作者：xiabodan 出处：http://blog.csdn.net/xiabodan

二叉树

二叉树的申明：

struct node 
{
  int data;
  struct node *left;
  struct node *right;
};

新建一个节点

/* newNode() allocates a new node with the given data and NULL left and 
   right pointers. */
struct node* newNode(int data)
{
  // Allocate memory for new node 
  struct node* node = (struct node*)malloc(sizeof(struct node));

  // Assign data to this node
  node->data = data;

  // Initialize left and right children as NULL
  node->left = NULL;
  node->right = NULL;
  return(node);
}

二叉查找树

使得二叉树成为二叉查找树的重要性质就是树中的每个节点X，它的左子树所有的关键字值小于X的关键字，而它的右子树中的所有关键字值大于X的关键字值。这就意味着该树所有的元素可以用某种统一的方式排序。

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

typedef int elementtype;
typedef struct node* position;
typedef struct node* bsearchtree;

bsearchtree MakeEmpty(bsearchtree T);
position find(elementtype data,bsearchtree T);
position findmax(bsearchtree T);
position findmin(bsearchtree T);
bsearchtree insert(elementtype data,bsearchtree T);
bsearchtree delete(elementtype data,bsearchtree T);
void print_tree(bsearchtree T);



struct node {

    elementtype data;
    position    left;
    position    right;

};

bsearchtree MakeEmpty(bsearchtree T)
{
    if(NULL != T)
    {
        MakeEmpty(T->left);
        MakeEmpty(T->right);
        free(T);
    }
    return NULL;
}

position find(elementtype data,bsearchtree T)
{
    if(NULL == T)
        return NULL;
    if(T->data > data)
        return find(data,T->left);
    if(T->data < data)
        return find(data,T->right);
    else
        return T;
}

position findmin(bsearchtree T)
{
    if(NULL == T)
        return NULL;
    if(T->left == NULL)
        return T;
    else
        return findmin(T->left);
}

position findmax(bsearchtree T)
{
    if(NULL != T)
        while(T->right != NULL)
            T = T->right;
    return T;
}

bsearchtree insert(elementtype data,bsearchtree T)
{
    if(NULL == T)   
    {
        T = (position)malloc(sizeof(position));
        T->data     = data;
        T->left     = NULL;
        T->right    = NULL;
    }
    else
    {
        if(data < T->data)
            T->left = insert( data, T->left);
        if(data > T->data)
            T->right = insert(data, T->right);
        //when T->data == data do nothing
    }

    return T;//return root node
}
bsearchtree delete(elementtype data,bsearchtree T)
{
    position tem;
    if(NULL == T)
        printf("delete:error T is empty");
    else if(data<T->data)
        T->left = delete(data,T->left)  ; //go left to find data
    else if(data>T->data)
        T->right= delete(data,T->right) ; //go right to find data
    else if(T->left && T->right)          //data is  found here ,and need to be deleted element   have  both children
    {
        //replace wih smallest in right subtree
        tem = findmin(T->right);          
        T->data = tem->data;
        T->right = delete(T->data,T->right);
    }
    else  //need to be deleted element   just have one children
    {
        tem = T;
        if(NULL == T->left )
            T = T->right;
        if(NULL == T->right)
            T = T->left;
        free(tem);
    }

    return T;
}   

void print_tree(bsearchtree T)
{
    if(NULL ==T)
        return;
    print_tree(T->left);
    printf("  %d \n",T->data);
    print_tree(T->right);
}

int main(int argc, char** argv)
{
    bsearchtree T;
    position P;
    T = insert(12,T);
    T = insert(2,T);
    T = insert(22,T);
    T = insert(7,T);
    T = insert(54,T);
    T = insert(23,T);
    T = insert(18,T);
    T = insert(48,T);
    T = insert(112,T);
    T = insert(42,T);
    T = insert(222,T);
    T = insert(57,T);
    T = insert(84,T);
    T = insert(16,T);
    T = insert(455,T);
    T = insert(59,T);
    print_tree(T);

    //P = find( 22,T);
    if(T  != NULL) {
        T = delete(22,T);
        printf("After deletion:\n");
        print_tree(T);
    }
    return 0;
}