数据结构与算法-红黑树-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_43338497/article/details/119922528

这篇博客详细介绍了红黑树的数据结构及其性质，包括插入、删除和查找操作。通过示例代码展示了红黑树如何保持平衡以及修复颜色属性以保持平衡。此外，还提供了一个完整的红黑树实现，包括旋转和修复操作，用于插入和删除节点。

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红黑树的性质

1.每个节点是红的或者黑的；
2.根节点是黑的；
3.每个叶子节点时黑的（所有叶子节点都隐藏，并且为黑色）；
4.如果一个节点是红的，则它的两个儿子都是黑的(两个红色节点不能相邻，既红色节点的父子节点均为黑色)；
5.对每个节点，从该节点到其子孙节点的所有路径上包含相同数目的黑节点（红色节点用于方便区分）。

红黑树的代码


typedef int KEY_TYPE;

//数据结构-节点
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;

//数据节点-树的表示
typedef struct _rbtree {
	rbtree_node *root;
	rbtree_node *nil;
} rbtree;

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

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

rbtree_node *rbtree_successor(rbtree *T, rbtree_node *x) 
{
	rbtree_node *y = x->parent;

	if (x->right != T->nil) 
	{
		return rbtree_mini(T, x->right);
	}

	while ((y != T->nil) && (x == y->right)) 
	{
		x = y;
		y = y->parent;
	}
	return y;
}


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
}


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;
}

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
		{ 
			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);
}

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;
}

rbtree_node *rbtree_search(rbtree *T, KEY_TYPE key) 
{
	rbtree_node *node = T->root;
	while (node != T->nil) 
	{
		if (key < node->key) 
		{
			node = node->left;
		} 
		else if (key > node->key) 
		{
			node = node->right;
		} 
		else 
		{
			return node;
		}	
	}
	return T->nil;
}


void rbtree_traversal(rbtree *T, rbtree_node *node) 
{
	if (node != T->nil) 
	{
		rbtree_traversal(T, node->left);
		printf("key:%d, color:%d\n", node->key, node->color);
		rbtree_traversal(T, node->right);
	}
}

int main() 
{
	int keyArray[20] = {24,25,13,35,23, 26,67,47,38,98, 20,19,17,49,12, 21,9,18,14,15};

	rbtree *T = (rbtree *)malloc(sizeof(rbtree));
	if (T == NULL) 
	{
		printf("malloc failed\n");
		return -1;
	}
	
	T->nil = (rbtree_node*)malloc(sizeof(rbtree_node));
	T->nil->color = BLACK;
	T->root = T->nil;

	rbtree_node *node = T->nil;
	int i = 0;
	for (i = 0;i < 20;i ++) 
	{
		node = (rbtree_node*)malloc(sizeof(rbtree_node));
		node->key = keyArray[i];
		node->value = NULL;

		rbtree_insert(T, node);		
	}

	rbtree_traversal(T, T->root);
	printf("----------------------------------------\n");

	for (i = 0;i < 20;i ++) 
	{
		rbtree_node *node = rbtree_search(T, keyArray[i]);
		rbtree_node *cur = rbtree_delete(T, node);
		free(cur);

		rbtree_traversal(T, T->root);
		printf("----------------------------------------\n");
	}
}