红黑树

红黑树相比普通二叉搜索树确实要“高级”啊，参考各种资料勉强把代码凑出来了，可能还有bug，但是还是没有搞懂，明天继续研究。。。

#include <stdio.h>#include <stdlib.h>enum rb_tree_color_type{red   = 0,black = 1,};struct rb_tree_node{enum rb_tree_color_type color;int                     data;struct rb_tree_node *   parent;struct rb_tree_node *   left;struct rb_tree_node *   right;};struct rb_tree{struct rb_tree_node *root;};/* 创建一个结点 */struct rb_tree_node *rb_tree_node_alloc(int val){struct rb_tree_node *ret = (struct rb_tree_node *) malloc(sizeof(struct rb_tree_node));ret->color               = red;ret->data                = val;ret->parent              = NULL;ret->left                = NULL;ret->right               = NULL;return ret;}/* 销毁一个结点 */void rb_tree_node_dealloc(struct rb_tree_node *n){n->parent = NULL;n->left   = NULL;n->right  = NULL;free(n);}/* 销毁整棵子树 */void rb_tree_node_destroy(struct rb_tree_node *n){if (n->left != NULL){rb_tree_node_destroy(n->left);}if (n->right != NULL){rb_tree_node_destroy(n->right);}rb_tree_node_dealloc(n);}/* 返回子树中最小的元素 */struct rb_tree_node *rb_tree_node_minimum(struct rb_tree_node *n){while (n->left != NULL){n = n->left;}return n;}/* 返回子树中最大的元素 */struct rb_tree_node *rb_tree_node_maximum(struct rb_tree_node *n){while (n->right != NULL){n = n->right;}return n;}/* 查找结点在中序遍历序列中的前趋 */struct rb_tree_node *rb_tree_node_predecessor(struct rb_tree_node *n){struct rb_tree_node *ret;if (n->left != NULL){ret = rb_tree_node_maximum(n->left);}else{ret = n->parent;while (ret != NULL && ret->left == n){n   = ret;ret = ret->parent;}}return ret;}/* 查找结点在中序遍历序列中的后继 */struct rb_tree_node *rb_tree_node_successor(struct rb_tree_node *n){struct rb_tree_node *ret;if (n->right != NULL){ret = rb_tree_node_minimum(n->right);}else{ret = n->parent;while (ret != NULL && ret->right == n){n   = ret;ret = ret->parent;}}return ret;}/* 输出子树的中序遍历序列 */void rb_tree_node_inorder_traversal(struct rb_tree_node *n){if (n->left != NULL){rb_tree_node_inorder_traversal(n->left);}printf("%d ", n->data);if (n->right != NULL){rb_tree_node_inorder_traversal(n->right);}}/* 左旋转 */void rb_tree_left_rotate(struct rb_tree *t, struct rb_tree_node *n){struct rb_tree_node *child = n->right;n->right = child->left;if (child->left != NULL){child->left->parent = n;}child->parent = n->parent;if (n->parent == NULL){t->root = child;}else{if (n->parent->left == n){n->parent->left = child;}else{n->parent->right = child;}}child->left = n;n->parent   = child;}/* 右旋转 */void rb_tree_right_rotate(struct rb_tree *t, struct rb_tree_node *n){struct rb_tree_node *child = n->left;n->left = child->right;if (child->right != NULL){child->right->parent = n;}child->parent = n->parent;if (n->parent == NULL){t->root = child;}else{if (n->parent->left == n){n->parent->left = child;}else{n->parent->right = child;}}child->right = n;n->parent    = child;}/* 调整红黑树以保持性质 */void rb_tree_insert_fixup(struct rb_tree *t, struct rb_tree_node *n){struct rb_tree_node *parent;struct rb_tree_node *gparent;struct rb_tree_node *uncle;struct rb_tree_node *temp;while ((parent = n->parent) != NULL && parent->color == red){gparent = parent->parent;if (gparent->left == parent){uncle = gparent->right;if (uncle != NULL && uncle->color == red){uncle->color   = black;parent->color  = black;gparent->color = red;n              = gparent;}else{if (parent->right == n){temp   = n;n      = parent;parent = temp;rb_tree_left_rotate(t, n);}parent->color  = black;gparent->color = red;rb_tree_right_rotate(t, gparent);}}else{uncle = gparent->left;if (uncle != NULL && uncle->color == red){uncle->color   = black;parent->color  = black;gparent->color = red;n              = gparent;}else{if (parent->left == n){temp   = n;n      = parent;parent = temp;rb_tree_right_rotate(t, n);}parent->color  = black;gparent->color = red;rb_tree_left_rotate(t, gparent);}}}t->root->color = black;}/* 插入 */void rb_tree_insert(struct rb_tree *t, int val){struct rb_tree_node *parent = NULL;struct rb_tree_node *child  = t->root;/* 查找应该插入的位置parent */while (child != NULL){parent = child;if (val < child->data){child = child->left;}else{child = child->right;}}child = rb_tree_node_alloc(val);/* 如果parent == NULL说明为空树 */if (parent == NULL){t->root = child;}else{child->parent = parent;if (val < parent->data){parent->left = child;}else{parent->right = child;}}rb_tree_insert_fixup(t, child);}/* 调整红黑树以保持性质 */void rb_tree_erase_fixup(struct rb_tree *t, struct rb_tree_node *n){struct rb_tree_node *parent;struct rb_tree_node *brother;while ((n != NULL && n->color == black) && t->root != n){parent = n->parent;if (parent->left == n){brother = parent->right;if (brother->color == red){brother->color = black;parent->color  = red;rb_tree_left_rotate(t, parent);brother = parent->right;}if ((brother->left  != NULL && brother->left->color  == black) &&(brother->right != NULL && brother->right->color == black)){brother->color = red;n              = n->parent;}else{if (brother->right != NULL && brother->right->color == black){if (brother->left != NULL){brother->left->color = black;}brother->color = red;rb_tree_right_rotate(t, brother);brother = parent->right;}brother->color = parent->color;parent->color  = black;if (brother->right != NULL){brother->right->color = black;}rb_tree_left_rotate(t, parent);n = t->root;}}else{brother = parent->left;if (brother->color == red){brother->color = black;parent->color  = red;rb_tree_right_rotate(t, parent);brother = parent->left;}if ((brother->left  != NULL && brother->left->color  == black) &&(brother->right != NULL && brother->right->color == black)){brother->color = red;n              = n->parent;}else{if (brother->left != NULL && brother->left->color == black){if (brother->right != NULL){brother->right->color = black;}brother->color = red;rb_tree_left_rotate(t, brother);brother = parent->left;}brother->color = parent->color;parent->color  = black;if (brother->left != NULL){brother->left->color = black;}rb_tree_left_rotate(t, parent);n = t->root;}}}if (n != NULL){n->color = black;}}/* 删除 */void rb_tree_erase(struct rb_tree *t, struct rb_tree_node *n){struct rb_tree_node *del;struct rb_tree_node *child;if (n == NULL){return;}/* 查找应该删除的结点del，del最多只有一个子结点 */if (n->left == NULL || n->right == NULL){del = n;}else{del = rb_tree_node_successor(n);/* 若待删除的结点不为n，将待删除结点的数据赋给n */n->data = del->data;}/* 调整子节点的父结点指针 */if (del->left != NULL){child = del->left;}else{child = del->right;}if (child != NULL){child->parent = del->parent;}/* 若父结点为NULL，说明待删除的结点为树的根结点，此时需要重新调整树的根结点 */if (del->parent == NULL){t->root = child;}/* 调整父结点的子结点指针 */else if (del->parent->left == del){del->parent->left = child;}else{del->parent->right = child;}/* 销毁结点 */rb_tree_node_dealloc(del);if (del->color == black){rb_tree_erase_fixup(t, child);}}/* 查找，深度优先遍历 */struct rb_tree_node *rb_tree_search(struct rb_tree *t, int val){struct rb_tree_node *ret = t->root;while (ret != NULL){if (val == ret->data){break;}else if (val < ret->data){ret = ret->left;}else{ret = ret->right;}}return ret;}/* 树结构初始化 */void rb_tree_init(struct rb_tree *t){t->root = NULL;}/* 销毁整棵树 */void rb_tree_destroy(struct rb_tree *t){if (t->root != NULL){rb_tree_node_destroy(t->root);t->root = NULL;}}/* 输出树的中序遍历序列 */void rb_tree_inorder_traversal(struct rb_tree *t){if (t->root != NULL){rb_tree_node_inorder_traversal(t->root);printf("\n");}}int main(void){struct rb_tree t;struct rb_tree_node *n;rb_tree_init(&t);rb_tree_insert(&t, 1);rb_tree_insert(&t, 2);rb_tree_insert(&t, 3);rb_tree_insert(&t, 4);rb_tree_insert(&t, 5);rb_tree_inorder_traversal(&t);n = rb_tree_search(&t, 1);rb_tree_erase(&t, n);rb_tree_inorder_traversal(&t);n = rb_tree_search(&t, 3);rb_tree_erase(&t, n);rb_tree_inorder_traversal(&t);n = rb_tree_search(&t, 4);rb_tree_erase(&t, n);rb_tree_inorder_traversal(&t);n = rb_tree_search(&t, 2);rb_tree_erase(&t, n);rb_tree_inorder_traversal(&t);n = rb_tree_search(&t, 5);rb_tree_erase(&t, n);rb_tree_inorder_traversal(&t);rb_tree_destroy(&t);return 0;}