二叉查找树C语言实现及其可视化

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

                 

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);elseinsert(&((*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：

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。

查看图片如下:

                         

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：

                                

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);elsereturn 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;elsereturn tree;}printf("have no element(find): %d\n", value);return NULL;}

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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);elseinsert(&((*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;elseif( !(tree->left) ) return tree;elsefind_min(tree->left);}SearchTree find_max(SearchTree tree){if( !tree )return NULL;elseif( !(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);elsereturn 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;elsereturn 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;}