二叉查找树C语言实现及其可视化

2019年3月16日 242次阅读 来源: 二叉查找树

0， 二叉搜索树的定义：(二叉查找树)(二叉排序树)
      （1）若左子树非空，则左子树上的所有的节点的值都小于根节点的值
      （2）若右子树非空，则右子树上的所有的节点的值都大于根节点的值

      （3）其左右子树都是二叉搜索树

                  《二叉查找树C语言实现及其可视化》

1，二叉查找树的表示法

struct TreeNode;
typedef struct TreeNode *PtrSearchTree;
typedef PtrSearchTree SearchTree;
struct TreeNode
{
	int value;
	PtrSearchTree left;
	PtrSearchTree right;
};

2，二叉查找树的插入：插入的元素始终位于叶子节点。

void insert(SearchTree* tree, int value)
{
	if( *tree == NULL )
	{
		if( ! ((*tree) = (PtrSearchTree)malloc(sizeof(struct TreeNode))) )
		{
			printf("insert malloc error\n");
			exit(0);
		}
		(*tree)->value = value;
		(*tree)->left = (*tree)->right = NULL;
	}
	else
	{
		if( value < (*tree)->value )
			insert(&((*tree)->left), value);
		else
			insert(&((*tree)->right), value);
	}
}

3，二叉查找树的创建，调用插入函数即可。

note：

1  SearchTree tree = NULL；其中的 “= NULL”，在window下的gcc进行编译运行时可以省略， 但是在linux编译运行时如果没有将其值设置为NULL， 则提醒了“段错误”。应该是编译器的不同造成的， 不过为每个指针赋值，而不是由其变为野指针确实是个好的习惯。

2   getchar()是为了吃掉用户输入的数字之间的空格，并且在用户输入完成按下Enter键之后可以捕获到‘\n’.

SearchTree create()
{
	SearchTree tree = NULL;
	printf("Create Binary Search Tree\nplease enter the element, seperated by space, and stop input by Enter:\n");
	int key;
	while(1)
	{
		scanf("%d", &key);
		insert(&tree, key);
		if( getchar() == '\n' )
			break;
	}
	return tree;
}

4， 二叉查找树的可视化。为了对其进行可视化，需要借助与graphviz，他的安装在上一篇中有简单的介绍，并且其中使用的dot语言可在官网查看，很容易学习。

void visualization(SearchTree tree, char* filename)
{
	FILE *fw;
	if( NULL == (fw = fopen(filename, "w")) )
	{
		printf("open file error");
		exit(0);
	}
	fprintf(fw, "digraph\n{\nnode [shape = Mrecord, style = filled, color = black, fontcolor = white];\n");
	write2dot(tree, fw);
	fprintf(fw, "}");
	fclose(fw);
}
void write2dot(SearchTree tree, FILE* fw)
{
	if(tree == NULL)
		return ;
	else
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->value, tree->value);
	}
	if(tree->left)
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->left->value, tree->left->value);
		fprintf(fw, "%d:f0:sw -> %d:f1;\n", tree->value, tree->left->value);
	}
	if(tree->right)
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->right->value, tree->right->value);
		fprintf(fw, "%d:f2:se -> %d:f1;\n", tree->value, tree->right->value);
	}
	write2dot(tree->left, fw);
	write2dot(tree->right, fw);
}

函数注释：

         (1)  visualization函数将参数tree指定的树，使用dot语言写入到参数filename指定的文件中（文件以.dot为后缀）

         (2) write2dot函数相当于一个遍历树的过程，在遍历过程中， 构成该树的dot文件。

程序的运行过程实例如下：

《二叉查找树C语言实现及其可视化》

运行完成后会在同目录下产生一个.dot文件，在本程序中文件名为：searchtree.dot

使用dot命令产生图片，如下图所示，就生成了名为searchtree.png的图片。

《二叉查找树C语言实现及其可视化》

查看图片如下:

                          《二叉查找树C语言实现及其可视化》

5， 二叉树的删除

若删除元素为叶子节点，则直接删除，将原本指向该节点的双亲节点的相应的指针域置空，

若删除度为1的节点，将其输出节点的子树直接挂在删除节点的父节点上，

若删除度为2的节点，找其左子树的最大值或者右子树的最小值替代该节点的值，然后在其左子树或者右子树删除找到的最大值或者最小值。

SearchTree delete(SearchTree tree, int value)
{
	PtrSearchTree temp = NULL;
	if( !tree )
	{
		printf("have no element(delete): %d\n", value);
		return NULL;
	}
	else if( value < tree->value )
		tree->left = delete(tree->left, value);
	else if( value > tree->value )
		tree->right = delete(tree->right, value);
	else
	{
		if( tree->left && tree->right )
		{
			temp = find_min(tree->right);
			tree->value = temp->value;
			tree->right = delete(tree->right, temp->value);
		}
		else
		{
			temp = tree;
			if( !(tree->left) )tree = tree->right;
			else if( !(tree->right) )tree = tree->left;
			free(temp);
		}
	}
	return tree;
}

在程序中删除83，得到如下的二叉树：

                                《二叉查找树C语言实现及其可视化》

6，查找（递归和迭代）

                  note：函数的返回类型为指针类型。

SearchTree find_recursion(SearchTree tree, int value) { if( !tree ) { printf("have no element(find): %d\n", value); return NULL; } if( value < tree->value ) find_recursion(tree->left, value); else if( value > tree->value ) find_recursion(tree->right, value); else return tree; } SearchTree find_iteration(SearchTree tree, int value) { while(tree) { if( value < tree->value ) tree = tree->left; else if( value > tree->value ) tree = tree->right; else return tree; } printf("have no element(find): %d\n", value); return NULL; }

源码

#include<stdio.h>
#include<stdlib.h>

struct TreeNode;
typedef struct TreeNode *PtrSearchTree;
typedef PtrSearchTree SearchTree;
struct TreeNode
{
	int value;
	PtrSearchTree left;
	PtrSearchTree right;
};

SearchTree create();
void insert(SearchTree* tree, int value);
void write2dot(SearchTree tree, FILE* fw);
void visualization(SearchTree tree, char* filename);
SearchTree find_min(SearchTree tree);
SearchTree find_max(SearchTree tree);
SearchTree find_iteration(SearchTree tree, int value);
SearchTree find_recursion(SearchTree tree, int value);
SearchTree delete(SearchTree tree, int value);

int main(int argc, char** argv)
{
	SearchTree s_tree_1 = create();
	visualization(s_tree_1, "searchtree.dot");

	PtrSearchTree min = find_min(s_tree_1);
	PtrSearchTree max = find_max(s_tree_1);
	printf("the min and max is %d, %d, respectively\n", min->value, max->value);
	int search = 83;
	PtrSearchTree find_result_1 = find_iteration(s_tree_1, search);
	PtrSearchTree find_result_2 = find_iteration(s_tree_1, search);
	if( find_result_1 && find_result_2 )
		printf("search for %d, and the result from iteration and recursion is: %d, %d\n", search, find_result_1->value, find_result_2->value);

	s_tree_1 = delete(s_tree_1, 83);
	visualization(s_tree_1, "searchtree_afterdelete.dot");
	return 0;
}

SearchTree create()
{
	SearchTree tree = NULL;
	printf("Create Binary Search Tree\nplease enter the element, seperated by space, and stop input by Enter:\n");
	int key;
	while(1)
	{
		scanf("%d", &key);
		insert(&tree, key);
		if( getchar() == '\n' )
			break;
	}
	return tree;
}
void insert(SearchTree* tree, int value)
{
	if( *tree == NULL )
	{
		if( ! ((*tree) = (PtrSearchTree)malloc(sizeof(struct TreeNode))) )
		{
			printf("insert malloc error\n");
			exit(0);
		}
		(*tree)->value = value;
		(*tree)->left = (*tree)->right = NULL;
	}
	else
	{
		if( value < (*tree)->value )
			insert(&((*tree)->left), value);
		else
			insert(&((*tree)->right), value);
	}
}
void visualization(SearchTree tree, char* filename)
{
	FILE *fw;
	if( NULL == (fw = fopen(filename, "w")) )
	{
		printf("open file error");
		exit(0);
	}
	fprintf(fw, "digraph\n{\nnode [shape = Mrecord, style = filled, color = black, fontcolor = white];\n");
	write2dot(tree, fw);
	fprintf(fw, "}");
	fclose(fw);
}
void write2dot(SearchTree tree, FILE* fw)
{
	if(tree == NULL)
		return ;
	else
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->value, tree->value);
	}
	if(tree->left)
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->left->value, tree->left->value);
		fprintf(fw, "%d:f0:sw -> %d:f1;\n", tree->value, tree->left->value);
	}
	if(tree->right)
	{
		fprintf(fw, "%d [label = \"<f0> | <f1> %d | <f2> \", color = black, fontcolor = white, style = filled];\n", tree->right->value, tree->right->value);
		fprintf(fw, "%d:f2:se -> %d:f1;\n", tree->value, tree->right->value);
	}
	write2dot(tree->left, fw);
	write2dot(tree->right, fw);
}
SearchTree find_min(SearchTree tree)
{
	if( !tree )
		return NULL;
	else
		if( !(tree->left) ) return tree;
		else
			find_min(tree->left);
}
SearchTree find_max(SearchTree tree)
{
	if( !tree )
		return NULL;
	else
		if( !(tree->right) ) return tree;
		else find_max(tree->right);
}
SearchTree find_recursion(SearchTree tree, int value)
{
	if( !tree )
	{
		printf("have no element(find): %d\n", value);
		return NULL;
	}
	if( value < tree->value )
		find_recursion(tree->left, value);
	else if( value > tree->value )
		find_recursion(tree->right, value);
	else
		return tree;
}
SearchTree find_iteration(SearchTree tree, int value)
{
	while(tree)
	{
		if( value < tree->value )
			tree = tree->left;
		else if( value > tree->value )
			tree = tree->right;
		else
			return tree;
	}
	printf("have no element(find): %d\n", value);
	return NULL;
}
SearchTree delete(SearchTree tree, int value)
{
	PtrSearchTree temp = NULL;
	if( !tree )
	{
		printf("have no element(delete): %d\n", value);
		return NULL;
	}
	else if( value < tree->value )
		tree->left = delete(tree->left, value);
	else if( value > tree->value )
		tree->right = delete(tree->right, value);
	else
	{
		if( tree->left && tree->right )
		{
			temp = find_min(tree->right);
			tree->value = temp->value;
			tree->right = delete(tree->right, temp->value);
		}
		else
		{
			temp = tree;
			if( !(tree->left) )tree = tree->right;
			else if( !(tree->right) )tree = tree->left;
			free(temp);
		}
	}
	return tree;
}


    原文作者：二叉查找树
    原文地址: https://blog.csdn.net/robin_Xu_shuai/article/details/53406205
    本文转自网络文章，转载此文章仅为分享知识，如有侵权，请联系博主进行删除。
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