C语言实现二叉树

#include<stdio.h>
struct tree
{
    int data;
    int l_ch;
    int r_ch;
};
void add_node(struct tree* arr_1,int *arr,int start_index,int index)
{
    arr_1[index].data=arr[index];
    if(arr_1[start_index].data<arr[index])
        if(arr_1[start_index].r_ch==-1)
            arr_1[start_index].r_ch=index;
        else
            add_node(arr_1,arr,arr_1[start_index].r_ch,index);
    else
        if(arr_1[start_index].l_ch==-1)
            arr_1[start_index].l_ch=index;
        else
            add_node(arr_1,arr,arr_1[start_index].l_ch,index);
        
}
void creat_tree(struct tree arr_1[],int *arr,int size)
{
    int index;
    for(index=0;index<size;index++)
    {
    if(index!=0)
        add_node(arr_1,arr,0,index);
    else
        arr_1[0].data=arr[0];
    }
}
void init_tree(struct tree* arr_1,int size)
{
    int index;
    for(index=0;index<size;index++)
    {
        arr_1[index].data=-1;
        arr_1[index].l_ch=-1;
        arr_1[index].r_ch=-1;
    }
}
void first_trav(struct tree* arr_1,int index)
{
    printf("%d ",arr_1[index].data);
    if(arr_1[index].l_ch!=-1)
        first_trav(arr_1,arr_1[index].l_ch);
    if(arr_1[index].r_ch!=-1)
        first_trav(arr_1,arr_1[index].r_ch);
}
void mid_trav(struct tree* arr_1,int index)
{
    if(arr_1[index].l_ch!=-1)
        mid_trav(arr_1,arr_1[index].l_ch);
    printf("%d ",arr_1[index].data);
    if(arr_1[index].r_ch!=-1)
        mid_trav(arr_1,arr_1[index].r_ch);
}
void last_trav(struct tree* arr_1,int index)
{
    if(arr_1[index].l_ch!=-1)
        last_trav(arr_1,arr_1[index].l_ch);
    if(arr_1[index].r_ch!=-1)
        last_trav(arr_1,arr_1[index].r_ch);
    printf("%d ",arr_1[index].data);
}
void show_tree(struct tree* arr_1)
{
    first_trav(arr_1,0);
    printf("
");
    mid_trav(arr_1,0);
    printf("
");
    last_trav(arr_1,0);
    printf("
");
}
int main()
{
    int arr[10]={10,2,1,56,40,90,7,6};
    struct tree arr_1[8];
    init_tree(arr_1,sizeof(arr_1)/sizeof(arr_1[0]));
    creat_tree(arr_1,arr,sizeof(arr_1)/sizeof(arr_1[0]));
    show_tree(arr_1);
}

二叉树的性质
1：在二叉树的第i层上最多有2^(i-1)个节点
2：深度为K的二叉树之多有2^(k-1)个节点
####注：这里的深度K意思就是有K层的二叉树
3：对于任何一棵二叉树T，如果其终端节点有No个，度为2的节点数有N2，则No=N2+1
4: 具有n个节点的完全二叉树的深度为[log2n]+1([x]表示不大于x的最大整数）