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这份代码是有问题的,修正的在这里:
- /*-----------------------------------------------------------
- RB-Tree的插入和删除操作的实现算法
- 参考资料:
- 1) <<Introduction to algorithm>>
- 2) <<STL源码剖析>>
- 3) sgi-stl中stl_tree.h中的实现算法
- 4) [url]http://epaperpress.com/sortsearch/index.html[/url]
- 5) [url]http://www.ececs.uc.edu/~franco/C321/html/RedBlack/redblack.html[/url]
- 作者:李创 ([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 <time.h>
- typedef int KEY;
- enum NODECOLOR
- {
- BLACK = 0,
- RED = 1
- };
- typedef struct RBTree
- {
- struct RBTree *parent;
- struct RBTree *left, *right;
- KEY key;
- NODECOLOR color;
- }RBTree, *PRBTree;
- PRBTree RB_InsertNode(PRBTree root, KEY key);
- PRBTree RB_InsertNode_Fixup(PRBTree root, PRBTree z);
- PRBTree RB_DeleteNode(PRBTree root, KEY key);
- PRBTree RB_DeleteNode_Fixup(PRBTree root, PRBTree x , PRBTree x_parent);
- PRBTree Find_Node(PRBTree root, KEY key);
- void Left_Rotate(PRBTree A, PRBTree& root);
- void Right_Rotate(PRBTree A, PRBTree& root);
- void Mid_Visit(PRBTree T);
- void Mid_DeleteTree(PRBTree T);
- void Print_Node(PRBTree node);
- /*-----------------------------------------------------------
- | A B
- | / \ ==> / \
- | a B A y
- | / \ / \
- | b y a b
- -----------------------------------------------------------*/
- void Left_Rotate(PRBTree A, PRBTree& root)
- {
- PRBTree B;
- B = A->right;
- A->right = B->left;
- if (NULL != B->left)
- B->left->parent = A;
- B->parent = A->parent;
- // 这样三个判断连在一起避免了A->parent = NULL的情况
- if (A == root)
- {
- root = B;
- }
- else if (A == A->parent->left)
- {
- A->parent->left = B;
- }
- else
- {
- A->parent->right = B;
- }
- B->left = A;
- A->parent = B;
- }
- /*-----------------------------------------------------------
- | A B
- | / \ / \
- | B y ==> a A
- | / \ / \
- |a b b y
- -----------------------------------------------------------*/
- void Right_Rotate(PRBTree A, PRBTree& root)
- {
- PRBTree B;
- B = A->left;
- A->left = B->right;
- if (NULL != B->right)
- B->right->parent = A;
- B->parent = A->parent;
- // 这样三个判断连在一起避免了A->parent = NULL的情况
- if (A == root)
- {
- root = B;
- }
- else if (A == A->parent->left)
- {
- A->parent->left = B;
- }
- else
- {
- A->parent->right = B;
- }
- A->parent = B;
- B->right = A;
- }
- /*-----------------------------------------------------------
- | 函数作用:查找key值对应的结点指针
- | 输入参数:根节点root,待查找关键值key
- | 返回参数:如果找到返回结点指针,否则返回NULL
- -------------------------------------------------------------*/
- PRBTree Find_Node(PRBTree root, KEY key)
- {
- PRBTree x;
- // 找到key所在的node
- x = root;
- do
- {
- if (key == x->key)
- break;
- if (key < x->key)
- {
- if (NULL != x->left)
- x = x->left;
- else
- break;
- }
- else
- {
- if (NULL != x->right)
- x = x->right;
- else
- break;
- }
- } while (NULL != x);
- return x;
- }
- /*-----------------------------------------------------------
- | 函数作用:在树中插入key值
- | 输入参数:根节点root,待插入结点的关键值key
- | 返回参数:根节点root
- -------------------------------------------------------------*/
- PRBTree RB_InsertNode(PRBTree root, KEY key)
- {
- PRBTree x, y;
- PRBTree z;
- if (NULL == (z = (PRBTree)malloc(sizeof(RBTree))))
- {
- printf("Memory alloc error\n");
- return NULL;
- }
- z->key = key;
- // 得到z的父节点, 如果KEY已经存在就直接返回
- x = root, y = NULL;
- while (NULL != x)
- {
- y = x;
- if (key < x->key)
- {
- if (NULL != x->left)
- {
- x = x->left;
- }
- else
- {
- break;
- }
- }
- else if (key > x->key)
- {
- if (NULL != x->right)
- {
- x = x->right;
- }
- else
- {
- break;
- }
- }
- else
- {
- return root;
- }
- }
- if (NULL == y || y->key > key)
- {
- if (NULL == y)
- root = z;
- else
- y->left = z;
- }
- else
- {
- y->right = z;
- }
- // 设置z的左右子树为空并且颜色是red,注意新插入的节点颜色都是red
- z->parent = y;
- z->left = z->right = NULL;
- z->color = RED;
- // 对红黑树进行修正
- return RB_InsertNode_Fixup(root, z);
- }
- /*-----------------------------------------------------------
- | 函数作用:对插入key值之后的树进行修正
- | 输入参数:根节点root,插入的结点z
- | 返回参数:根节点root
- -------------------------------------------------------------*/
- PRBTree RB_InsertNode_Fixup(PRBTree root, PRBTree z)
- {
- PRBTree y;
- while (root != z && RED == z->parent->color) // 当z不是根同时父节点的颜色是red
- {
- if (z->parent == z->parent->parent->left) // 父节点是祖父节点的左子树
- {
- y = z->parent->parent->right; // y为z的伯父节点
- if (NULL != y && RED == y->color) // 伯父节点存在且颜色是red
- {
- z->parent->color = BLACK; // 更改z的父节点颜色是B
- y->color = BLACK; // 更改z的伯父节点颜色是B
- z->parent->parent->color = RED; // 更改z的祖父节点颜色是B
- z = z->parent->parent; // 更新z为它的祖父节点
- }
- else // 无伯父节点或者伯父节点颜色是b
- {
- if (z == z->parent->right) // 如果新节点是父节点的右子树
- {
- z = z->parent;
- Left_Rotate(z, root);
- }
- z->parent->color = BLACK; // 改变父节点颜色是B
- z->parent->parent->color = RED; // 改变祖父节点颜色是R
- Right_Rotate(z->parent->parent, root);
- }
- }
- else // 父节点为祖父节点的右子树
- {
- y = z->parent->parent->left; // y为z的伯父节点
- if (NULL != y && RED == y->color) // 如果y的颜色是red
- {
- z->parent->color = BLACK; // 更改父节点的颜色为B
- y->color = BLACK; // 更改伯父节点的颜色是B
- z->parent->parent->color = RED; // 更改祖父节点颜色是R
- z = z->parent->parent; // 更改z指向祖父节点
- }
- else // y不存在或者颜色是B
- {
- if (z == z->parent->left) // 如果是父节点的左子树
- {
- z = z->parent;
- Right_Rotate(z, root);
- }
- z->parent->color = BLACK; // 改变父节点的颜色是B
- z->parent->parent->color = RED; // 改变祖父节点的颜色是RED
- Left_Rotate(z->parent->parent, root);
- }
- }
- } // while(RED == z->parent->color)
- // 根节点的颜色始终都是B
- root->color = BLACK;
- return root;
- }
- /*-----------------------------------------------------------
- | 函数作用:在树中删除key值
- | 输入参数:根节点root,待插入结点的关键值key
- | 返回参数:根节点root
- -------------------------------------------------------------*/
- PRBTree RB_DeleteNode(PRBTree root, KEY key)
- {
- PRBTree x, y, z, x_parent;
- // 首先查找需要删除的节点
- z = Find_Node(root, key);
- if (NULL == z)
- return root;
- y = z, x = NULL, x_parent = NULL;
- // y是x按照中序遍历树的后继
- if (NULL == y->left)
- {
- x = y->right;
- }
- else
- {
- if (NULL == y->right)
- {
- x = y->left;
- }
- else
- {
- y = y->right;
- while (NULL != y->left)
- y = y->left;
- x = y->right;
- }
- }
- if (y != z)
- {
- z->left->parent = y;
- y->left = z->left;
- if (y != z->right)
- {
- x_parent = y->parent;
- if (NULL != x)
- x->parent = y->parent;
- y->parent->left = x;
- y->right = z->right;
- z->right->parent = y;
- }
- else
- {
- x_parent = y;
- }
- if (root == z)
- {
- root = y;
- }
- else if (z == z->parent->left)
- {
- z->parent->left = y;
- }
- else
- {
- z->parent->right = y;
- }
- y->parent = z->parent;
- NODECOLOR color = y->color;
- y->color = z->color;
- z->color = color;
- y = z;
- }
- else
- {
- x_parent = y->parent;
- if (NULL != x)
- x->parent = y->parent;
- if (root == z)
- {
- root = y;
- }
- else if (z == z->parent->left)
- {
- z->parent->left = x;
- }
- else
- {
- z->parent->right = x;
- }
- }
- if (BLACK == y->color)
- {
- root = RB_DeleteNode_Fixup(root, x, x_parent);
- }
- free(y);
- return root;
- }
- /*-----------------------------------------------------------
- | 函数作用:对删除key值之后的树进行修正
- | 输入参数:根节点root,删除的结点的子结点x
- | 返回参数:根节点root
- -------------------------------------------------------------*/
- PRBTree RB_DeleteNode_Fixup(PRBTree root, PRBTree x, PRBTree x_parent)
- {
- PRBTree w;
- while (x != root && BLACK == x->color)
- {
- if (x == x_parent->left) // 如果x是左子树
- {
- w = x_parent->right; // w是x的兄弟结点
- if (RED == w->color) // 如果w的颜色是红色
- {
- w->color = BLACK;
- x_parent->color = RED;
- Left_Rotate(x_parent, root);
- w = x_parent->right;
- }
- if ((NULL == w->left || BLACK == w->left->color) &&
- (NULL == w->right || BLACK == w->right->color))
- {
- w->color = RED;
- x = x_parent;
- x_parent = x_parent->parent;
- }
- else
- {
- if (NULL == w->right || BLACK == w->right->color)
- {
- if (NULL != w->left)
- w->left->color = BLACK;
- w->color = RED;
- Right_Rotate(w, root);
- w = x_parent->right;
- }
- w->color = x_parent->color;
- x_parent->color = BLACK;
- if (NULL != w->right)
- w->right->color = BLACK;
- Left_Rotate(x->parent, root);
- break;
- }
- }
- else
- {
- w = x_parent->left; // w是x的兄弟结点
- if (RED == w->color) // 如果w的颜色是红色
- {
- w->color = BLACK;
- x_parent->color = RED;
- Right_Rotate(x_parent, root);
- w = x_parent->left;
- }
- if ((NULL == w->left || BLACK == w->left->color) &&
- (NULL == w->right || BLACK == w->right->color))
- {
- w->color = RED;
- x = x_parent;
- x_parent = x_parent->parent;
- }
- else
- {
- if (NULL == w->left || BLACK == w->left->color)
- {
- if (NULL != w->right)
- w->right->color = BLACK;
- w->color = RED;
- Left_Rotate(w, root);
- w = x_parent->left;
- }
- w->color = x_parent->color;
- x_parent->color = BLACK;
- if (NULL != w->left)
- w->left->color = BLACK;
- Right_Rotate(x->parent, root);
- break;
- }
- }
- }
- x->color = BLACK;
- return root;
- }
- void Print_Node(PRBTree node)
- {
- char* color[] = {"BLACK", "RED"};
- printf("Key = %d,\tcolor = %s", node->key, color[node->color]);
- if (NULL != node->parent)
- printf(",\tparent = %d", node->parent->key);
- if (NULL != node->left)
- printf(",\tleft = %d", node->left->key);
- if (NULL != node->right)
- printf(",\tright = %d", node->right->key);
- printf("\n");
- }
- // 中序遍历树, 加了一个判断, 如果输出的数据不满足序列关系就报错退出
- void Mid_Visit(PRBTree T)
- {
- if (NULL != T)
- {
- if (NULL != T->left)
- {
- if (T->left->key > T->key)
- {
- printf("wrong!\n");
- exit(-1);
- }
- Mid_Visit(T->left);
- }
- Print_Node(T);
- if (NULL != T->right)
- {
- if (T->right->key < T->key)
- {
- printf("wrong\n");
- exit(-1);
- }
- Mid_Visit(T->right);
- }
- }
- }
- // 中序删除树的各个节点
- void Mid_DeleteTree(PRBTree T)
- {
- if (NULL != T)
- {
- if (NULL != T->left)
- Mid_DeleteTree(T->left);
- PRBTree temp = T->right;
- free(T);
- T = NULL;
- if (NULL != temp)
- Mid_DeleteTree(temp);
- }
- }
- void Create_New_Array(int array[], int length)
- {
- for (int i = 0; i < length; i++)
- {
- array[i] = rand() % 256;
- }
- }
- int main(int argc, char *argv[])
- {
- srand(time(NULL));
- PRBTree root = NULL;
- int i;
- for (i = 0; i < 100000; i++)
- {
- root = RB_InsertNode(root, rand() % 10000);
- }
- Mid_Visit(root);
- // 删除整颗树
- Mid_DeleteTree(root);
- return 0;
- }
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