红黑树的应用：

	1.Linux进程调度CFS
	2.Nginx Timer事件管理
	3.Epoll事件块的管理

红黑树性质：

	1. 每个节点是红的或者黑的
	2. 根节点是黑的
	3. 每个叶子结点都隐藏，并且是黑的
	4. 如果一个节点是红的，则它的两个儿子都是黑的
	5. 对每个节点，从该节点到其子孙节点的所有路径上的包含相同数目的黑节点
	6. 红黑树平衡的是黑色节点的高度，而不是总节点的高速

红黑树的实现：

红黑树节点具有key，value，左子树，右子树，父节点，颜色。
因为叶子节点均隐藏，所以可以用一个节点代替，令叶子节点的父节点指向该节点即可。

typedef int KEY_TYPE;

typedef struct _rbtree_node {
	unsigned char color;
	struct _rbtree_node *right;
	struct _rbtree_node *left;
	struct _rbtree_node *parent;
	KEY_TYPE key;
	void *value;
} rbtree_node;

typedef struct _rbtree {
	rbtree_node *root;
	rbtree_node *nil;
} rbtree;

寻找节点子树的最大值和最小值

//最小值
rbtree_node *rbtree_mini(rbtree *T, rbtree_node *x) {
	while (x->left != T->nil) {
		x = x->left;
	}
	return x;
}

//最大值
rbtree_node *rbtree_maxi(rbtree *T, rbtree_node *x) {
	while (x->right != T->nil) {
		x = x->right;
	}
	return x;
}

红黑树的左旋与右旋

请时刻注意：红黑树在插入节点之前就已经是一棵红黑树了，满足红黑树的一切性质。
一开始插入的节点为红色，且在回溯过程中插入节点一直为红色，否则就不满足黑色路径相同这一性质。

无论是左旋还是右旋，都要改3对指针，也就是6个。

//左旋
void rbtree_left_rotate(rbtree *T, rbtree_node *x) {

	rbtree_node *y = x->right;  // x  --> y  ,  y --> x,   right --> left,  left --> right

	x->right = y->left; //1 1
	if (y->left != T->nil) { //1 2
		y->left->parent = x;
	}

	y->parent = x->parent; //1 3
	if (x->parent == T->nil) { //1 4
		T->root = y;
	} else if (x == x->parent->left) {
		x->parent->left = y;
	} else {
		x->parent->right = y;
	}

	y->left = x; //1 5
	x->parent = y; //1 6
}

//右旋
void rbtree_right_rotate(rbtree *T, rbtree_node *y) {

	rbtree_node *x = y->left;

	y->left = x->right;
	if (x->right != T->nil) {
		x->right->parent = y;
	}

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

	x->right = y;
	y->parent = x;
}

红黑树插入节点

红黑树插入节点要考虑父节点颜色和所在祖父节点左右子树情况，叔父节点颜色。

void rbtree_insert_fixup(rbtree *T, rbtree_node *z) {

	while (z->parent->color == RED) { //z ---> RED
		if (z->parent == z->parent->parent->left) {
			rbtree_node *y = z->parent->parent->right;
			if (y->color == RED) {
				z->parent->color = BLACK;
				y->color = BLACK;
				z->parent->parent->color = RED;

				z = z->parent->parent; //z --> RED
			} else {

				if (z == z->parent->right) {
					z = z->parent;
					rbtree_left_rotate(T, z);
				}

				z->parent->color = BLACK;
				z->parent->parent->color = RED;
				rbtree_right_rotate(T, z->parent->parent);
			}
		}else {
			rbtree_node *y = z->parent->parent->left;
			if (y->color == RED) {
				z->parent->color = BLACK;
				y->color = BLACK;
				z->parent->parent->color = RED;

				z = z->parent->parent; //z --> RED
			} else {
				if (z == z->parent->left) {
					z = z->parent;
					rbtree_right_rotate(T, z);
				}

				z->parent->color = BLACK;
				z->parent->parent->color = RED;
				rbtree_left_rotate(T, z->parent->parent);
			}
		}
		
	}

	T->root->color = BLACK;
}


void rbtree_insert(rbtree *T, rbtree_node *z) {

	rbtree_node *y = T->nil;
	rbtree_node *x = T->root;

	while (x != T->nil) {
		y = x;
		if (z->key < x->key) {
			x = x->left;
		} else if (z->key > x->key) {
			x = x->right;
		} else { //Exist  key相同情况，根据工程要求具体实现，这里不做任何处理
			return ;
		}
	}

	z->parent = 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;

	rbtree_insert_fixup(T, z);
}

删除红黑树节点

void rbtree_delete_fixup(rbtree *T, rbtree_node *x) {

	while ((x != T->root) && (x->color == BLACK)) {
		if (x == x->parent->left) {

			rbtree_node *w= x->parent->right;
			if (w->color == RED) {
				w->color = BLACK;
				x->parent->color = RED;

				rbtree_left_rotate(T, x->parent);
				w = x->parent->right;
			}

			if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
				w->color = RED;
				x = x->parent;
			} else {

				if (w->right->color == BLACK) {
					w->left->color = BLACK;
					w->color = RED;
					rbtree_right_rotate(T, w);
					w = x->parent->right;
				}

				w->color = x->parent->color;
				x->parent->color = BLACK;
				w->right->color = BLACK;
				rbtree_left_rotate(T, x->parent);

				x = T->root;
			}

		} else {

			rbtree_node *w = x->parent->left;
			if (w->color == RED) {
				w->color = BLACK;
				x->parent->color = RED;
				rbtree_right_rotate(T, x->parent);
				w = x->parent->left;
			}

			if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
				w->color = RED;
				x = x->parent;
			} else {

				if (w->left->color == BLACK) {
					w->right->color = BLACK;
					w->color = RED;
					rbtree_left_rotate(T, w);
					w = x->parent->left;
				}

				w->color = x->parent->color;
				x->parent->color = BLACK;
				w->left->color = BLACK;
				rbtree_right_rotate(T, x->parent);

				x = T->root;
			}

		}
	}

	x->color = BLACK;
}

rbtree_node *rbtree_delete(rbtree *T, rbtree_node *z) {

	rbtree_node *y = T->nil;
	rbtree_node *x = T->nil;

	if ((z->left == T->nil) || (z->right == T->nil)) {
		y = z;
	} else {
		y = rbtree_successor(T, z);
	}

	if (y->left != T->nil) {
		x = y->left;
	} else if (y->right != T->nil) {
		x = y->right;
	}

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

	if (y != z) {
		z->key = y->key;
		z->value = y->value;
	}

	if (y->color == BLACK) {
		rbtree_delete_fixup(T, x);
	}

	return y;
}