/* **********************************************************************
* binarytree: An Asymptote module to draw binary trees                 *
*                                                                      *
* Copyright(C) 2006                                                    *
* Tobias Langner tobias[at]langner[dot]nightlabs[dot]de                *
*                                                                      *
* Modified by John Bowman                                              *
*                                                                      *
* Condensed mode:                                                      *
* Copyright(C) 2012                                                    *
* Gerasimos Dimitriadis dimeg [at] intracom [dot] gr                   *
*                                                                      *
************************************************************************
*                                                                      *
* This library is free software; you can redistribute it and/or        *
* modify it under the terms of the GNU Lesser General Public           *
* License as published by the Free Software Foundation; either         *
* version 3 of the License, or(at your option) any later version.      *
*                                                                      *
* This library is distributed in the hope that it will be useful,      *
* but WITHOUT ANY WARRANTY; without even the implied warranty of       *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU    *
* Lesser General Public License for more details.                      *
*                                                                      *
* You should have received a copy of the GNU Lesser General Public     *
* License along with this library; if not, write to the                *
*     Free Software Foundation, Inc.,                                  *
*     51 Franklin St, Fifth Floor,                                     *
*     Boston, MA  02110-1301  USA                                      *
*                                                                      *
* Or get it online:                                                    *
*     http: //www.gnu.org/copyleft/lesser.html                         *
*                                                                      *
***********************************************************************/

// default values
real minDistDefault=0.2cm;
real nodeMarginDefault=0.1cm;

// structure to represent nodes in a binary tree
struct binarytreeNode {
 int key;
 binarytreeNode left;
 binarytreeNode right;
 binarytreeNode parent;
 bool spans_calculated=false;
 int left_span,total_left_span;
 int right_span,total_right_span;
 void update_spans();

 // Get the horizontal span of the tree consisting of the current
 // node plus the whole subtree that is rooted at the right child
 // (condensed mode)
 int getTotalRightSpan() {
   if(spans_calculated == false) {
     update_spans();
   }

   return total_right_span;
 }

 // Get the horizontal span of the tree consisting of the current
 // node plus the whole subtree that is rooted at the left child
 // (condensed mode)
 int getTotalLeftSpan() {
   if(spans_calculated == false) {
     update_spans();
   }
   return total_left_span;
 }

 // Get the horizontal distance between this node and its right child
 // (condensed mode)
 int getRightSpan() {
   if(spans_calculated == false) {
     update_spans();
   }
   return right_span;
 }

 // Get the horizontal distance between this node and its left child
 // (condensed mode)
 int getLeftSpan() {
   if(spans_calculated == false) {
     update_spans();
   }
   return left_span;
 }

 // Update all span figures for this node.
 // condensed mode)
 update_spans=new void() {
                          if(spans_calculated == true)
                            return;

                          left_span=0;
                          total_left_span=0;
                          right_span=0;
                          total_right_span=0;

                          if(left != null) {
                            left_span=left.getTotalRightSpan()+1;
                            total_left_span=left_span+left.getTotalLeftSpan();
                          }

                          if(right != null) {
                            right_span=right.getTotalLeftSpan()+1;
                            total_right_span=right_span+right.getTotalRightSpan();
                          }
                          spans_calculated=true;
 };

 // set the left child of this node
 void setLeft(binarytreeNode left) {
   this.left=left;
   this.left.parent=this;
 }

 // set the right child of this node
 void setRight(binarytreeNode right) {
   this.right=right;
   this.right.parent=this;
 }

 // return a boolean indicating whether this node is the root
 bool isRoot() {
   return parent == null;
 }

 // return the level of the subtree rooted at this node.
 int getLevel() {
   if(isRoot())
     return 1;
   else
     return parent.getLevel()+1;
 }

 // set the children of this binarytreeNode
 void setChildren(binarytreeNode left, binarytreeNode right) {
   setLeft(left);
   setRight(right);
 }

 // create a new binarytreeNode with key <key>
 static binarytreeNode binarytreeNode(int key) {
   binarytreeNode toReturn=new binarytreeNode;
   toReturn.key=key;
   return toReturn;
 }

 // returns the height of the subtree rooted at this node.
 int getHeight() {
   if(left == null && right == null)
     return 1;
   if(left == null)
     return right.getHeight()+1;
   if(right == null)
     return left.getHeight()+1;

   return max(left.getHeight(),right.getHeight())+1;
 }
}

binarytreeNode operator init() {return null;}

// "constructor" for binarytreeNode
binarytreeNode binarytreeNode(int key)=binarytreeNode.binarytreeNode;

// draw the tree rooted at the given <node> at the given position <pos>, with
// <height>=the height of the containing tree,
// <minDist>=the minimal horizontal distance of two nodes at the lowest level,
// <levelDist>=the vertical distance between two levels,
// <nodeDiameter>=the diameter of one node.
object draw(picture pic=currentpicture, binarytreeNode node, pair pos,
           int height, real minDist, real levelDist, real nodeDiameter,
           pen p=currentpen, bool condensed=false) {
 Label label=Label(math((string) node.key),pos);

 binarytreeNode left=node.left;
 binarytreeNode right=node.right;

 // return the distance for two nodes at the given <level> when the
 // containing tree has height <height>
 // and the minimal distance between two nodes is <minDist> .
 real getDistance(int level, int height, real minDist) {
   return(nodeDiameter+minDist)*2^(height-level);
 }

 // return the horiontal distance between node <n> and its left child
 // (condensed mode)
 real getLeftDistance(binarytreeNode n) {
   return(nodeDiameter+minDist) *(real)n.getLeftSpan() * 0.5;
 }

 // return the horiontal distance between node <n> and its right child
 // (condensed mode)
 real getRightDistance(binarytreeNode n) {
   return(nodeDiameter+minDist) *(real)n.getRightSpan() * 0.5;
 }

 real dist=getDistance(node.getLevel(),height,minDist)/2;

 // draw the connection between the two nodes at the given positions
 // by calculating the connection points and drawing the corresponding
 // arrow.
 void deferredDrawNodeConnection(pair parentPos, pair childPos) {
   pic.add(new void(frame f, transform t) {
       pair start,end;
       // calculate connection path
       transform T=shift(nodeDiameter/2*unit(t*childPos-t*parentPos));
       path arr=(T*t*parentPos)--(inverse(T)*t*childPos);
       draw(f,PenMargin(arr,p).g,p,Arrow(5));
     });
   pic.addPoint(parentPos);
   pic.addPoint(childPos);
 }

 if(left != null) {
   pair childPos;
   if(condensed == false) {
     childPos=pos-(0,levelDist)-(dist/2,0);
   }
   else {
     childPos=pos-(0,levelDist)-((real)getLeftDistance(node),0);
   }
   draw(pic,left,childPos,height,minDist,levelDist,nodeDiameter,p,condensed);
   deferredDrawNodeConnection(pos,childPos);
 }

 if(right != null) {
   pair childPos;
   if(condensed == false) {
     childPos=pos-(0,levelDist)+(dist/2,0);
   }
   else {
     childPos=pos-(0,levelDist)+((real)getRightDistance(node),0);
   }
   draw(pic,right,childPos,height,minDist,levelDist,nodeDiameter,p,condensed);
   deferredDrawNodeConnection(pos,childPos);
 }

 picture obj;
 draw(obj,circle((0,0),nodeDiameter/2),p);
 label(obj,label,(0,0),p);

 add(pic,obj,pos);

 return label;
}

struct key {
 int n;
 bool active;
}

key key(int n, bool active=true) {key k; k.n=n; k.active=active; return k;}

key operator cast(int n) {return key(n);}
int operator cast(key k) {return k.n;}
int[] operator cast(key[] k) {
 int[] I;
 for(int i=0; i < k.length; ++i)
   I[i]=k[i].n;
 return I;
}

key nil=key(0,false);

// structure to represent a binary tree.
struct binarytree {
 binarytreeNode root;
 int[] keys;

 // add the given <key> to the tree by searching for its place and
 // inserting it there.
 void addKey(int key) {
   binarytreeNode newNode=binarytreeNode(key);

   if(root == null) {
     root=newNode;
     keys.push(key);
     return;
   }

   binarytreeNode n=root;
   while(n != null) {
     if(key < n.key) {
       if(n.left != null)
         n=n.left;
       else {
         n.setLeft(newNode);
         keys.push(key);
         return;
       }
     } else if(key > n.key) {
       if(n.right != null)
         n=n.right;
       else {
         n.setRight(newNode);
         keys.push(key);
         return;
       }
     }
   }
 }

 // return the height of the tree
 int getHeight() {
   if(root == null)
     return 0;
   else
     return root.getHeight();
 }

 // add all given keys to the tree sequentially
 void addSearchKeys(int[] keys) {
   for(int i=0; i < keys.length; ++i) {
     int key=keys[i];
     // Ignore duplicate keys
     if(find(this.keys == key) == -1)
       addKey(key);
   }
 }

 binarytreeNode build(key[] keys, int[] ind) {
   if(ind[0] >= keys.length) return null;
   key k=keys[ind[0]];
   ++ind[0];
   if(!k.active) return null;
   binarytreeNode bt=binarytreeNode(k);
   binarytreeNode left=build(keys,ind);
   binarytreeNode right=build(keys,ind);
   bt.left=left; bt.right=right;
   if(left != null) left.parent=bt;
   if(right != null) right.parent=bt;
   return bt;
 }

 void addKeys(key[] keys) {
   int[] ind={0};
   root=build(keys,ind);
   this.keys=keys;
 }


 // return all key in the tree
 int[] getKeys() {
   return keys;
 }
}

binarytree searchtree(...int[] keys)
{
 binarytree bt;
 bt.addSearchKeys(keys);
 return bt;
}

binarytree binarytree(...key[] keys)
{
 binarytree bt;
 bt.addKeys(keys);
 return bt;
}

// draw the given binary tree.
void draw(picture pic=currentpicture, binarytree tree,
         real minDist=minDistDefault, real nodeMargin=nodeMarginDefault,
         pen p=currentpen, bool condensed=false)
{
 int[] keys=tree.getKeys();

 // calculate the node diameter so that all keys fit into it
 frame f;
 for(int i=0; i < keys.length; ++i)
   label(f,math(string(keys[i])),p);

 real nodeDiameter=abs(max(f)-min(f))+2*nodeMargin;
 real levelDist=nodeDiameter*1.8;

 draw(pic,tree.root,(0,0),tree.getHeight(),minDist,levelDist,nodeDiameter,p,
      condensed);
}

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