二叉搜索树

二叉搜索树是红黑树的基础。

关于红黑树的链接：

http://blog.csdn.net/v_JULY_v/article/details/6105630

linux kernel 源码中关于红黑树的链接：
https://github.com/torvalds/linux/blob/master/lib/rbtree.c
https://github.com/torvalds/linux/blob/master/include/linux/rbtree_augmented.h
https://github.com/torvalds/linux/blob/master/include/linux/rbtree.h

源码：

//BinaryTree.h

<span style="font-size:18px;">#ifndef BINARY_TREE_H#define BINARY_TREE_H#include "common.h"typedef struct BinSrchNode{struct BinSrchNode* left,*right,*p;int key;}BSNODE,*BSTREE;#endif</span>

<span style="font-size:18px;">BSNODE* TreeInsert(BSNODE* root,BSNODE* node);BSNODE* NewNode(BSNODE* node);BSNODE* IterativeTreeSearch(BSNODE* x,int k);BSNODE* TreeMaxmum(BSNODE* x);BSNODE* TreeMinmum(BSNODE* x);BSNODE* TreeSuccesor(BSNODE* x);BSNODE* TreeDelete(BSNODE* root,BSNODE* toDel);void SearchTree();void SearchTree(){int i,j;BSNODE* Root=NULL;BSNODE node;BSNODE* tmp;int toBeInsert[] = {5,2,8,4,1,6,9,15,12,13,11,16,14,10};node.key = 10;Root = TreeInsert(Root,&node);//         10//       /  \//   /           \//   5           15// /  \         /  \//2    8       12  16//   /    /  \    / \  //  1    6    9  11  13//               /  \            //              10    14for(i=0; i<sizeof(toBeInsert)/sizeof(int); i++){BSNODE node;node.key = toBeInsert[i];Root = TreeInsert(Root,&node);}for(i=0; i<17; i++){tmp = IterativeTreeSearch(Root,i);if(tmp){printf("\n%d ",tmp->key);//&& tmp->key != 5if (tmp->key == 12){i = i;}Root = TreeDelete(Root,tmp);printf("=---=");for(j=0; j<20; j++){tmp = IterativeTreeSearch(Root,j);if(tmp){printf("%d ",tmp->key);}}}}}BSNODE* TreeInsert(BSNODE* root,BSNODE* node){BSNODE *predecesor = NULL,*tmp = root;//while循环用来寻找新节点的插入位置，小于向左大于向右走//循环停止条件：直到到达树叶位置。//predecesor保存了树叶的地址，也是循环过程中循环变量tmp的前任。while(tmp != NULL){predecesor = tmp;if(node->key < tmp->key){tmp = tmp->left;}else {tmp = tmp->right;}}node->p = predecesor;tmp = NewNode(node);if(predecesor == NULL)//如果是空树{return tmp;}else if(node->key < predecesor->key){predecesor->left = tmp;}else{predecesor->right = tmp;}return root;}BSNODE* NewNode(BSNODE* node){BSNODE* pNode = (BSNODE*)malloc(sizeof(BSNODE));pNode->key = node->key;pNode->p = node->p;pNode->left = NULL;pNode->right = NULL;return pNode;}BSNODE* IterativeTreeSearch(BSNODE* x,int k){while(x != NULL && x->key != k){if(k < x->key){x = x->left;}else{x = x->right;}}return x;}BSNODE* TreeMinmum(BSNODE* x){while(x->left != NULL){x = x->left;}return x;}BSNODE* TreeMaxmum(BSNODE* x){while(x->right != NULL){x = x->right;}return x;}BSNODE* TreeSuccesor(BSNODE* x){BSNODE* p;if(x->right != NULL)//如果当前结点有右孩子那么他的后继定在其右孩子中{return TreeMinmum(x);}//如果没有右孩子，则其后继在下一个被中序遍历的结点上。//while循环用来寻找下一个被遍历的结点。//循环条件：没有到达根节点或子是父的右孩子。//循环截止条件为到达根节点或者到了子树是父结点的左分支结点p = x->p;while(p != NULL && x == p->right){x = p;p = p->p;}return p;}static BSNODE* Transplant(BSNODE* root, BSNODE* oldNode,BSNODE* newNode){if(oldNode->p == NULL)//如果被替换结点是根节点{root = newNode;}else if(oldNode == oldNode->p->left)//如果被替换结点是其父结点的左分支{oldNode->p->left = newNode;}else{oldNode->p->right = newNode;}if(newNode != NULL){newNode->p = oldNode->p;}return root;}BSNODE* TreeDelete(BSNODE* root,BSNODE* toDel){BSNODE* successor;if(toDel->left == NULL)//如果被删除结点的左孩子是空，则用其右孩子将其替换掉{root = Transplant(root,toDel,toDel->right);}else if (toDel->right == NULL)//反之{root = Transplant(root,toDel,toDel->left);}//后继的位置可以直接由其右孩子继承，else//否则比较复杂了，后继用来替换被删结点，因为后继的左孩子为空，{successor = TreeMinmum(toDel->right);//右子树结点中最小的子孙结点是其后继。if (successor != NULL && successor->p != toDel){//后继右旋操作。右旋可以将root = Transplant(root,successor,successor->right);//successor->right = toDel->right;successor->right->p = successor;}root = Transplant(root,toDel,successor);//用后继替换被删结点successor->left = toDel->left;successor->left->p = successor;}return root;}</span>