// This may look like C code, but it is really -*- C++ -*-
/* 
Copyright (C) 1988 Free Software Foundation
    written by Doug Lea (dl@rocky.oswego.edu)

This file is part of GNU CC.

GNU CC is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY.  No author or distributor
accepts responsibility to anyone for the consequences of using it
or for whether it serves any particular purpose or works at all,
unless he says so in writing.  Refer to the GNU CC General Public
License for full details.

Everyone is granted permission to copy, modify and redistribute
GNU CC, but only under the conditions described in the
GNU CC General Public License.   A copy of this license is
supposed to have been given to you along with GNU CC so you
can know your rights and responsibilities.  It should be in a
file named COPYING.  Among other things, the copyright notice
and this notice must be preserved on all copies.  
*/

#ifdef __GNUG__
#pragma implementation
#endif
#include <stream.h>
#include "<T>.BSTSet.h"


/*
 traversal primitives
*/


<T>BSTNode* <T>BSTSet::leftmost()
{
  <T>BSTNode* t = root;
  if (t != 0) while (t->lt != 0) t = t->lt;
  return t;
}

<T>BSTNode* <T>BSTSet::rightmost()
{
  <T>BSTNode* t = root;
  if (t != 0) while (t->rt != 0) t = t->rt;
  return t;
}

<T>BSTNode* <T>BSTSet::succ(<T>BSTNode* t)
{
  if (t == 0)
    return 0;
  if (t->rt != 0)
  {
    t = t->rt;
    while (t->lt != 0) t = t->lt;
    return t;
  }
  else
  {
    for (;;)
    {
      if (t->par == 0 || t == t->par->lt)
        return t->par;
      else
        t = t->par;
    }
  }
}

<T>BSTNode* <T>BSTSet::pred(<T>BSTNode* t)
{
  if (t == 0)
    return 0;
  else if (t->lt != 0)
  {
    t = t->lt;
    while (t->rt != 0) t = t->rt;
    return t;
  }
  else
  {
    for (;;)
    {
      if (t->par == 0 || t == t->par->rt)
        return t->par;
      else
        t = t->par;
    }
  }
}


Pix <T>BSTSet::seek(<T&> key)
{
  <T>BSTNode* t = root;
  for (;;)
  {
    if (t == 0)
      return 0;
    int comp = <T>CMP(key, t->item);
    if (comp == 0)
      return Pix(t);
    else if (comp < 0)
      t = t->lt;
    else
      t = t->rt;
  }
}


Pix <T>BSTSet::add(<T&> item)
{
  if (root == 0)
  {
    ++count;
    root = new <T>BSTNode(item);
    return Pix(root);
  }

  <T>BSTNode* t = root;
  <T>BSTNode* p = root;
  int comp;
  for (;;)
  {
    if (t == 0)
    {
      ++count;
      t = new <T>BSTNode(item);
      if (comp > 0)
        p->lt = t;
      else
        p->rt = t;
      t->par = p;
      return Pix(t);
    }
    p = t;
    comp = <T>CMP(t->item, item);
    if (comp == 0)
      return Pix(t);
    else if (comp > 0)
      t = t->lt;
    else
      t = t->rt;
  }
}


void <T>BSTSet::del(<T&> key)
{
  <T>BSTNode* t = root;
  <T>BSTNode* p = root;
  int comp;
  for (;;)
  {
    if (t == 0)
      return;
    comp = <T>CMP(key, t->item);
    if (comp == 0)
    {
      --count;
      <T>BSTNode* repl;
      if (t->lt == 0)
        repl = t->rt;
      else if (t->rt == 0)
        repl = t->lt;
      else
      {
        <T>BSTNode* prepl = t;
        repl = t->lt;
        while (repl->rt != 0)
        {
          prepl = repl;
          repl = repl->rt;
        }
        if (prepl != t)
        {
          prepl->rt = repl->lt;
          if (prepl->rt != 0) prepl->rt->par = prepl;
          repl->lt = t->lt;
          if (repl->lt != 0) repl->lt->par = repl;
        }
        repl->rt = t->rt;
        if (repl->rt != 0) repl->rt->par = repl;
      }
      if (t == root)
      {
        root = repl;
        if (repl != 0) repl->par = 0;
      }
      else
      {
        if (t == p->lt)
          p->lt = repl;
        else
          p->rt = repl;
        if (repl != 0) repl->par = p;
      }
      delete t;
      return;
    }
    p = t;
    if (comp < 0)
      t = t->lt;
    else
      t = t->rt;
  }
}


void <T>BSTSet::_kill(<T>BSTNode* t)
{
  if (t != 0)
  {
    _kill(t->lt);
    _kill(t->rt);
    delete t;
  }
}

<T>BSTNode* <T>BSTSet::_copy(<T>BSTNode* t)
{
  if (t == 0)
    return 0;
  else
  {
    <T>BSTNode* u = new <T>BSTNode(t->item, _copy(t->lt), _copy(t->rt));
    if (u->lt != 0) u->lt->par = u;
    if (u->rt != 0) u->rt->par = u;
    return u;
  }
}


int <T>BSTSet::operator == (<T>BSTSet& y)
{
  if (count != y.count)
    return 0;
  else
  {
    <T>BSTNode* t = leftmost();
    <T>BSTNode* u = y.leftmost();
    for (;;)
    {
      if (t == 0)
        return 1;
      else if (!<T>EQ(t->item, u->item))
        return 0;
      else
      {
        t = succ(t);
        u = y.succ(u);
      }
    }
  }
}

int <T>BSTSet::operator <= (<T>BSTSet& y)
{
  if (count > y.count)
    return 0;
  else
  {
    <T>BSTNode* t = leftmost();
    <T>BSTNode* u = y.leftmost();
    for (;;)
    {
      if (t == 0)
        return 1;
      else if (u == 0)
        return 0;
      int cmp = <T>CMP(t->item, u->item);
      if (cmp == 0)
      {
        t = succ(t);
        u = y.succ(u);
      }
      else if (cmp < 0)
        return 0;
      else
        u = y.succ(u);
    }
  }
}


// linear-time, zero space overhead binary tree rebalancing from
// Stout & Warren, ``Tree rebalancing in linear space and time''
// CACM, Sept, 1986, p902.


void <T>BSTSet::balance()
{
  if (count <= 2) return; // don't bother -- 
                          // also we assume non-null root, below

  // make re-attaching the root easy via trickery

  struct _fake_node { _fake_node *lt, *rt, *par; } fake_root;

  fake_root.rt = (_fake_node*)root; 
  fake_root.par = 0;
  <T>BSTNode* pseudo_root = (<T>BSTNode*)&fake_root;

  // phase 1: tree-to-vine

  <T>BSTNode* vine_tail = pseudo_root;
  <T>BSTNode* remainder = root;

  while (remainder != 0)
  {
    if (remainder->lt == 0)
    {
      vine_tail = remainder;
      remainder = remainder->rt;
    }
    else
    {
      <T>BSTNode* tmp = remainder->lt;
      remainder->lt = tmp->rt;
      if (remainder->lt != 0) remainder->lt->par = remainder;
      tmp->rt = remainder;
      remainder->par = tmp;
      vine_tail->rt = remainder = tmp;
    }
  }

  // phase 2: vine-to-tree
  
  // Uses the slightly simpler version adapted from
  // Day ``Balancing a binary tree'' Computer Journal, Nov. 1976,
  // since it's not generally important whether the `stray' leaves are
  // on the left or on the right.

  unsigned int spines = count - 1;
  while (spines > 1)
  {
    int compressions = spines >> 1; // compress every other node
    spines -= compressions + 1;     // halve for next time

    <T>BSTNode* scanner = pseudo_root;
    while (compressions-- > 0)
    {
      <T>BSTNode* child = scanner->rt;
      <T>BSTNode* grandchild = child->rt;
      scanner->rt = grandchild;
      grandchild->par = scanner;
      child->rt = grandchild->lt;
      if (child->rt != 0) child->rt->par = child;
      grandchild->lt = child;
      child->par = grandchild;
      scanner = grandchild;
    }
  }

  root = pseudo_root->rt;
  root->par = 0;
}


int <T>BSTSet::OK()
{
  int v = 1;
  if (root == 0) 
    v = count == 0;
  else
  {
    int n = 1;
    <T>BSTNode* trail = leftmost();
    <T>BSTNode* t = succ(trail);
    while (t != 0)
    {
      ++n;
      v &= <T>CMP(trail->item, t->item) < 0;
      trail = t;
      t = succ(t);
    }
    v &= n == count;
  }
  if (!v) error("invariant failure");
  return v;
}