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红黑树的实现

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2012-06-14 12:59:52

原文地址：红黑树的实现 作者：datao0907

 的具体好处(Linux内核中的调度器，内存管理，C++map等等)，这里就不用多讲了,下面只是粘贴其具体的实现代码。
使用的数据结构:
  1. struct rb_node {
  2.   struct rb_node *parent;
  3.   struct rb_node *left;
  4.   struct rb_node *right;
  5.   unsigned int color:1;
  6.   long key;
  7. };

  9. struct rb_root {
  10.   struct rb_node *root;
  11.   unsigned long len;
  12. };
添加节点
具体的插入代码接口为:
  1. int rb_tree_insert(struct rb_root *root,struct rb_node *node)
  2. {
  3.     struct rb_node *p;
  4.         
  5.     _rb_tree_find(root,node,&p);
  6.     
  7.     if(p->key < node->key)
  8.     {
  9.      p->right = node;
  10.      node->parent = p;
  11.     }
  12.     else {
  13.      p->left = node;
  14.      node->parent = p;
  15.     }

  17.     root->len ++;

  19.     _rb_tree_insert_fixup(root,node);

  21.     return 0;
  22. }
查找代码为:
  1. int rb_tree_insert(struct rb_root *root,struct rb_node *node)
  2. {
  3.     struct rb_node *p;
  4.         
  5.     _rb_tree_find(root,node,&p);
  6.     
  7.     if(p->key < node->key)
  8.     {
  9.      p->right = node;
  10.      node->parent = p;
  11.     }
  12.     else {
  13.      p->left = node;
  14.      node->parent = p;
  15.     }

  17.     root->len ++;

  19.     _rb_tree_insert_fixup(root,node);

  21.     return 0;
  22. }
其中，最复杂的为颜色调整部分了，如下:
  1. static void _rb_tree_insert_fixup(struct rb_root *root,struct rb_node *p)
  2. {
  3.     struct rb_node *q;

  5.     while(p && p->parent && p->parent->color == RED)
  6.     {
  7.      
  8.     if(p->parent->parent && p->parent == p->parent->parent->left)    
  9.      {
  10.         q = p->parent->parent->right;
  11.         if(q && q->color == RED)
  12.         {
  13.          p->parent->color = BLACK;
  14.          p->parent->parent->color = RED;
  15.          q->color = BLACK;
  16.          p = p->parent->parent;
  17.          continue;
  18.         }

  20.         if(p->parent->right && p->parent->right == p)
  21.          {
  22.          p = p->parent;
  23.          left_rotate(root,p);
  24.          }
  25.         
  26.         if(p && p->parent)
  27.         p->parent->color = BLACK;
  28.         if(p && p->parent && p->parent->parent)
  29.         {
  30.          p->parent->parent->color = RED;
  31.          right_rotate(root,p->parent->parent);
  32.         }            
  33.      }
  34.     else
  35.     {    
  36.         if(p->parent->parent && p->parent->parent->left)
  37.         {
  38.          q = p->parent->parent->left;
  39.          if(q && q->color == RED)
  40.          {
  41.             p->parent->parent->color = RED;
  42.             p->parent->color = BLACK;
  43.             q->color = BLACK;
  44.             p = p->parent->parent;
  45.             continue;
  46.          }
  47.         }

  49.         if(p->parent->left && p->parent->left == p)
  50.         {
  51.             p = p->parent;
  52.             right_rotate(root,p);
  53.         }
  54.     
  55.         if(p && p->parent)
  56.         p->parent->color = BLACK;
  57.         if(p && p->parent && p->parent->parent)
  58.         {
  59.             p->parent->parent->color = RED;
  60.             left_rotate(root,p->parent->parent);
  61.         }
  62.     }    
  63.     }

  65.     root->root->color = BLACK;
  66.     
  67. }

删除节点

这段代码基本来自Linux内核(lib/rb_tree.c)中，进行了少量的修改
  1. /*
  2. *from linux kernel
  3. */
  4. int rb_tree_erase(struct rb_root *root,struct rb_node *node)
  5. {
  6.     struct rb_node *child,*parent;
  7.     int color;
  8.     
  9.     if(!node->left)    
  10.         child = node->right;
  11.     else if(!node->right)    
  12.         child = node->left;
  13.     else
  14.     {
  15.         struct rb_node *old = node,*left;

  17.         node = node->right;
  18.         while((left = node->left) != NULL)
  19.             node = left;
  20.         child = node->right;
  21.         parent = node->parent;
  22.         color = node->color;
  23.         
  24.         if(child) child->parent = parent;
  25.         if(parent == old) {
  26.             parent->right = child;
  27.             parent = node;
  28.         } else
  29.             parent->left = child;
  30.         
  31.         node->parent = old->parent;
  32.         node->color = old->color;
  33.         node->right = old->right;
  34.         node->left = old->left;
  35.         
  36.         if(old->parent)
  37.         {
  38.             if(old->parent->left == old)
  39.                 old->parent->left = node;
  40.             else    old->parent->right = node;
  41.         } else
  42.             root->root = node;
  43.         
  44.         old->left->parent = node;
  45.         if(old->right)
  46.             old->right->parent = node;
  47.         goto color;
  48.     }
  49.     parent = node->parent;
  50.     color = node->color;

  52.     if(child)
  53.         child->parent = parent;
  54.     if(parent)
  55.     {
  56.         if(parent->left == node)
  57.             parent->left = child;
  58.         else     parent->right = child;
  59.     } else
  60.         root->root = child;
  61. color:
  62.     if(color == BLACK)
  63.         __rb_tree_erase_fixup(root,parent,child);

  65.     root->len --;
  66.     
  67.     return 0;
  68. }
接着又是调整颜色的代码:
  1. void __rb_tree_erase_fixup(struct rb_root *root,struct rb_node *parent,\
  2.                 struct rb_node *x)
  3. {
  4.     struct rb_node *w;

  6.     while( x != root->root && (!x || x->color==BLACK))
  7.     {
  8.         if( x == parent->left)
  9.         {
  10.             w = parent->right;
  11.             //case 1
  12.             if(w->color == RED)    
  13.             {
  14.                 w->color = BLACK;
  15.                 parent->color = RED;
  16.                 left_rotate(root,parent);
  17.                 w = parent->right;
  18.             }
  19.             //case 2
  20.             if((!w->left || w->left->color == BLACK) && \
  21.                 (!w->right || w->right->color==BLACK))
  22.             {
  23.                 w->color = RED;
  24.                 x = parent;
  25.                 parent = x->parent;
  26.             }
  27.             // case 3
  28.             else
  29.             {
  30.             if( !w->right || w->right->color == BLACK)
  31.             {
  32.                 w->color = RED;
  33.                 if(w->left)
  34.                     w->left->color = BLACK;
  35.                 right_rotate(root,w);
  36.                 w = parent->right;
  37.             }
  38.                 
  39.             //case 4
  40.             w->color = parent->color;
  41.             if(w->right)
  42.                 w->right->color = BLACK;
  43.             parent->color = BLACK;
  44.             left_rotate(root,parent);
  45.             x = root->root;
  46.             break;
  47.             }
  48.             
  49.         }
  50.         else//same as if ,left<-->right
  51.         {
  52.             w = parent->left;
  53.             //case 1
  54.             if(RED == w->color)
  55.             {
  56.                 w->color = BLACK;
  57.                 parent->color = RED;    
  58.                 right_rotate(root,parent);
  59.                 w = parent->left;
  60.             }
  61.             //case 2
  62.             if((!w->right || w->right->color == BLACK) && \
  63.                 (!w->left || w->left->color == BLACK))
  64.             {
  65.                 w->color = RED;
  66.                 x = parent;
  67.                 parent = x->parent;
  68.             }
  69.             else
  70.             {
  71.             if(!w->left || w->left->color == BLACK)
  72.             {
  73.                 w->color = RED;
  74.                 if(w->right)
  75.                     w->right->color = BLACK;
  76.                 left_rotate(root,w);
  77.                 w = parent->left;
  78.             }    
  79.             //case 4
  80.             w->color = parent->color;
  81.             if(w->left)
  82.                 w->left->color = BLACK;
  83.             parent->color = BLACK;
  84.             right_rotate(root,parent);
  85.             x = root->root;
  86.             break;
  87.             }
  88.         }
  89.     }
  90.     if(x)
  91.     x->color = BLACK;
  92. }
PS:删除部分，本来是将书上的伪码实现，最后发现老是编译段错误，最后就直接修改linux内核中，哎！
参考资料
1.算法导论(影印版)
2.linux-2.6.24.3内核源码
3.
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