二叉查找树的基本操作例程

对于二叉查找树的最大难处，我觉得是在于删除，当删除一个元素时，简单地说有两种情况，一种是节点，一种是叶子。假设被删除值为D

1.叶子，很简单，找到叶子的父节点，然后将这个父节点指向该叶子的树枝赋为0；有一种特殊情况是就一个根，那么释放根，然后返回0。

2.节点，需要做两步，找到该节点的左子树的最大值或者右子树的最小值，假设为F，用F替代被删除节点的值D，然后再删除F，而F肯定是叶子，采用1中的方法。

这种算法删除时最坏的情况就是删除点是一个节点，首先遍历一遍找到该节点D，然后再遍历该节点的某个子树找到F，再遍历一遍找到F的父节点，logn1+2logn2，小于3logn，可以再提高的是叶子节点和它的父亲可以一次性完成，而不需要两次，那么算法复杂度是2logn。当然写的复杂一些的话，可以一遍遍历就将所有要改变的节点保留下来，此时算法复杂度是logn

以下是实现代码：

typedef struct _node
{
    int element;
    struct _node *lefttree;
    struct _node *righttree;
}node;

node * insert(node * root,int element)
{
    if(root == 0)
    {
        root = (node *)malloc(sizeof(node));
        if(root == 0)
            return 0;
        root->element = element;
        root->lefttree = root->righttree = 0;
    }
    else if(root->element > element)
    {
        root->lefttree = insert(root->lefttree,element);
    }
    else if(root->element < element)
    {
        root->righttree = insert(root->righttree,element);
    }
    return root;
}

node * find(node * root,int element)
{
    if(root == 0)
        return 0;
    if(root->element > element)
        return find(root->lefttree,element);
    else if(root->element < element)
        return find(root->righttree,element);
    return root;
}

void printtree(node * root)
{
    if(root == 0)
        return 0;
    printtree(root->lefttree);
    printf("%d\t",root->element);
    printtree(root->righttree);
}
node* destroytree(node *root)
{
    if(root == 0)
        return 0;
    root->lefttree = destroytree(root->lefttree);
    root->righttree = destroytree(root->righttree);
    free(root);
    return 0;
}

node *findmax(node *root)
{
    if(root == 0)
        return 0;
    if(root->righttree == 0)
        return root;
    return findmax(root->righttree);
}
node *findmin(node *root)
{
    if(root == 0)
        return 0;
    if(root->lefttree == 0)
        return root;
    return findmin(root->lefttree);
}
node *findparent(node *root,int element)
{
    if(root == 0)
        return 0;
    else if(root->lefttree && root->lefttree->element == element)
        return root;
    else if(root->righttree && root->righttree->element == element)
        return root;
    else if(root->element > element)
        return findparent(root->lefttree,element);
    else if(root->element < element)
        return findparent(root->righttree,element);
    else
        return 0xffffffff;
}
node* deleteelement(node *root,int element)
{
    node *parent;
    node *self;
    if(root == 0)
        return -1;
    self = find(root,element);
    if(self == 0)
        return 0;
    if(self->lefttree)
    {
        node *tmp = findmax(self->lefttree);
        self->element = tmp->element;
        parent = findparent(self->lefttree,tmp->element);
        if(parent == 0xffffffff)
        {
            self->lefttree = 0;
        }
        else
        {
            parent->righttree = 0;
        }
        free(tmp);
    }
    else if(self->righttree)
    {
        node *tmp = findmin(self->righttree);
        self->element = tmp->element;
        parent = findparent(self->righttree,tmp->element);
        if(parent == 0xffffffff)
        {
            self->righttree = 0;
        }
        else
        {
            parent->lefttree = 0;
        }
        free(tmp);
    }
    else
    {
        parent = findparent(root,self->element);
        if(parent == 0xffffffff)
        {
            free(root);
        }
        else
        {
            if(parent->lefttree&&parent->lefttree->element == element)
                parent->lefttree = 0;
            else
                parent->righttree = 0;
            free(self);
        }
    }
    return root;
}
int main()
{
    int a[10] = {5,6,8,1,2,9,3,7,4,0};
    int i = 0;
    node *root = 0;
    node *parent = 0;
    root = insert(root,a[0]);
    for(i = 1;i<10;i++)
        insert(root,a[i]);
    root = deleteelement(root,0);
    /*for(i = 0;i<11;i++)
    {
        parent = findparent(root,i);
        if(parent == 0xffffffff)
            printf("root = %d\n",i);
        else if(parent == 0)
            printf("not exist = %d\n",i);
        else
            printf("%d‘s parent = %d\n",i,parent->element);
    }*/
    printtree(root);
    destroytree(root);
    return 1;
}