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不多说啥了,这里不讲理论, 需要的可以自己去看书(如算法导论等), 就给出一份实现代码, 供有需要的人参考之用, 前后写了好久, 参考的是linux内核中红黑树的实现代码:http://lxr.linux.no/linux/lib/rbtree.c
实现的操作有:插入, 查找, 删除.
- /*-----------------------------------------------------------
- RB-Tree的插入和删除操作的实现算法
- 参考资料:
- 1) <<Introduction to algorithm>>
- 2) [url]http://lxr.linux.no/linux/lib/rbtree.c[/url]
- 作者:[url]http://www.cppblog.com/converse/[/url]
- 您可以自由的传播,修改这份代码,转载处请注明原作者
- 红黑树的几个性质:
- 1) 每个结点只有红和黑两种颜色
- 2) 根结点是黑色的
- 3)空节点是黑色的(红黑树中,根节点的parent以及所有叶节点lchild、rchild都不指向NULL,而是指向一个定义好的空节点)。
- 4) 如果一个结点是红色的,那么它的左右两个子结点的颜色是黑色的
- 5) 对于每个结点而言,从这个结点到叶子结点的任何路径上的黑色结点
- 的数目相同
- -------------------------------------------------------------*/
-
- #include <stdio.h>
- #include <stdlib.h>
- #include <string.h>
- typedef int key_t;
- typedef int data_t;
- typedef enum color_t
- {
- RED = 0,
- BLACK = 1
- }color_t;
- typedef struct rb_node_t
- {
- struct rb_node_t *left, *right, *parent;
- key_t key;
- data_t data;
- color_t color;
- }rb_node_t;
- /* forward declaration */
- rb_node_t* rb_insert(key_t key, data_t data, rb_node_t* root);
- rb_node_t* rb_search(key_t key, rb_node_t* root);
- rb_node_t* rb_erase(key_t key, rb_node_t* root);
- int main()
- {
- int i, count = 900000;
- 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;
- }
- static rb_node_t* rb_new_node(key_t key, data_t data)
- {
- rb_node_t *node = (rb_node_t*)malloc(sizeof(struct rb_node_t));
- if (!node)
- {
- printf("malloc error!\n");
- exit(-1);
- }
- node->key = key, node->data = data;
- return node;
- }
- /*-----------------------------------------------------------
- | node right
- | / \ ==> / \
- | a right node y
- | / \ / \
- | b y a b
- -----------------------------------------------------------*/
- static rb_node_t* rb_rotate_left(rb_node_t* node, rb_node_t* root)
- {
- rb_node_t* right = node->right;
- if ((node->right = right->left))
- {
- right->left->parent = node;
- }
- right->left = node;
- 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;
- return root;
- }
- /*-----------------------------------------------------------
- | node left
- | / \ / \
- | left y ==> a node
- | / \ / \
- | a b b y
- -----------------------------------------------------------*/
- 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;
- }
- static rb_node_t* rb_insert_rebalance(rb_node_t *node, rb_node_t *root)
- {
- rb_node_t *parent, *gparent, *uncle, *tmp;
- while ((parent = node->parent) && parent->color == RED)
- {
- gparent = parent->parent;
- if (parent == gparent->left)
- {
- uncle = gparent->right;
- if (uncle && uncle->color == RED)
- {
- uncle->color = BLACK;
- parent->color = BLACK;
- gparent->color = RED;
- node = gparent;
- }
- else
- {
- if (parent->right == node)
- {
- root = rb_rotate_left(parent, root);
- tmp = parent;
- parent = node;
- node = tmp;
- }
- parent->color = BLACK;
- gparent->color = RED;
- root = rb_rotate_right(gparent, root);
- }
- }
- else
- {
- uncle = gparent->left;
- if (uncle && uncle->color == RED)
- {
- uncle->color = BLACK;
- parent->color = BLACK;
- gparent->color = RED;
- node = gparent;
- }
- else
- {
- if (parent->left == node)
- {
- root = rb_rotate_right(parent, root);
- tmp = parent;
- parent = node;
- node = tmp;
- }
- parent->color = BLACK;
- gparent->color = RED;
- root = rb_rotate_left(gparent, root);
- }
- }
- }
- root->color = BLACK;
- return root;
- }
- 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;
- while ((!node || node->color == BLACK) && node != root)
- {
- if (parent->left == node)
- {
- other = parent->right;
- if (other->color == RED)
- {
- other->color = BLACK;
- parent->color = RED;
- root = rb_rotate_left(parent, root);
- other = parent->right;
- }
- if ((!other->left || other->left->color == BLACK) &&
- (!other->right || other->right->color == BLACK))
- {
- other->color = RED;
- node = parent;
- parent = node->parent;
- }
- else
- {
- if (!other->right || other->right->color == BLACK)
- {
- if ((o_left = other->left))
- {
- o_left->color = BLACK;
- }
- other->color = RED;
- root = rb_rotate_right(other, root);
- other = parent->right;
- }
- other->color = parent->color;
- parent->color = BLACK;
- if (other->right)
- {
- other->right->color = BLACK;
- }
- root = rb_rotate_left(parent, root);
- node = root;
- break;
- }
- }
- 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;
- }
- return root;
- }
- 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;
- }
- rb_node_t* rb_insert(key_t key, data_t data, rb_node_t* root)
- {
- rb_node_t *parent = NULL, *node;
- parent = NULL;
- if ((node = rb_search_auxiliary(key, root, &parent)))
- {
- return root;
- }
- node = rb_new_node(key, data);
- 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);
- }
- rb_node_t* rb_search(key_t key, rb_node_t* root)
- {
- return rb_search_auxiliary(key, root, NULL);
- }
- rb_node_t* rb_erase(key_t key, rb_node_t *root)
- {
- rb_node_t *child, *parent, *old, *left, *node;
- color_t color;
- if (!(node = rb_search_auxiliary(key, root, NULL)))
- {
- 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);
- }
- return root;
- }
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[ 本帖最后由 converse 于 2008-11-11 19:20 编辑 ] |
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