//红黑树插入删除简单实现
#include<istream>
#include<ctime>
using namespace std;
typedef int key_t;
typedef char data_t;
typedef enum { RED, BLACK }color_t;
typedef struct rb_node_t
{
key_t key;
rb_node_t * parent;
rb_node_t *left;
color_t color;
data_t data;
rb_node_t *right;
}rb_node_t;
//一、左旋代码分析
/*———————————————————–
| node right
| / / ==> / /
| a right node y
| / / / /
| b y a b //左旋
———————————————————–*/
rb_node_t *rb_new_node(key_t key, data_t data)
{
rb_node_t *s = (rb_node_t*)malloc(sizeof(rb_node_t));
if (NULL == s) exit(1);
s->key = key;
s->data = data;
s->color = BLACK;
s->parent = s->left = s->right = NULL;
return s;
}
void FreeNode(rb_node_t *root)
{
free(root);
root = NULL;
}
static rb_node_t * rb_rotate_left(rb_node_t* node, rb_node_t* root)
{
rb_node_t* right = node->right; //指定指针指向 right<–node->right
if ((node->right = right->left))
{
right->left->parent = node; //好比上面的注释图，node成为b的父母
}
right->left = node; //node成为right的左孩子
if ((right->parent = node->parent))
{
if (node == node->parent->right)
{
node->parent->right = right;
}
else
{
node->parent->left = right;
}
}
else
{
root = right;
}
node->parent = right; //right成为node的父母
return root;
}
//二、右旋
/*———————————————————–
| node left
| / / / /
| left y ==> a node
| / / / /
| a b b y //右旋与左旋差不多，分析略过
———————————————————–*/
static rb_node_t* rb_rotate_right(rb_node_t* node, rb_node_t* root)
{
rb_node_t* left = node->left;
if ((node->left = left->right))
{
left->right->parent = node;
}
left->right = node;
if ((left->parent = node->parent))
{
if (node == node->parent->right)
{
node->parent->right = left;
}
else
{
node->parent->left = left;
}
}
else
{
root = left;
}
node->parent = left;
return root;
}
//三、红黑树查找结点
//—————————————————-
//rb_search_auxiliary：查找
//rb_node_t* rb_search：返回找到的结点
//—————————————————-
static rb_node_t* rb_search_auxiliary(key_t key, rb_node_t* root, rb_node_t** save)
{
rb_node_t *node = root, *parent = NULL;
int ret;
while (node)
{
parent = node;
ret = node->key – key;
if (0 < ret)
{
node = node->left;
}
else if (0 > ret)
{
node = node->right;
}
else
{
return node;
}
}
if (save)
{
*save = parent;
}
return NULL;
}
//返回上述rb_search_auxiliary查找结果
rb_node_t* rb_search(key_t key, rb_node_t* root)
{
return rb_search_auxiliary(key, root, NULL);
}
//五、红黑树的3种插入情况
//接下来，咱们重点分析针对红黑树插入的3种情况，而进行的修复工作。
//————————————————————–
//红黑树修复插入的3种情况
//为了在下面的注释中表示方便，也为了让下述代码与我的倆篇文章相对应，
//用z表示当前结点，p[z]表示父母、p[p[z]]表示祖父、y表示叔叔。
//———————————————————
static rb_node_t* rb_insert_rebalance(rb_node_t *node, rb_node_t *root)
{
rb_node_t *parent, *gparent, *uncle, *tmp; //父母p[z]、祖父p[p[z]]、叔叔y、临时结点*tmp
while ( (parent = node->parent) && parent->color == RED)
{ //parent 为node的父母，且当父母的颜色为红时
gparent = parent->parent; //gparent为祖父
if (parent == gparent->left) //当祖父的左孩子即为父母时。
//其实上述几行语句，无非就是理顺孩子、父母、祖父的关系。:D。
{
uncle = gparent->right; //定义叔叔的概念，叔叔y就是父母的右孩子。
if (uncle && uncle->color == RED) //情况1：z的叔叔y是红色的
{
uncle->color = BLACK; //将叔叔结点y着为黑色
parent->color = BLACK; //z的父母p[z]也着为黑色。解决z，p[z]都是红色的问题。
gparent->color = RED;
node = gparent; //将祖父当做新增结点z，指针z上移俩层，且着为红色。
//上述情况1中，只考虑了z作为父母的右孩子的情况。
}
else //情况2：z的叔叔y是黑色的，
{
if (parent->right == node) //且z为右孩子
{
root = rb_rotate_left(parent, root); //左旋[结点z，与父母结点]
tmp = parent;
parent = node;
node = tmp; //parent与node 互换角色
}
//情况3：z的叔叔y是黑色的，此时z成为了左孩子。
//注意，1：情况3是由上述情况2变化而来的。
//……2：z的叔叔总是黑色的，否则就是情况1了。
parent->color = BLACK; //z的父母p[z]着为黑色
gparent->color = RED; //原祖父结点着为红色
root = rb_rotate_right(gparent, root); //右旋[结点z，与祖父结点]
}
}
else
{
// if (parent == gparent->right) 当祖父的右孩子即为父母时。（解释请看本文评论下第23楼，同时，感谢SupremeHover指正！）
uncle = gparent->left; //祖父的左孩子作为叔叔结点。[原理还是与上部分一样的]
if (uncle && uncle->color == RED) //情况1：z的叔叔y是红色的
{
uncle->color = BLACK;
parent->color = BLACK;
gparent->color = RED;
node = gparent; //同上。
}
else //情况2：z的叔叔y是黑色的，
{
if (parent->left == node) //且z为左孩子
{
root = rb_rotate_right(parent, root); //以结点parent、root右旋
tmp = parent;
parent = node;
node = tmp; //parent与node 互换角色
}
//经过情况2的变化，成为了情况3.
parent->color = BLACK;
gparent->color = RED;
root = rb_rotate_left(gparent, root); //以结点gparent和root左旋
}
}
}
root->color = BLACK; //根结点，不论怎样，都得置为黑色。
return root; //返回根结点。
}
//四、红黑树的插入
//———————————————————
//红黑树的插入结点
rb_node_t* rb_insert(key_t key, data_t data, rb_node_t* root)
{
rb_node_t *parent = NULL, *node = NULL;
if ((node = rb_search_auxiliary(key, root, &parent))) //调用rb_search_auxiliary找到插入结点的地方
{
return root;
}
node = rb_new_node(key, data); //分配结点
node->parent = parent;
node->left = node->right = NULL;
node->color = RED;
if (parent)
{
if (parent->key > key)
{
parent->left = node;
}
else
{
parent->right = node;
}
}
else
{
root = node;
}
return rb_insert_rebalance(node, root); //插入结点后，调用rb_insert_rebalance修复红黑树的性质
}
//七、红黑树的4种删除情况
//—————————————————————-
//红黑树修复删除的4种情况
//为了表示下述注释的方便，也为了让下述代码与我的倆篇文章相对应，
//x表示要删除的结点，*other、w表示兄弟结点，
//—————————————————————-
static rb_node_t* rb_erase_rebalance(rb_node_t *node, rb_node_t *parent, rb_node_t *root)
{
rb_node_t *other, *o_left, *o_right; //x的兄弟*other，兄弟左孩子*o_left,*o_right
while ((!node || node->color == BLACK) && node != root)
{
if (parent->left == node)
{
other = parent->right;
if (other->color == RED) //情况1：x的兄弟w是红色的
{
other->color = BLACK;
parent->color = RED; //上俩行，改变颜色，w->黑、p[x]->红。
root = rb_rotate_left(parent, root); //再对p[x]做一次左旋
other = parent->right; //x的新兄弟new w 是旋转之前w的某个孩子。其实就是左旋后的效果。
}
if ((!other->left || other->left->color == BLACK) &&
(!other->right || other->right->color == BLACK))
//情况2：x的兄弟w是黑色，且w的俩个孩子也都是黑色的
{ //由于w和w的俩个孩子都是黑色的，则在x和w上得去掉一黑色，
other->color = RED; //于是，兄弟w变为红色。
node = parent; //p[x]为新结点x
parent = node->parent; //x<-p[x]
}
else //情况3：x的兄弟w是黑色的，
{ //且，w的左孩子是红色，右孩子为黑色。
if (!other->right || other->right->color == BLACK)
{
if ((o_left = other->left)) //w和其左孩子left[w]，颜色交换。
{
o_left->color = BLACK; //w的左孩子变为由黑->红色
}
other->color = RED; //w由黑->红
root = rb_rotate_right(other, root); //再对w进行右旋，从而红黑性质恢复。
other = parent->right; //变化后的，父结点的右孩子，作为新的兄弟结点w。
}
//情况4：x的兄弟w是黑色的
other->color = parent->color; //把兄弟节点染成当前节点父节点的颜色。
parent->color = BLACK; //把当前节点父节点染成黑色
if (other->right) //且w的右孩子是红
{
other->right->color = BLACK; //兄弟节点w右孩子染成黑色
}
root = rb_rotate_left(parent, root); //并再做一次左旋
node = root; //并把x置为根。
break;
}
}
//下述情况与上述情况，原理一致。分析略。
else
{
other = parent->left;
if (other->color == RED)
{
other->color = BLACK;
parent->color = RED;
root = rb_rotate_right(parent, root);
other = parent->left;
}
if ((!other->left || other->left->color == BLACK) &&
(!other->right || other->right->color == BLACK))
{
other->color = RED;
node = parent;
parent = node->parent;
}
else
{
if (!other->left || other->left->color == BLACK)
{
if ((o_right = other->right))
{
o_right->color = BLACK;
}
other->color = RED;
root = rb_rotate_left(other, root);
other = parent->left;
}
other->color = parent->color;
parent->color = BLACK;
if (other->left)
{
other->left->color = BLACK;
}
root = rb_rotate_right(parent, root);
node = root;
break;
}
}
}
if (node)
{
node->color = BLACK; //最后将node[上述步骤置为了根结点]，改为黑色。
}
return root; //返回root
}
//六、红黑树的删除
rb_node_t* rb_erase(key_t key, rb_node_t *root)
{
rb_node_t *child = NULL, *parent, *old, *left, *node;
color_t color;
if (!(node = rb_search_auxiliary(key, root, NULL))) //调用rb_search_auxiliary查找要删除的结点
{
printf(“key %d is not exist!/n”);
return root;
}
old = node;
if (node->left && node->right)
{
node = node->right;
while ((left = node->left) != NULL)
{
node = left;
}
child = node->right;
parent = node->parent;
color = node->color;
if (child)
{
child->parent = parent;
}
if (parent)
{
if (parent->left == node)
{
parent->left = child;
}
else
{
parent->right = child;
}
}
else
{
root = child;
}
if (node->parent == old)
{
parent = node;
}
node->parent = old->parent;
node->color = old->color;
node->right = old->right;
node->left = old->left;
if (old->parent)
{
if (old->parent->left == old)
{
old->parent->left = node;
}
else
{
old->parent->right = node;
}
}
else
{
root = node;
}
old->left->parent = node;
if (old->right)
{
old->right->parent = node;
}
}
else
{
if (!node->left)
{
child = node->right;
}
else if (!node->right)
{
child = node->left;
}
parent = node->parent;
color = node->color;
if (child)
{
child->parent = parent;
}
if (parent)
{
if (parent->left == node)
{
parent->left = child;
}
else
{
parent->right = child;
}
}
else
{
root = child;
}
}
free(old);
if (color == BLACK)
{
root = rb_erase_rebalance(child, parent, root); //调用rb_erase_rebalance来恢复红黑树性质
}
return root;
}
//八、测试用例//主函数
int main()
{
int i, count = 100;
key_t key;
rb_node_t* root = NULL, *node = NULL;
srand(time(NULL));
for (i = 1; i < count; ++i)
{
key = rand() % count;
if ((root = rb_insert(key, i, root)))
{
printf(“[i = %d] insert key %d success!\n”, i, key);
}
else
{
printf(“[i = %d] insert key %d error!\n”, i, key);
exit(-1);
}
if ((node = rb_search(key, root)))
{
printf(“[i = %d] search key %d success!\n”, i, key);
}
else
{
printf(“[i = %d] search key %d error!\n”, i, key);
exit(-1);
}
if (!(i % 10))
{
if ((root = rb_erase(key, root)))
{
printf(“[i = %d] erase key %d success\n”, i, key);
}
else
{
printf(“[i = %d] erase key %d error\n”, i, key);
}
}
}
return 0;
}
