C Primer Plus–高級數據結構表示之二叉樹
二叉搜索樹 Binary Search Tree
二叉樹是一種高級數據結構。樹中的每個節點都包含一個項目和兩個指向其他節點的指針。
每個節點都有兩個子節點:左節點、右節點。在左節點中的項目是父節點中項目的前序向,而在右節點中的項目是父節點項目的後序向。
二叉樹中每一個節點本身是其後代節點的根,此節點與其後代節點構成一個子樹,子樹有左右之分。
用C構建二叉樹ADT
首先明確二叉樹結構:
二叉樹或者是一個空的節點集合(空樹),或者是一個指定某個節點爲根的節點集合。每個節點有兩個作爲其後代的樹,稱爲左子樹和右子樹。
每個子樹本身又是一個二叉樹,也包含它是個空樹的可能性。
二叉搜索樹是有序的二叉樹,它的每個節點包含一個項目,它的所有左子樹的項目排在根項目的前面,而根項目排在所有右子樹項目的前面。
而且二叉樹的類型操作有:
- 樹初始化爲空樹
- 查詢樹是否爲空
- 查詢樹是否已滿
- 查詢樹中項目個數
- 向樹中添加項目
- 從樹中刪除項目
- 從樹中搜索一個項目
- 遍歷樹中所有項目
- 清空樹
樹結構的定義
假設一個項目中包含一部電影的名字,上映年份,我們定義項目爲Item
:定義節點Node
結構,包含一部電影,節點的左子節點,節點的右子節點指針;定義結構Tree
包含根節點指針、樹的項目個數。
#define TITLE_MAX_CHARS 40
typedef struct movie {
char title[TITLE_MAX_CHARS];
int year;
} Item;
typedef struct node {
Item movie;
struct movie * left;
struct movie * right;
} Node;
typedef struct tree {
Node * root;
int size;
} Tree;
定義好了數據結構,下面進行樹操作的定義:
//初始化樹
void InitializeTree(Tree * ptoTree);
//樹是空的嗎?
bool TreeIsEmpty(const Tree * ptoTree);
//樹滿了嗎?假定我們隊樹的最大項目樹有要求
bool TreeIsFull(const Tree * ptoTree);
//查詢樹的項目數
bool TreeSize(const Tree * ptoTree);
//向樹添加項目
bool AddMovieToTree(const Item * ptoItem,Tree * ptoTree);
//從樹刪除項目
bool DleteMovieFromTree(const Item * ptoItem,Tree * ptoTree);
//項目是否重複?
bool IsInTree(const Item * ptoItem, Tree * ptoTree);
//遍歷樹的項目
void TraverseTree(const Tree * ptoTree,void (* ptoFunc) (Item item));
完整程序如下:
binarySearchTree.h
:
//
// Created by bob on 2018/11/14.
//
#ifndef LEARNINGC_BINARYSEARCHTREE_H
#define LEARNINGC_BINARYSEARCHTREE_H
#include <stdbool.h>
#define MAX_ITEMS 40
#define TITLE_MAX_CHARS 40
typedef struct movie {
char title[TITLE_MAX_CHARS];
int year;
} Item;
typedef struct node {
Item movie;
struct node * left;
struct node * right;
} Node;
typedef struct tree {
Node * root;
int size;
} Tree;
typedef struct pair {
Node * parent;
Node * child;
} Pair;
void InitializeTree(Tree * ptoTree);
bool TreeIsEmpty(const Tree * ptoTree);
bool TreeIsFull(const Tree * ptoTree);
int TreeSize(const Tree * ptoTree);
bool AddMovieToTree(const Item * ptoItem,Tree * ptoTree);
bool DleteMovieFromTree(const Item * ptoItem,Tree * ptoTree);
bool IsInTree(const Item * ptoItem, Tree * ptoTree);
void TraverseTree(const Tree * ptoTree,void (* ptoFunc) (Item item));
void ClearTree(Tree * ptoTree);
#endif //LEARNINGC_BINARYSEARCHTREE_H
binarySearchTree.c
:
//
// Created by bob on 2018/11/14.
//
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include "binarySearchTree.h"
static Pair SeekItem(const Item *, const Tree *);
static bool ToLeft(const Item * p1, const Item * p2);
static bool ToRight(const Item * p1, const Item * p2);
static Node * MakeNode(const Item * ptoItem);
static bool AddNodeToTree(Node * new_node, Node * root);
static bool DeleteNode(Node ** p);
static void Traverse(const Tree * ptoTree,void (*pfunc) (Item movie));
static void InOrder(const Node * parent, void (*pfunc) (Item movie));
static void DeleteAllNodes(Node * parent);
Pair SeekItem(const Item * ptoItem, const Tree * ptoTree) {
Pair scan;
scan.parent = NULL;
scan.child = ptoTree->root;
if(scan.child == NULL)
return scan;
while (scan.child != NULL){
if(ToLeft(ptoItem,&(scan.child->movie))){
scan.parent = scan.child;
scan.child = scan.child->left;
} else if(ToRight(ptoItem,&(scan.child->movie))){
scan.parent = scan.child;
scan.child = scan.child->right;
} else{
break;
}
}
return scan;
}
bool ToLeft(const Item *p1, const Item *p2) {
int compl;
if((compl = strcmp(p1->title,p2->title)) < 0)
return true;
else if((compl = strcmp(p1->title,p2->title)) == 0 && p1->year < p2->year)
return true;
else
return false;
}
bool ToRight(const Item *p1, const Item *p2) {
int compl;
if((compl = strcmp(p1->title,p2->title)) > 0)
return true;
else if((compl = strcmp(p1->title,p2->title)) == 0 && p1->year > p2->year)
return true;
else
return false;
}
Node * MakeNode(const Item *ptoItem) {
Node * new_node;
new_node = (Node *) malloc(sizeof(Node));
if(new_node == NULL){
fprintf(stderr,"Can not allocate memory to create a node.\n");
return NULL;
}
if(ptoItem != NULL){
new_node->movie = * ptoItem;
new_node->left = NULL;
new_node->right = NULL;
}
return new_node;
}
bool AddNodeToTree(Node *new_node, Node * root) {
if(ToLeft(&new_node->movie,&root->movie)){
if(root->left == NULL)
root->left = new_node;
else
AddNodeToTree(new_node,root->left);
}else if(ToRight(&new_node->movie,&root->movie)){
if(root->right == NULL)
root->right = new_node;
else
AddNodeToTree(new_node,root->right);
}else{
fprintf(stderr,"Error in locating the inserting index of this node.\n");
exit(1);
}
return true;
}
bool DeleteNode(Node ** p) {
Node * p_temp;
puts("Deleting the movie:");
puts((*p)->movie.title);
if((*p)->left == NULL){
p_temp = *p;
*p = (*p)->right;
free(p_temp);
} else if((*p)->right == NULL){
p_temp = *p;
*p = (*p)->left;
free(p_temp);
}else{
for (p_temp = (*p)->left;p_temp->right != NULL;p_temp = p_temp->right)
continue;
p_temp->right = (*p)->right;
p_temp = *p;
*p = (*p)->left;
free(p_temp);
}
}
void Traverse(const Tree *ptoTree, void (*pfunc)(Item)) {
if(ptoTree != NULL)
InOrder(ptoTree->root,pfunc);
}
void InOrder(const Node *parent, void (*pfunc)(Item)) {
if(parent != NULL){
InOrder(parent->left,pfunc);
(*pfunc)(parent->movie);
InOrder(parent->right,pfunc);
}
}
void DeleteAllNodes(Node *parent) {
Node * ptoRight;
if(parent != NULL){
ptoRight = parent->right;
DeleteAllNodes(parent->left);
free(parent);
DeleteAllNodes(ptoRight);
}
}
void InitializeTree(Tree *ptoTree) {
ptoTree -> root = NULL;
ptoTree->size=0;
}
bool TreeIsEmpty(const Tree *ptoTree) {
if(ptoTree->root == NULL)
return 1;
else
return 0;
}
bool TreeIsFull(const Tree *ptoTree) {
if(ptoTree->size >= MAX_ITEMS)
return true;
else
return false;
}
int TreeSize(const Tree *ptoTree) {
return ptoTree->size;
}
bool AddMovieToTree(const Item * ptoItem, Tree * ptoTree) {
if(ptoItem == NULL | strlen(ptoItem->title) == 0 | ptoItem->year < 1800){
fprintf(stderr,"The movie you are adding has something wrong.");
return false;
}
if(TreeIsFull(ptoTree)){
fprintf(stderr,"The tree is full. You can not add a movie to a full tree");
return false;
}
if(SeekItem(ptoItem,ptoTree).child != NULL){
fprintf(stderr,"Trying to add duplicate movie.\n");
}
Node * new_node;
new_node = MakeNode(ptoItem);
// if(new_node == NULL){
//
// }//無需判斷new_node是否爲空指針,MakeNode函數裏已經做過了
ptoTree->size++;
if(ptoTree->root == NULL)
ptoTree->root = new_node;
else
AddNodeToTree(new_node,ptoTree->root);
return true;
}
bool DleteMovieFromTree(const Item *ptoItem, Tree *ptoTree) {
Pair scan;
scan = SeekItem(ptoItem,ptoTree);
if(scan.child == NULL)
return false;
if(scan.parent == NULL)
DeleteNode(&ptoTree->root);
else if(scan.parent->left == scan.child)
//這裏不能傳scan.child,雖染這兩個指向的是同一個node,但我們必須得傳父節點持有的指針的指針
DeleteNode(&scan.parent->left);
else
DeleteNode(&scan.parent->right);
ptoTree->size--;
return true;
}
bool IsInTree(const Item *ptoItem, Tree *ptoTree) {
return SeekItem(ptoItem,ptoTree).child != NULL;
}
void TraverseTree(const Tree *ptoTree, void (*ptoFunc)(Item)) {
Traverse(ptoTree,ptoFunc);
}
void ClearTree(Tree *ptoTree) {
if(ptoTree == NULL)
return;
else
DeleteAllNodes(ptoTree->root);
ptoTree->root = NULL;
ptoTree->size = 0;
}
好亂,日後再改。