树三：创建二叉树
指路法定位结点：
- 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
- 在C语言中可以用 bit 位来进行指路：
#define BT_LEFT 0
#define BT_RIGHT 1
typedef unsigned long long BTPos;
二叉树的存储结构：
/* 结点指针域定义 */ typedef struct _tag_BTreeNode BTreeNode; struct _tag_BTreeNode { BTreeNode* left; BTreeNode* right; };
/* 头结点定义 */ typedef struct _tag_BTree BTree; struct _tag_BTree { int count; BTreeNode* root; };
/* 数据元素定义示例 */ struct Node { BTreeNode header; char v; };
定位操作：
/* main.c */ #include <stdio.h> #include <stdlib.h> #include "BTree.h" 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); } }
