第35课 - 创建二叉树
1. 指路法定位结点
从根节点开始。。。
结点1的位置：{NUll}
结点2的位置：{左}
结点3的位置：{右}
结点4的位置：{左，左}
结点5的位置：{左，右}
结点6的位置：{右，左}
结点7的位置：{右，右}
结点8的位置：{左，左，左}
结点9的位置：{左，左，右}
结点10的位置：{左，右，左}
指路法通过根结点与目标结点的相对位置进行定位。
指路法可以避开二叉树递归的性质“线性”定位。
思想：在C语言中可以利用bit位进行指路。
#define BT_LEFT 0
#define BT_RIGHT 1
typedef unsigned long long BTP0s;
2. 二叉树存储结构
用结构体来定义二叉树中的指针域。
二叉树的头结点也可以用结构体实现。
3. 二叉树的操作
（1）定位
while((count > 0)&&(current != NULL))
{
bit = pos &1;
pos = pos >>1;
count--;
parent = current;
if( bit == BT_LEFT)
{
current = current->left;
}
else if( bit == BT_RIGHT)
{
current = current->right;
}
}
技巧：利用二进制中的0和1分别代表left和right。
位运算是实现指路法的基础。
4. 程序
main.c
#include <stdio.h>
#include <stdlib.h>
#include "BTree.h"
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
struct Node
{
BTreeNode header;
char v;
};
void printf_data(BTreeNode* node)
{
if( node != NULL )
{
printf("%c", ((struct Node*)node)->v);
}
}
int main(int argc, char *argv[])
{
BTree* tree = BTree_Create();
struct Node n1 = {{NULL, NULL}, 'A'};
struct Node n2 = {{NULL, NULL}, 'B'};
struct Node n3 = {{NULL, NULL}, 'C'};
struct Node n4 = {{NULL, NULL}, 'D'};
struct Node n5 = {{NULL, NULL}, 'E'};
struct Node n6 = {{NULL, NULL}, 'F'};
BTree_Insert(tree, (BTreeNode*)&n1, 0, 0, 0);
BTree_Insert(tree, (BTreeNode*)&n2, 0x00, 1, 0);
BTree_Insert(tree, (BTreeNode*)&n3, 0x01, 1, 0);
BTree_Insert(tree, (BTreeNode*)&n4, 0x00, 2, 0);
BTree_Insert(tree, (BTreeNode*)&n5, 0x02, 2, 0);
BTree_Insert(tree, (BTreeNode*)&n6, 0x02, 3, 0);
printf("Height: %d\n", BTree_Height(tree));
printf("Degree: %d\n", BTree_Degree(tree));
printf("Count: %d\n", BTree_Count(tree));
printf("Position At (0x02, 2): %c\n", ((struct Node*)BTree_Get(tree, 0x02, 2))->v);
printf("Full Tree: \n");
BTree_Display(tree, printf_data, 4, '-');
BTree_Delete(tree, 0x00, 1);
printf("After Delete B: \n");
printf("Height: %d\n", BTree_Height(tree));
printf("Degree: %d\n", BTree_Degree(tree));
printf("Count: %d\n", BTree_Count(tree));
printf("Full Tree: \n");
BTree_Display(tree, printf_data, 4, '-');
BTree_Clear(tree);
printf("After Clear: \n");
printf("Height: %d\n", BTree_Height(tree));
printf("Degree: %d\n", BTree_Degree(tree));
printf("Count: %d\n", BTree_Count(tree));
BTree_Display(tree, printf_data, 4, '-');
BTree_Destroy(tree);
return 0;
}
BTree.h
#ifndef _BTREE_H_
#define _BTREE_H_
#define BT_LEFT 0
#define BT_RIGHT 1
typedef void BTree;
typedef unsigned long long BTPos;
typedef struct _tag_BTreeNode BTreeNode;
struct _tag_BTreeNode
{
BTreeNode* left;
BTreeNode* right;
};
typedef void (BTree_Printf)(BTreeNode*);
BTree* BTree_Create();
void BTree_Destroy(BTree* tree);
void BTree_Clear(BTree* tree);
int BTree_Insert(BTree* tree, BTreeNode* node, BTPos pos, int count, int flag);
BTreeNode* BTree_Delete(BTree* tree, BTPos pos, int count);
BTreeNode* BTree_Get(BTree* tree, BTPos pos, int count);
BTreeNode* BTree_Root(BTree* tree);
int BTree_Height(BTree* tree);
int BTree_Count(BTree* tree);
int BTree_Degree(BTree* tree);
void BTree_Display(BTree* tree, BTree_Printf* pFunc, int gap, char div);
#endif
BTree.c
#include <stdio.h>
#include <malloc.h>
#include "BTree.h"
typedef struct _tag_BTree TBTree;
struct _tag_BTree
{
int count;
BTreeNode* root;
};
static void recursive_display(BTreeNode* node, BTree_Printf* pFunc, int format, int gap, char div) // O(n)
{
int i = 0;
if( (node != NULL) && (pFunc != NULL) )
{
for(i=0; i<format; i++)
{
printf("%c", div);
}
pFunc(node);
printf("\n");
if( (node->left != NULL) || (node->right != NULL) )
{
recursive_display(node->left, pFunc, format + gap, gap, div);
recursive_display(node->right, pFunc, format + gap, gap, div);
}
}
else
{
for(i=0; i<format; i++)
{
printf("%c", div);
}
printf("\n");
}
}
static int recursive_count(BTreeNode* root) // O(n)
{
int ret = 0;
if( root != NULL )
{
ret = recursive_count(root->left) + 1 + recursive_count(root->right);
}
return ret;
}
static int recursive_height(BTreeNode* root) // O(n)
{
int ret = 0;
if( root != NULL )
{
int lh = recursive_height(root->left);
int rh = recursive_height(root->right);
ret = ((lh > rh) ? lh : rh) + 1;
}
return ret;
}
static int recursive_degree(BTreeNode* root) // O(n)
{
int ret = 0;
if( root != NULL )
{
if( root->left != NULL )
{
ret++;
}
if( root->right != NULL )
{
ret++;
}
if( ret == 1 )
{
int ld = recursive_degree(root->left);
int rd = recursive_degree(root->right);
if( ret < ld )
{
ret = ld;
}
if( ret < rd )
{
ret = rd;
}
}
}
return ret;
}
BTree* BTree_Create() // O(1)
{
TBTree* ret = (TBTree*)malloc(sizeof(TBTree));
if( ret != NULL )
{
ret->count = 0;
ret->root = NULL;
}
return ret;
}
void BTree_Destroy(BTree* tree) // O(1)
{
free(tree);
}
void BTree_Clear(BTree* tree) // O(1)
{
TBTree* btree = (TBTree*)tree;
if( btree != NULL )
{
btree->count = 0;
btree->root = NULL;
}
}
int BTree_Insert(BTree* tree, BTreeNode* node, BTPos pos, int count, int flag) // O(n)
{
TBTree* btree = (TBTree*)tree;
int ret = (btree != NULL) && (node != NULL) && ((flag == BT_LEFT) || (flag == BT_RIGHT));
int bit = 0;
if( ret )
{
BTreeNode* parent = NULL;
BTreeNode* current = btree->root;
node->left = NULL;
node->right = NULL;
while( (count > 0) && (current != NULL) )
{
bit = pos & 1;
pos = pos >> 1;
parent = current;
if( bit == BT_LEFT )
{
current = current->left;
}
else if( bit == BT_RIGHT )
{
current = current->right;
}
count--;
}
if( flag == BT_LEFT )
{
node->left = current;
}
else if( flag == BT_RIGHT )
{
node->right = current;
}
if( parent != NULL )
{
if( bit == BT_LEFT )
{
parent->left = node;
}
else if( bit == BT_RIGHT )
{
parent->right = node;
}
}
else
{
btree->root = node;
}
btree->count++;
}
return ret;
}
BTreeNode* BTree_Delete(BTree* tree, BTPos pos, int count) // O(n)
{
TBTree* btree = (TBTree*)tree;
BTreeNode* ret = NULL;
int bit = 0;
if( btree != NULL )
{
BTreeNode* parent = NULL;
BTreeNode* current = btree->root;
while( (count > 0) && (current != NULL) )
{
bit = pos & 1;
pos = pos >> 1;
parent = current;
if( bit == BT_LEFT )
{
current = current->left;
}
else if( bit == BT_RIGHT )
{
current = current->right;
}
count--;
}
if( parent != NULL )
{
if( bit == BT_LEFT )
{
parent->left = NULL;
}
else if( bit == BT_RIGHT )
{
parent->right = NULL;
}
}
else
{
btree->root = NULL;
}
ret = current;
btree->count = btree->count - recursive_count(ret);
}
return ret;
}
BTreeNode* BTree_Get(BTree* tree, BTPos pos, int count) // O(n)
{
TBTree* btree = (TBTree*)tree;
BTreeNode* ret = NULL;
int bit = 0;
if( btree != NULL )
{
BTreeNode* current = btree->root;
while( (count > 0) && (current != NULL) )
{
bit = pos & 1;
pos = pos >> 1;
if( bit == BT_LEFT )
{
current = current->left;
}
else if( bit == BT_RIGHT )
{
current = current->right;
}
count--;
}
ret = current;
}
return ret;
}
BTreeNode* BTree_Root(BTree* tree) // O(1)
{
TBTree* btree = (TBTree*)tree;
BTreeNode* ret = NULL;
if( btree != NULL )
{
ret = btree->root;
}
return ret;
}
int BTree_Height(BTree* tree) // O(n)
{
TBTree* btree = (TBTree*)tree;
int ret = 0;
if( btree != NULL )
{
ret = recursive_height(btree->root);
}
return ret;
}
int BTree_Count(BTree* tree) // O(1)
{
TBTree* btree = (TBTree*)tree;
int ret = 0;
if( btree != NULL )
{
ret = btree->count;
}
return ret;
}
int BTree_Degree(BTree* tree) // O(n)
{
TBTree* btree = (TBTree*)tree;
int ret = 0;
if( btree != NULL )
{
ret = recursive_degree(btree->root);
}
return ret;
}
void BTree_Display(BTree* tree, BTree_Printf* pFunc, int gap, char div) // O(n)
{
TBTree* btree = (TBTree*)tree;
if( btree != NULL )
{
recursive_display(btree->root, pFunc, 0, gap, div);
}
}
小结：
二叉树在结构上不依赖组织链表。
通过指路法可以方便的定位二叉树中的结点。
基于指路法的二叉树在插入、删除和获取操作的实现细节上与单链表相似。
单链表就是特殊的额二叉树，实现上当然相似，只是更简单而已。