节点向下出发，到所有终端节点的各条路径上黑节点个数相同

2. RBT节点添加

向RBT添加节点，该节点默认初始化为红色。（若为黑色则第五个条件不满足，若为红色可能不满足第四个条件，但第五个条件不好调控，所以选择红色。）
添加步骤如下图：

3. RBT节点删除

代码实现：

#include<stdio.h>
#include<stdlib.h>enum COLOR{RED,BLACK};typedef struct rbt
{int nValue;int nColor;struct rbt *pLeft;struct rbt *pRight;struct rbt *pFather;
}RBT;RBT *pRBT = NULL;void RightRotate(RBT **pTree)
{if(*pTree == NULL || (*pTree)->pLeft == NULL)return;RBT *pNode = *pTree;RBT *pMark = pNode->pLeft;//三个孩子关系pNode->pLeft = pMark->pRight;pMark->pRight = pNode;if(pNode->pFather != NULL){if(pNode == pNode->pFather->pLeft){pNode->pFather->pLeft = pMark;}else{pNode->pFather->pRight = pMark;}}else{//换根pRBT = pMark;}//三个父亲关系if(pNode->pLeft != NULL){pNode->pLeft->pFather = pNode;}pMark->pFather = pNode->pFather;pNode->pFather = pMark;
}
void LeftRotate(RBT **pTree)
{if(*pTree == NULL || (*pTree)->pRight == NULL)return;RBT *pNode = *pTree;RBT *pMark = pNode->pRight;//三个孩子关系pNode->pRight = pMark->pLeft;pMark->pLeft = pNode;if(pNode->pFather != NULL){if(pNode == pNode->pFather->pLeft){pNode->pFather->pLeft = pMark;}else{pNode->pFather->pRight = pMark;}}else{//换根pRBT = pMark;}//三个父亲关系if(pNode->pRight != NULL){pNode->pRight->pFather = pNode;}pMark->pFather = pNode->pFather;pNode->pFather = pMark;
}RBT *Search(RBT *pTree,int nNum)
{if(pTree == NULL)return NULL;while(pTree){if(pTree->nValue > nNum){//左侧if(pTree->pLeft == NULL){return pTree;}pTree = pTree->pLeft;}else if(pTree->nValue < nNum){if(pTree->pRight == NULL){return pTree;}pTree = pTree->pRight;}else{printf("data error.\n");exit(1);}}
}RBT *GetUncle(RBT *pNode)
{if(pNode == pNode->pFather->pLeft){return pNode->pFather->pRight;}else{return pNode->pFather->pLeft;}
}void AddNode(RBT *pTree,int nNum)
{//查找RBT *pNode = NULL;pNode = Search(pTree,nNum);//申请空间RBT *pTemp = NULL;pTemp = (RBT*)malloc(sizeof(RBT));pTemp->nValue = nNum;pTemp->nColor = RED;pTemp->pFather = pNode;pTemp->pLeft = NULL;pTemp->pRight = NULL;//情况分析//1.空树if(pNode == NULL){pRBT = pTemp;pRBT->nColor = BLACK;return;}//非空树//连接if(pTemp->nValue < pNode->nValue){pNode->pLeft = pTemp;}else{pNode->pRight = pTemp;}//2.父亲是黑的if(pNode->nColor == BLACK){return;}//3.父亲是红的RBT *pUncle = NULL;RBT *pGrandFather = NULL;while(pNode->nColor == RED){pGrandFather = pNode->pFather;pUncle = GetUncle(pNode);//3.1叔叔是红色if(pUncle != NULL && pUncle->nColor == RED){pNode->nColor = BLACK;pUncle->nColor = BLACK;pGrandFather->nColor = RED;pTemp = pGrandFather;pNode = pTemp->pFather;//根if(pNode == NULL){pRBT->nColor = BLACK;break;}continue;}//3.2叔叔是黑的if(pUncle == NULL || pUncle->nColor == BLACK){//3.2.1父亲是爷爷的左if(pNode == pGrandFather->pLeft){//3.2.1.1当前节点是父亲的右if(pTemp == pNode->pRight){pTemp = pNode;LeftRotate(&pTemp);pNode = pTemp->pFather;}//3.2.1.2当前节点是父亲的左侧if(pTemp == pNode->pLeft){pNode->nColor = BLACK;pGrandFather->nColor = RED;RightRotate(&pGrandFather);break;}}//3.2.2父亲是爷爷的右if(pNode == pGrandFather->pRight){//3.2.2.1当前节点是父亲的左if(pTemp == pNode->pLeft){pTemp = pNode;RightRotate(&pTemp);pNode = pTemp->pFather;}//3.2.2.2当前节点是父亲的右if(pTemp == pNode->pRight){pNode->nColor = BLACK;pGrandFather->nColor = RED;LeftRotate(&pGrandFather);break;}}}}
}void CreateRBT(int arr[],int nLength)
{if(arr == NULL || nLength <= 0)return;int i;for(i = 0;i<nLength;i++){AddNode(pRBT,arr[i]);}
}void Traversal(RBT *pTree)
{if(pTree == NULL)return;printf("val == %d\tcol == %d\n",pTree->nValue,pTree->nColor);Traversal(pTree->pLeft);Traversal(pTree->pRight);
}RBT *FindNode(RBT *pTree,int nNum)
{if(pTree == NULL)return NULL;while(pTree){if(pTree->nValue == nNum){return pTree;}else if(pTree->nValue > nNum){pTree = pTree->pLeft;}else{pTree = pTree->pRight;}}return NULL;
}void DelNode(RBT *pTree,int nNum)
{//查找RBT *pTemp = NULL;pTemp = FindNode(pTree,nNum);if(pTemp == NULL)return;//分析孩子情况RBT *pMark = NULL;if(pTemp->pLeft != NULL && pTemp->pRight != NULL){pMark = pTemp;pTemp = pTemp->pLeft;while(pTemp->pRight != NULL){pTemp = pTemp->pRight;}//值覆盖pMark->nValue = pTemp->nValue;}//颜色RBT *pNode = pTemp->pFather;//1.根 且无孩子if(pNode == NULL && pTemp->pLeft == NULL && pTemp->pRight == NULL){pRBT = NULL;free(pTemp);pTemp = NULL;return;}//2.根 且有一个红孩子if(pNode == NULL && (pTemp->pLeft != NULL || pTemp->pRight != NULL)){pRBT = pTemp->pLeft ? pTemp->pLeft : pTemp->pRight;pRBT->nColor = BLACK;pRBT->pFather = NULL;free(pTemp);pTemp = NULL;return;}//3.非根 红色 if(pTemp->nColor == RED){if(pTemp == pNode->pLeft){pNode->pLeft = NULL;}else{pNode->pRight = NULL;}free(pTemp);pTemp = NULL;return;}//4.非根 黑色 且有一个红孩子if(pTemp->nColor == BLACK && (pTemp->pLeft != NULL || pTemp->pRight != NULL)){if(pTemp == pNode->pLeft){pNode->pLeft = pTemp->pLeft ? pTemp->pLeft:pTemp->pRight;pNode->pLeft->pFather = pNode;pNode->pLeft->nColor = BLACK;}else{pNode->pRight = pTemp->pLeft ? pTemp->pLeft:pTemp->pRight;pNode->pRight->pFather = pNode;pNode->pRight->nColor = BLACK;}free(pTemp);pTemp = NULL;return;}//5.非根 黑 且无孩子RBT *pBrother = GetUncle(pTemp);//假删除if(pTemp == pNode->pLeft){pNode->pLeft = NULL;}else{pNode->pRight = NULL;}pMark = pTemp;while(1){//5.1兄弟是红的if(pBrother->nColor == RED){pBrother->nColor = BLACK;pNode->nColor = RED;//5.1.1兄弟是父亲的左if(pBrother == pNode->pLeft){RightRotate(&pNode);pBrother = pNode->pLeft;continue;}//5.1.2兄弟是父亲的右if(pBrother == pNode->pRight){LeftRotate(&pNode);pBrother = pNode->pRight;continue;}}//5.2兄弟是黑的if(pBrother->nColor == BLACK){//5.2.1两个侄子全黑if((pBrother->pLeft == NULL && pBrother->pRight == NULL)||((pBrother->pLeft != NULL && pBrother->pLeft->nColor == BLACK)&&(pBrother->pRight != NULL && pBrother->pRight->nColor == BLACK))){//5.2.1.1父亲是红的if(pNode->nColor == RED){pNode->nColor = BLACK;pBrother->nColor = RED;break;}//5.2.1.2父亲是黑色的if(pNode->nColor == BLACK){pBrother->nColor = RED;pTemp = pNode;pNode = pTemp->pFather;//根if(pNode == NULL){break;}pBrother = GetUncle(pTemp);continue;}}//5.2.2左侄子红，右侄子黑if((pBrother->pLeft != NULL && pBrother->pLeft->nColor == RED)&&(pBrother->pRight == NULL || pBrother->pRight->nColor == BLACK)){//5.2.2.1兄弟是父亲的右if(pBrother == pNode->pRight){pBrother->nColor = RED;pBrother->pLeft->nColor = BLACK;RightRotate(&pBrother);pBrother = pNode->pRight;continue;}//5.2.2.2兄弟是父亲的左if(pBrother == pNode->pLeft){pBrother->nColor = pNode->nColor;pNode->nColor = BLACK;pBrother->pLeft->nColor = BLACK;RightRotate(&pNode);break;}}//5.2.3右侄子是红if(pBrother->pRight != NULL && pBrother->pRight->nColor == RED){//5.2.3.1兄弟是父亲的左if(pBrother == pNode->pLeft){pBrother->nColor = RED;pBrother->pRight->nColor = BLACK;LeftRotate(&pBrother);pBrother = pNode->pLeft;continue;}//5.2.3.2兄弟是父亲的右if(pBrother == pNode->pRight){pBrother->nColor = pNode->nColor;pNode->nColor = BLACK;pBrother->pRight->nColor = BLACK;LeftRotate(&pNode);break;}}}}free(pMark);pMark = NULL;
}int main()
{int arr[] = {11,2,14,1,7,15,5,8};CreateRBT(arr,sizeof(arr)/sizeof(arr[0]));Traversal(pRBT);printf("---------------------------\n");//AddNode(pRBT,4);//Traversal(pRBT);DelNode(pRBT,1);Traversal(pRBT);printf("---------------------------\n");DelNode(pRBT,11);Traversal(pRBT);printf("---------------------------\n");DelNode(pRBT,15);Traversal(pRBT);printf("---------------------------\n");DelNode(pRBT,2);Traversal(pRBT);printf("---------------------------\n");return 0;
}

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红黑树RBT基本概念与实现

1. 基本概念

2. RBT节点添加

3. RBT节点删除

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