red-black tree

Posted 2021-03-11 kirosola

一颗红黑树是满足下面红黑性质的二叉搜索树

①每个结点或是红的，或是黑的。

②根结点是黑的

③每个叶结点（NIL）是黑的

④如果一个结点是红色的，则它的两个子结点是黑色的。

⑤对每个结点，从该结点到其所有后代叶结点的简单路径上，均包含相同数目的黑色结点。

插入时总是要考虑它的叔叔，删除时总要考虑它的兄弟。而且插入时维护的主要是颜色（性质4），而删除时维护的主要是黑色结点数量（性质5）

旋转

void left_rotate(ROOT &T, RBTREE x)
{
	RBTREE y;
	
	y = x->left;
	x->right = y->left;
	if (y->left != T->nil)
		y->left->p = x;
	y->p= x->p;
	if (x->p == T->nil)
		T->root = y;
	else if (x->p->left == x)
		x->p->left = y;
	else x->p->right = y;
	y->left = x;
	x->p = y;
}

 

void right_rotate(ROOT &T,RBTREE y)
{
	RBTREE x;

	x = y->right;
	y->left = x->right;

	if (x->right == T->nil)
		x->right->p = y;
	x->p = y->p;
	if (y->p == T->nil)
		T->root = x;
	else if (y->p->left = y)
		y->p->left = x;
	else
		y->p->right = x;
	x->right = y;
	y->p = x;
}

　　插入

void rb_insert(ROOT &T, RBTREE z)
{
	RBTREE x, y;
	y = T->nil;
	x = T->root;

	while (x != T->nil)
	{
		y = x;
		if (z->key < x->key)
			x = x->left;
		else
			x = x->right;
	}
	z->p = y;
	if (y == T->nil)
		T->root = z;
	else if (z->key < y->key)
		y->left = z;
	else
		y->right = z;
	z->left = T->nil;
	z->right = T->nil;
	z->color = RED;
	rb_insert_fixup(T, z);
}

　　

 

void rb_insert_fixup(ROOT &T, RBTREE z)
{
	RBTREE y; 
	while (z->p->color == RED)
	{
		if (z->p == z->p->p->left)
		{
			y = z->p->p->right;
			if (y->color == RED)          //case1.1
			{
				z->p->color = BLACK;
				z->p->p->color = RED;
				y->color = BLACK;
				z = z->p->p;
			}
			else if (z == z->p->right)     //case2中的case2.2
			{
				z = z->p;
				left_rotate(T, z);
			}
			z->p->color = BLACK;          //case2.1
			z->p->color = RED;
			right_rotate(T, z->p->p);

		}
		else//(z->p == z->p->p->right)
		{
			y = z->p->p->left;
			if (y->color == RED)          //case1.2
			{
				z->p->color = BLACK;
				z->p->p->color = RED;
				y->color = BLACK;
				z = z->p->p;
			}
			else if (z = z->p->left)       //case2中的2.4
			{
				z = z->p;
				right_rotate(T, z);
			}
			z->p->color = BLACK;           //case2.3
			z->p->color = RED;
			left_rotate(T, z->p->p);

		}
	}
}