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);
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:
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); 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;
}