#include <stdio.h>
#include <stdlib.h>

#define BLOCKSIZE 256

typedef int item_t;
typedef int key_t;

typedef struct lca_n_t {
               int             depth;
               item_t         *item;
               struct lca_n_t  *up;
               struct lca_n_t  *next;
               struct lca_n_t  *prev;   } lca_node_t;


typedef lca_node_t  object_t;
typedef struct tr_n_t { key_t        key;
                    struct tr_n_t  *left;
                    struct tr_n_t *right;
                    int           height; 
                      } tree_node_t;



lca_node_t *currentblock = NULL;
int    size_left;
lca_node_t *free_list = NULL;

tree_node_t *get_node()
{ lca_node_t *tmp;
  if( free_list != NULL )
  {  tmp = free_list;
     free_list = free_list ->up;
  }
  else
  {  if( currentblock == NULL || size_left == 0)
     {  currentblock = 
                (lca_node_t *) malloc( BLOCKSIZE * sizeof(lca_node_t) );
        size_left = BLOCKSIZE;
     }
     tmp = currentblock++;
     size_left -= 1;
  }
  return( (tree_node_t *) tmp );
}

void return_node(tree_node_t *node)
{  lca_node_t *tmp;
   tmp = (lca_node_t *) node;
   tmp->up = free_list;
   free_list = tmp;
}


lca_node_t *get_lca_node()
{  return( (lca_node_t *) get_node() );
}
 
void return_lca_node(lca_node_t *node)
{   return_node( (tree_node_t *) node );
}
/*-----------------------------------------------------*/

lca_node_t *create_tree(item_t *new_item)
{  lca_node_t *new_node;
 new_node = get_lca_node();
   new_node->item = new_item;
   new_node->depth = 0;    new_node->prev = NULL;
   new_node->up = NULL;    new_node->next = NULL;
   return( new_node );   
}

lca_node_t *add_leaf(lca_node_t *node, item_t *new_item)
{  lca_node_t *new_node;
   /* create tree node */
   new_node = get_lca_node();
   new_node->item = new_item;
   new_node->depth = node->depth + 1;
   new_node->up = node;   new_node->prev = NULL;
   /* now create new list of forward pointers */
   {  lca_node_t *tmp; int i;
      tmp = new_node; 
      for( i = new_node->depth; i>1 ; i /=2 )
      {  /* add node to new_node list */
         tmp->next = get_lca_node();
         tmp->next->prev = tmp;
         tmp->next->depth = tmp->depth;
         if( tmp->up->up->next == NULL )
         {  /* create new target node */
            tmp->up->up->next = get_lca_node();
            tmp->up->up->next->prev = tmp->up->up;
            tmp->up->up->next->depth = tmp->up->up->depth;
            tmp->up->up->next->next = NULL;
            tmp->up->up->next->up = NULL;
         } /* now set forward pointer */
         tmp->next->up = tmp->up->up->next;
         tmp = tmp->next;
      } /* and finish list */
      tmp->next = NULL;
   }
   return( new_node );
}

int depth(lca_node_t *node)
{  return( node->depth );
}



lca_node_t *lca(lca_node_t *node1, lca_node_t *node2 )
{  lca_node_t *tmp; int diff; 
   if( node1->depth < node2->depth )
   {  tmp = node1;  node1 = node2; node2 = tmp; 
   } /* now node1 has larger depth. Move up to the same depth */
   { int diff; 
     diff = node1->depth - node2->depth;
     while( diff > 1 )
     {  if( diff% 2 == 1 )
           node1 = node1->up->next;
        else
           node1 = node1->next;
        diff /= 2;
     }  
     if( diff == 1 )
       node1 = node1->up;  
     while( node1->prev != NULL )
        node1 = node1->prev; /* move back to beginning of list */ 
   } /* now both nodes at same depth */
   if( node1 == node2 )
      return( node1 );
   /* if not the same, perform exponential search */
   {  int current_depth, step_size;
      current_depth = node1->depth; step_size = 1;
      while( current_depth >= 2* step_size )
      {  node1 = node1->next;
         node2 = node2->next;
         step_size *= 2;
      }  /* maximum stepsize, now go up, and decrease stepsize */
      while( current_depth >= 1 )
      {  if( step_size > current_depth )
         {  node1 = node1->prev; node2 = node2->prev;
  	    step_size /= 2; /* steps too large, halve size */
         }
         else if( node1->up != node2->up )
	 {  node1 = node1->up; /* step up still below lca */
            node2 = node2->up;
            current_depth -= step_size;
         }
         else /* node1->up == node2->up */
	 {  if( step_size > 1) /* upper bound for lca */
            {  node1 = node1->prev; node2 = node2->prev;
               step_size /= 2;
            }
	    else /* immediately below lca */
               return( node1->up );
         }
      }
      return( NULL ); /* different trees */
   }
}



/*-----------------------------------------------------*/
tree_node_t *create_s_tree(void)
{  tree_node_t *tmp_node;
   tmp_node = get_node();
   tmp_node->left = NULL;
   return( tmp_node );
}

void left_rotation(tree_node_t *n)
{  tree_node_t *tmp_node;
   key_t        tmp_key;
   tmp_node = n->left; 
   tmp_key  = n->key;
   n->left  = n->right;        
   n->key   = n->right->key;
   n->right = n->left->right;  
   n->left->right = n->left->left;
   n->left->left  = tmp_node;
   n->left->key   = tmp_key;
}

void right_rotation(tree_node_t *n)
{  tree_node_t *tmp_node;
   key_t        tmp_key;
   tmp_node = n->right; 
   tmp_key  = n->key;
   n->right = n->left;        
   n->key   = n->left->key;
   n->left  = n->right->left;  
   n->right->left = n->right->right;
   n->right->right  = tmp_node;
   n->right->key   = tmp_key;
}

object_t *find(tree_node_t *tree, key_t query_key)
{  tree_node_t *tmp_node;
   if( tree->left == NULL )
     return(NULL);
   else
   {  tmp_node = tree;
      while( tmp_node->right != NULL )
      {   if( query_key < tmp_node->key )
               tmp_node = tmp_node->left;
          else
               tmp_node = tmp_node->right;
      }
      if( tmp_node->key == query_key )
         return( (object_t *) tmp_node->left );
      else
         return( NULL );
   }
}


int insert(tree_node_t *tree, key_t new_key, object_t *new_object)
{  tree_node_t *tmp_node;
   int finished;
   if( tree->left == NULL )
   {  tree->left = (tree_node_t *) new_object;
      tree->key  = new_key;
      tree->height = 0;
      tree->right  = NULL; 
   }
   else
     {  tree_node_t * path_stack[100]; int  path_st_p = 0;
      tmp_node = tree; 
      while( tmp_node->right != NULL )
      {   path_stack[path_st_p++] = tmp_node;
          if( new_key < tmp_node->key )
               tmp_node = tmp_node->left;
          else
               tmp_node = tmp_node->right;
      }
      /* found the candidate leaf. Test whether key distinct */
      if( tmp_node->key == new_key )
         return( -1 );
      /* key is distinct, now perform the insert */ 
      {  tree_node_t *old_leaf, *new_leaf;
         old_leaf = get_node();
         old_leaf->left = tmp_node->left; 
         old_leaf->key = tmp_node->key;
         old_leaf->right  = NULL;
         old_leaf->height = 0;
         new_leaf = get_node();
         new_leaf->left = (tree_node_t *) new_object; 
         new_leaf->key = new_key;
         new_leaf->right  = NULL;
         new_leaf->height = 0; 
         if( tmp_node->key < new_key )
         {   tmp_node->left  = old_leaf;
             tmp_node->right = new_leaf;
             tmp_node->key = new_key;
         } 
         else
         {   tmp_node->left  = new_leaf;
             tmp_node->right = old_leaf;
         } 
         tmp_node->height = 1;
      }
      /* rebalance */
      finished = 0;
      while( path_st_p > 0 && !finished )
      {  int tmp_height, old_height;
         tmp_node = path_stack[--path_st_p];
         old_height= tmp_node->height;
         if( tmp_node->left->height - 
                                 tmp_node->right->height == 2 )
         {  if( tmp_node->left->left->height - 
                                 tmp_node->right->height == 1 )
            {  right_rotation( tmp_node );
               tmp_node->right->height = 
                            tmp_node->right->left->height + 1;
               tmp_node->height = tmp_node->right->height + 1;
            }
            else
            {  left_rotation( tmp_node->left );
               right_rotation( tmp_node );
               tmp_height = tmp_node->left->left->height; 
               tmp_node->left->height  = tmp_height + 1; 
               tmp_node->right->height = tmp_height + 1; 
               tmp_node->height = tmp_height + 2; 
            }
         }
         else if ( tmp_node->left->height - 
                                tmp_node->right->height == -2 )
         {  if( tmp_node->right->right->height - 
                                  tmp_node->left->height == 1 )
            {  left_rotation( tmp_node );
               tmp_node->left->height = 
                           tmp_node->left->right->height + 1;
               tmp_node->height = tmp_node->left->height + 1;
            }
            else
            {  right_rotation( tmp_node->right );
               left_rotation( tmp_node );
               tmp_height = tmp_node->right->right->height; 
               tmp_node->left->height  = tmp_height + 1; 
               tmp_node->right->height = tmp_height + 1; 
               tmp_node->height = tmp_height + 2; 
            }
         }
         else /* update height even if there was no rotation */ 
         {  if( tmp_node->left->height > tmp_node->right->height )
               tmp_node->height = tmp_node->left->height + 1;
            else
               tmp_node->height = tmp_node->right->height + 1;
         }
         if( tmp_node->height == old_height )
            finished = 1;
      }
      
   }
   return( 0 );
}



object_t *delete(tree_node_t *tree, key_t delete_key)
{  tree_node_t *tmp_node, *upper_node, *other_node;
   object_t *deleted_object; int finished;
   if( tree->left == NULL )
      return( NULL );
   else if( tree->right == NULL )
   {  if(  tree->key == delete_key )
      {  deleted_object = (object_t *) tree->left;
         tree->left = NULL;
         return( deleted_object );
      }
      else
         return( NULL );
   }
   else
   {  tree_node_t * path_stack[100]; int path_st_p = 0;
      tmp_node = tree;
      while( tmp_node->right != NULL )
      {   path_stack[path_st_p++] = tmp_node;  
          upper_node = tmp_node;
          if( delete_key < tmp_node->key )
          {  tmp_node   = upper_node->left; 
             other_node = upper_node->right;
          } 
          else
          {  tmp_node   = upper_node->right; 
             other_node = upper_node->left;
          } 
      }
      if( tmp_node->key != delete_key )
         deleted_object = NULL;
      else
      {  upper_node->key   = other_node->key;
         upper_node->left  = other_node->left;
         upper_node->right = other_node->right;
         upper_node->height = other_node->height;
         deleted_object = (object_t *) tmp_node->left;
         return_node( tmp_node );
         return_node( other_node );

      }
      /*start rebalance*/  
      finished = 0; path_st_p -= 1;
      while( path_st_p > 0 && !finished )
      {  int tmp_height, old_height;
         tmp_node = path_stack[--path_st_p];
         old_height= tmp_node->height;
         if( tmp_node->left->height - 
                                 tmp_node->right->height == 2 )
         {  if( tmp_node->left->left->height - 
                                 tmp_node->right->height == 1 )
	    {  right_rotation( tmp_node ); 
               tmp_node->right->height = 
                            tmp_node->right->left->height + 1;
               tmp_node->height = tmp_node->right->height + 1;
            }
            else
	    {  left_rotation( tmp_node->left ); 
               right_rotation( tmp_node );
               tmp_height = tmp_node->left->left->height; 
               tmp_node->left->height  = tmp_height + 1; 
               tmp_node->right->height = tmp_height + 1; 
               tmp_node->height = tmp_height + 2; 
            }
         }
         else if ( tmp_node->left->height - 
                                tmp_node->right->height == -2 )
         {  if( tmp_node->right->right->height - 
                                  tmp_node->left->height == 1 )
	    {  left_rotation( tmp_node ); 
               tmp_node->left->height = 
                           tmp_node->left->right->height + 1;
               tmp_node->height = tmp_node->left->height + 1;
            }
            else
            {  right_rotation( tmp_node->right );
               left_rotation( tmp_node );
               tmp_height = tmp_node->right->right->height; 
               tmp_node->left->height  = tmp_height + 1; 
               tmp_node->right->height = tmp_height + 1; 
               tmp_node->height = tmp_height + 2; 
            }
         }
         else /* update height even if there was no rotation */ 
         {  if( tmp_node->left->height > tmp_node->right->height )
               tmp_node->height = tmp_node->left->height + 1;
            else
               tmp_node->height = tmp_node->right->height + 1;
         }
         if( tmp_node->height == old_height )
	    finished = 1;
      }
      /*end rebalance*/
      return( deleted_object );
   }
}


void check_tree( tree_node_t *tr, int depth, int lower, int upper )
{  if( tr->left == NULL )
   {  printf("Tree Empty\n"); return; }
   if( tr->key < lower || tr->key >= upper )
         printf("Wrong Key Order \n");
   if( tr->right == NULL )
   {  if( *( (int *) tr->left) == 10*tr->key + 2 )
         printf("%d(%d)  ", tr->key, depth );
      else
         printf("Wrong Object \n");
   }
   else
   {  check_tree(tr->left, depth+1, lower, tr->key ); 
      check_tree(tr->right, depth+1, tr->key, upper ); 
   }
}

int main()
{  tree_node_t *searchtree;
   char nextop; 
   searchtree = create_s_tree();
   printf("Test lca structure\n");
   { int *new_item; lca_node_t *lca_n; 
     new_item = (int *) malloc(sizeof(int));
     *new_item = 0;
     lca_n = create_tree( new_item);
     insert( searchtree, 0, lca_n );
   }
   printf("Created root; root key 0\n");
   while( (nextop = getchar())!= 'q' )
   { if( nextop == 'a' )
     { int *new_item, old_item; 
       lca_node_t *new_node, *old_node; int success;
       new_item = (int *) malloc(sizeof(int));
       scanf(" %d %d", new_item, &old_item);
       old_node = find(searchtree, old_item);
       if( old_node != NULL )
       { printf("  found node with key %d\n", old_item);
         new_node = add_leaf( old_node, new_item );
         printf("  added new leaf with key %d below tha node\n", *new_item);
         success = insert( searchtree, *new_item, new_node );
         if ( success == 0 )
           printf("  inserted item %d successfully\n", *new_item);
         else
           printf("  insert failed, success = %d\n", success);
       }
     }  
     if( nextop == 'l' )
     { int item1, item2; lca_node_t *n1, *n2, *result;
       scanf(" %d %d", &item1, &item2);
       n1 = find( searchtree, item1);
       n2 = find( searchtree, item2);
       if( n1 != NULL && n2 != NULL )
       {  printf(" found both nodes.");
          result = lca( n1, n2 );
          if( result != NULL )
             printf(" the lca has item %d\n", *(result->item) );
          else
	    printf(" received invalid node\n");
       }
       else
         printf(" did not find the requested nodes \n");

     }
     if( nextop == 'd' )
     { int item; lca_node_t *n;
       scanf(" %d", &item);
       n = find( searchtree, item);
       printf("  the depth of item %d is %d\n",item, depth(n) );
     }
     if( nextop == '?' )
     { int item; lca_node_t *n, *m;
       scanf(" %d", &item); printf("looking for node with key %d\n", item);
       n = find( searchtree, item);
       if (n == NULL )
           printf(" wrong node key\n");
       else
       {   printf(" found node %d. The noes above it are\n", item );
           while( n->up != NULL )
	   {   n = n->up;
	      printf(" %d", *(n->item));
	   }
           printf("\n");
       }
     }
   }/* end of while-loop*/
   return(0);
}