红黑树的插入 删除以及左旋和右旋和搜索

红黑树结构体定义

性质1：每个节点要么是黑色，要么是红色。
性质2：根节点只能是黑色。
性质3：每个叶子节点（NIL）是黑色。
性质4：每个红色节点的两个子节点一定都是黑色。不能有两个红色节点相连。
性质5：任意一节点到每个叶子节点的路径都包含数量相同的黑结点。俗称：黑高！

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;

nil为哨兵机制 默认叶子节点全黑且隐藏

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;
}

插入 根据书上对于红黑树的插入定义来实现

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;
}

删除 同样依据书上的定义来实现

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;
}