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Revision 1.5 - (download) (as text) (annotate)
Tue Dec 19 17:32:48 2006 UTC (12 years, 11 months ago) by golsen
Branch: MAIN
Changes since 1.4: +182 -10 lines
Add a few new routines to gjonewicklib.pm

#
# Copyright (c) 2003-2006 University of Chicago and Fellowship
# for Interpretations of Genomes. All Rights Reserved.
#
# This file is part of the SEED Toolkit.
# 
# The SEED Toolkit is free software. You can redistribute
# it and/or modify it under the terms of the SEED Toolkit
# Public License. 
#
# You should have received a copy of the SEED Toolkit Public License
# along with this program; if not write to the University of Chicago
# at info@ci.uchicago.edu or the Fellowship for Interpretation of
# Genomes at veronika@thefig.info or download a copy from
# http://www.theseed.org/LICENSE.TXT.
#

package gjonewicklib;

#===============================================================================
#  perl functions for dealing with trees
#
#  Usage:
#      use gjonewicklib
#
#
#===============================================================================
#  Tree data structures:
#===============================================================================
#
#  Elements in newick text file are:
#
#     [c1] ( desc_1, desc_2, ... ) [c2] label [c3] : [c4] x [c5]
#
#  Note that:
#  
#     Comment list 1 can exist on any subtree, but its association with
#        tree components can be upset by rerooting
#     Comment list 2 cannot exist without a descendant list
#     Comment list 3 cannot exist without a label
#     Comment lists 4 and 5 cannot exist without a branch length
#
#  Elements in perl representation are:
#
#     $tree = \@rootnode;
#
#     @node = ( \@desc,  #  reference to list of descendants
#                $label, #  node label
#                $x,     #  branch length
#               \@c1,    #  reference to comment list 1
#               \@c2,    #  reference to comment list 2
#               \@c3,    #  reference to comment list 3
#               \@c4,    #  reference to comment list 4
#               \@c5     #  reference to comment list 5
#             )
#
#  At present, no routine tests or enforces the length of the list (a single
#  element list could be a valid internal node).
#
#  All empty lists can be [] or undef
#
#  Putting the comments at the end allows a shorter list nearly all the
#  time, but is different from the prolog representation.
#
#
#===============================================================================
#  Tree data extraction:
#===============================================================================
#
#  $listref  = newick_desc_ref( $noderef )
#  $label    = newick_lbl( $noderef )
#  $x        = newick_x( $noderef )
#  $listref  = newick_c1( $noderef )
#  $listref  = newick_c2( $noderef )
#  $listref  = newick_c3( $noderef )
#  $listref  = newick_c4( $noderef )
#  $listref  = newick_c5( $noderef )
#
#  @desclist = newick_desc_list( $noderef )
#  $n        = newick_n_desc( $noderef )
#  $descref  = newick_desc_i( $noderef, $i )    # 1-based numbering
#  $bool     = newick_is_tip( $noderef )
#
#  set_newick_desc_ref( $noderef, $listref )
#  set_newick_lbl( $noderef, $label )
#  set_newick_x( $noderef, $x )
#  set_newick_c1( $noderef, $listref )
#  set_newick_c2( $noderef, $listref )
#  set_newick_c3( $noderef, $listref )
#  set_newick_c4( $noderef, $listref )
#  set_newick_c5( $noderef, $listref )
#  set_newick_desc_list( $noderef, @desclist )
#  set_newick_desc_i( $noderef1, $i, $noderef2)
#
#  $bool    = newick_is_rooted( $noderef )      # 2 branches from root
#  $bool    = newick_is_unrooted( $noderef )    # 3 or more branches from root
#  $bool    = newick_is_tip_rooted( $noderef )  # 1 branch from root
#  $bool    = newick_is_bifurcating( $noderef )
#
#  $n       = newick_tip_count( $noderef )
#  @tiprefs = newick_tip_ref_list( $noderef )
#  @tips    = newick_tip_list( $noderef )
#  $tipref  = newick_first_tip_ref( $noderef )
#  $tip     = newick_first_tip( $noderef )
#  @tips    = newick_duplicated_tips( $noderef )
#  $bool    = newick_tip_in_tree( $noderef, $tipname )
#  @tips    = newick_shared_tips( $tree1, $tree2 )
#
#  $length  = newick_tree_length( $noderef )
#  $xmax    = newick_max_X( $noderef )
#  ( $tipref,  $xmax ) = newick_most_distant_tip_ref( $noderef )
#  ( $tipname, $xmax ) = newick_most_distant_tip( $noderef )
#
#-------------------------------------------------------------------------------
#  Paths from root of tree:
#-------------------------------------------------------------------------------
#
#  Path descriptions are of form:
#      ( $node0, $i0, $node1, $i1, $node2, $i2, ..., $nodeN )
#      () is returned upon failure
#
#  @path = path_to_tip( $treenode, $tipname )
#  @path = path_to_named_node( $treenode, $nodename )
#  @path = path_to_node_ref( $treenode, $noderef )
#
#  @path = path_to_node( $node,   $tip1, $tip2, $tip3   )  #  3 tip names
#  @path = path_to_node( $node, [ $tip1, $tip2, $tip3 ] )  #  Array of tips
#  @path = path_to_node( $node,   $tip1                 )  #  Use path_to_tip
#  @path = path_to_node( $node, [ $tip1 ]               )  #  Use path_to_tip
#
#  $distance = newick_path_length( @path )
#  $distance = tip_to_tip_distance( $tree, $tip1, $tip2 )
#  $distance = node_to_node_distance( $tree, $node1, $node2 )
#
#
#===============================================================================
#  Tree manipulations:
#===============================================================================
#
#  $treecopy = copy_newick_tree( $tree )
#
#-------------------------------------------------------------------------------
#  The following modify the existing tree, and passibly any components of that
#  tree that are reached by reference.  If the old version is still needed, copy
#  before modifying.
#-------------------------------------------------------------------------------
#
#  Modify labels:
#
#  $newtree = newick_relabel_nodes( $node, \%new_name )
#  $newtree = newick_relabel_nodes_i( $node, \%new_name )
#  $newtree = newick_relabel_tips( $node, \%new_name )
#  $newtree = newick_relabel_tips_i( $node, \%new_name )
#
#  Modify branches:
#
#  $n_changed = newick_set_undefined_branches( $node, $x )
#  $n_changed = newick_set_all_branches( $node, $x )
#  $n_changed = newick_fix_negative_branches( $tree )
#
#  Modify rooting and/or order:
#
#  $nrmtree = normalize_newick_tree( $tree )
#  $revtree = reverse_newick_tree( $tree )
#  $stdtree = std_unrooted_newick( $tree )
#  $newtree = aesthetic_newick_tree( $tree, $direction )
#  $rndtree = random_order_newick_tree( $tree )
#  $newtree = reroot_newick_by_path( @path )
#  $newtree = reroot_newick_to_tip( $tree, $tip )
#  $newtree = reroot_newick_next_to_tip( $tree, $tip )
#  $newtree = reroot_newick_to_node( $tree, @node )
#  $newtree = reroot_newick_to_node_ref( $tree, $noderef )
#  $newtree = reroot_newick_to_node_ref( $tree, $noderef )
#  $newtree = reroot_newick_to_approx_midpoint( $tree )    # unweighted
#  $newtree = reroot_newick_to_approx_midpoint_w( $tree )  # weight by tips
#  $newtree = uproot_tip_rooted_newick( $tree )
#  $newtree = uproot_newick( $tree )
#
#  $newtree = prune_from_newick( $tree, $tip )
#  $newtree = newick_subtree( $tree,  @tips )
#  $newtree = newick_subtree( $tree, \@tips )
#
#  $newtree = collapse_zero_length_branches( $tree )
#
#===============================================================================
#  Tree reading and writing:
#===============================================================================
#
#   writeNewickTree( $tree )
#   writeNewickTree( $tree, $file )
#   writePrettyTree( $tree, $file )
#  fwriteNewickTree( $file, $tree )
#  $treestring = swriteNewickTree( $tree )
#  $treestring = formatNewickTree( $tree )
#  @textlines  = text_plot_newick( $node, $width, $min_dx, $dy )
#   printer_plot_newick( $node, $file, $width, $min_dx, $dy )
#
#  $tree = parse_newick_tree_str( $string )
#
#===============================================================================


require Exporter;

our @ISA = qw(Exporter);
our @EXPORT = qw(
        newick_is_rooted
        newick_is_unrooted
        tree_rooted_on_tip
        newick_is_bifurcating
        newick_tip_count
        newick_tip_list
        newick_first_tip
        newick_duplicated_tips
        newick_tip_in_tree
        newick_shared_tips

        newick_tree_length
        newick_max_X
        newick_most_distant_tip_ref
        newick_most_distant_tip_name
        
        std_newick_name

        path_to_tip
        path_to_named_node
        path_to_node_ref
        path_to_node

        newick_path_length
        tip_to_tip_distance
        node_to_node_distance

        copy_newick_tree

        newick_relabel_nodes
        newick_relabel_nodes_i
        newick_relabel_tips
        newick_relabel_tips_i

        newick_set_undefined_branches
        newick_set_all_branches
        newick_fix_negative_branches

        normalize_newick_tree
        reverse_newick_tree
        std_unrooted_newick
        aesthetic_newick_tree
        unaesthetic_newick_tree
        random_order_newick_tree

        reroot_newick_by_path
        reroot_newick_to_tip
        reroot_newick_next_to_tip
        reroot_newick_to_node
        reroot_newick_to_node_ref
        reroot_newick_to_approx_midpoint
        reroot_newick_to_approx_midpoint_w
        uproot_tip_rooted_newick
        uproot_newick

        prune_from_newick
        newick_subtree
        collapse_zero_length_branches

        writeNewickTree
        fwriteNewickTree
        strNewickTree
        formatNewickTree
        parse_newick_tree_str

        printer_plot_newick
        text_plot_newick
        );

our @EXPORT_OK = qw(
        newick_desc_ref
        newick_lbl
        newick_x
        newick_c1
        newick_c2
        newick_c3
        newick_c4
        newick_c5
        newick_desc_list
        newick_n_desc
        newick_desc_i
        newick_is_tip
        newick_is_valid

        set_newick_desc_ref
        set_newick_lbl
        set_newick_x
        set_newick_c1
        set_newick_c2
        set_newick_c3
        set_newick_c4
        set_newick_c5

        set_newick_desc_list
        set_newick_desc_i

        add_to_newick_branch
        dump_tree
        );


use gjolists qw(
        common_prefix
        common_and_unique
        unique_suffixes
        
        unique_set
        duplicates
        random_order

        union
        intersection
        set_difference
        );


use strict;


#-------------------------------------------------------------------------------
#  Internally used definitions
#-------------------------------------------------------------------------------

sub array_ref { ref( $_[0] ) eq "ARRAY" }
sub hash_ref  { ref( $_[0] ) eq "HASH"  }


#===============================================================================
#  Extract tree structure values:
#===============================================================================
#
#     $listref = newick_desc_ref( $noderef )
#     $string  = newick_lbl( $noderef )
#     $real    = newick_x( $noderef )
#     $listref = newick_c1( $noderef )
#     $listref = newick_c2( $noderef )
#     $listref = newick_c3( $noderef )
#     $listref = newick_c4( $noderef )
#     $listref = newick_c5( $noderef )
#     @list    = newick_desc_list( $noderef )
#     $int     = newick_n_desc( $noderef )
#     $listref = newick_desc_i( $noderef )
#     $bool    = node_is_tip( $noderef )
#     $bool    = node_is_valid( $noderef )
#
#-------------------------------------------------------------------------------

sub newick_desc_ref { $_[0]->[0] }  # = ${$_[0]}[0]
sub newick_lbl      { $_[0]->[1] }
sub newick_x        { $_[0]->[2] }
sub newick_c1       { $_[0]->[3] }
sub newick_c2       { $_[0]->[4] }
sub newick_c3       { $_[0]->[5] }
sub newick_c4       { $_[0]->[6] }
sub newick_c5       { $_[0]->[7] }

sub newick_desc_list {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef           :
      array_ref( $node->[0] ) ? @{ $node->[0] } :
                                ()              ;
}

sub newick_n_desc {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef                  :
      array_ref( $node->[0] ) ? scalar @{ $node->[0] } :
                                0                      ;
}

sub newick_desc_i {
    my ( $node, $i ) = @_;
    ! array_ref( $node      ) ? undef              :
      array_ref( $node->[0] ) ? $node->[0]->[$i-1] :
                                undef              ;
}

sub node_is_tip {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef                :  # Not a node ref
      array_ref( $node->[0] ) ? @{ $node->[0] } == 0 :  # Empty descend list?
                                1                    ;  # No descend list
}

sub node_is_valid {      #  An array ref with nonempty descend list or a label
    my $node = $_[0];
    array_ref( $node ) && (  array_ref( $node->[0] ) && @{ $node->[0] }
                          || defined( $node->[1] )
                          )
}


#-------------------------------------------------------------------------------
#  Set tree structure values
#-------------------------------------------------------------------------------

sub set_newick_desc_ref { $_[0]->[0] = $_[1] }
sub set_newick_lbl      { $_[0]->[1] = $_[1] }
sub set_newick_x        { $_[0]->[2] = $_[1] }
sub set_newick_c1       { $_[0]->[3] = $_[1] }
sub set_newick_c2       { $_[0]->[4] = $_[1] }
sub set_newick_c3       { $_[0]->[5] = $_[1] }
sub set_newick_c4       { $_[0]->[6] = $_[1] }
sub set_newick_c5       { $_[0]->[7] = $_[1] }

sub set_newick_desc_list {
    my $node = shift;
    array_ref( $node ) || return;
    if ( array_ref( $node->[0] ) ) { @{ $node->[0] } =   @_   }
    else                           {    $node->[0]   = [ @_ ] }
}

sub set_newick_desc_i {
    my ( $node1, $i, $node2 ) = @_;
    array_ref( $node1 ) && array_ref( $node2 ) || return;
    if ( array_ref( $node1->[0] ) ) { $node1->[0]->[$i-1] =   $node2   }
    else                            { $node1->[0]         = [ $node2 ] }
}


#===============================================================================
#  Some tree property tests:
#===============================================================================
#  Tree is rooted (2 branches at root node)?
#
#  $bool = newick_is_rooted( $node )
#-------------------------------------------------------------------------------
sub newick_is_rooted {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef                :  # Not a node ref
      array_ref( $node->[0] ) ? @{ $node->[0] } == 2 :  # 2 branches
                                0                    ;  # No descend list
}


#-------------------------------------------------------------------------------
#  Tree is unrooted (> 2 branches at root node)?
#
#  $bool = newick_is_unrooted( $node )
#-------------------------------------------------------------------------------
sub newick_is_unrooted {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef                :  # Not a node ref
      array_ref( $node->[0] ) ? @{ $node->[0] } >= 3 :  # Over 2 branches
                                0                    ;  # No descend list
}


#-------------------------------------------------------------------------------
#  Tree is rooted on a tip (1 branch at root node)?
#
#  $bool = newick_is_tip_rooted( $node )
#-------------------------------------------------------------------------------
sub newick_is_tip_rooted {
    my $node = $_[0];
    ! array_ref( $node      ) ? undef                :  # Not a node ref
      array_ref( $node->[0] ) ? @{ $node->[0] } == 1 :  # 1 branch
                                0                    ;  # No descend list
}

#===============================================================================
#  Everything below this point refers to parts of the tree structure using
#  only the routines above.
#===============================================================================
#  Tree is bifurcating?  If so, return number of descendents of root node.
#
#  $n_desc = newick_is_bifurcating( $node )
#-------------------------------------------------------------------------------
sub newick_is_bifurcating {
    my ( $node, $not_root ) = @_;
    if ( ! array_ref( $node ) ) { return undef }    #  Bad arg

    my $n = newick_n_desc( $node );
    $n == 0 && ! $not_root                                             ? 0 :
    $n == 1 &&   $not_root                                             ? 0 :
    $n == 3 &&   $not_root                                             ? 0 :
    $n >  3                                                            ? 0 :
    $n >  2 && ! newick_is_bifurcating( newick_desc_i( $node, 3, 1 ) ) ? 0 :
    $n >  1 && ! newick_is_bifurcating( newick_desc_i( $node, 2, 1 ) ) ? 0 :
    $n >  0 && ! newick_is_bifurcating( newick_desc_i( $node, 1, 1 ) ) ? 0 :
                                                                         $n
}


#-------------------------------------------------------------------------------
#  Number of tips:
#
#  $n = newick_tip_count( $node )
#-------------------------------------------------------------------------------
sub newick_tip_count {
    my ( $node, $not_root ) = @_;

    my $imax = newick_n_desc( $node );
    if ( $imax < 1 ) { return 1 }

    #  Special case for tree rooted on tip

    my $n = ( $imax == 1 && ( ! $not_root ) ) ? 1 : 0;

    foreach ( newick_desc_list( $node ) ) { $n += newick_tip_count( $_, 1 ) }

    $n;
}


#-------------------------------------------------------------------------------
#  List of tip nodes:
#
#  @tips = newick_tip_ref_list( $node )
#-------------------------------------------------------------------------------
sub newick_tip_ref_list {
    my ( $node, $not_root ) = @_;

    my $imax = newick_n_desc( $node );
    if ( $imax < 1 ) { return $node }

    my @list = ();

    #  Tree rooted on tip?
    if ( $imax == 1 && ! $not_root && newick_lbl( $node ) ) { push @list, $node }

    foreach ( newick_desc_list( $node ) ) {
        push @list, newick_tip_ref_list( $_, 1 );
    }

    @list;
}


#-------------------------------------------------------------------------------
#  List of tips:
#
#  @tips = newick_tip_list( $node )
#-------------------------------------------------------------------------------
sub newick_tip_list {
    map { newick_lbl( $_ ) } newick_tip_ref_list( $_[0] );
}


#-------------------------------------------------------------------------------
#  First tip node in tree:
#
#  $tipref = newick_first_tip_ref( $node )
#-------------------------------------------------------------------------------
sub newick_first_tip_ref {
    my ( $node, $not_root ) = @_;
    valid_node( $node ) || return  undef;

    #  Arrived at tip, or start of a tip-rooted tree?
    my $n = newick_n_desc( $node );
    if ( ( $n < 1 ) || ( $n == 1 && ! $not_root ) ) { return $node }

    newick_first_tip_ref( newick_desc_i( $node, 1 ), 1 );
}


#-------------------------------------------------------------------------------
#  First tip name in tree:
#
#  $tip = newick_first_tip( $node )
#-------------------------------------------------------------------------------
sub newick_first_tip {
    my ( $noderef ) = @_;

    my $tipref;
    array_ref( $tipref = newick_first_tip_ref( $noderef ) ) ? newick_lbl( $tipref )
                                                          : undef;
}


#-------------------------------------------------------------------------------
#  List of duplicated tip labels.
#
#  @tips = newick_duplicated_tips( $node )
#-------------------------------------------------------------------------------
sub newick_duplicated_tips {
    duplicates( newick_tip_list( $_[0] ) );
}


#-------------------------------------------------------------------------------
#  Tip in tree?
#
#  $bool = newick_tip_in_tree( $node, $tipname )
#-------------------------------------------------------------------------------
sub newick_tip_in_tree {
    my ( $node, $tip, $not_root ) = @_;

    my $n = newick_n_desc( $node );
    if ( $n < 1 ) { return ( newick_lbl( $node ) eq $tip) ? 1 : 0 }

    #  Special case for tree rooted on tip

    if ( $n == 1 && ( ! $not_root ) && newick_lbl( $node ) eq $tip ) { return 1 }

    foreach ( newick_desc_list( $node ) ) {
        if ( newick_tip_in_tree( $_, $tip, 1 ) ) { return 1 }
    }

    0;    #  Fall through means not found
}


#-------------------------------------------------------------------------------
#  Tips shared between 2 trees.
#
#  @tips = newick_shared_tips( $tree1, $tree2 )
#-------------------------------------------------------------------------------
sub newick_shared_tips {
    my ( $Tree1, $Tree2 ) = @_;
    my ( @Tips1 ) = newick_tip_list( $Tree1 );
    my ( @Tips2 ) = newick_tip_list( $Tree2 );
    intersection( \@Tips1, \@Tips2 );
}


#-------------------------------------------------------------------------------
#  Tree length.
#
#  $length = newick_tree_length( $node )
#-------------------------------------------------------------------------------
sub newick_tree_length {
    my ( $node, $not_root ) = @_;

    my $x = $not_root ? newick_x( $node ) : 0;
    defined( $x ) || ( $x = 1 );                #  Convert undefined to 1

    foreach ( newick_desc_list( $node ) ) { $x += newick_tree_length( $_, 1 ) }

    $x;
}


#-------------------------------------------------------------------------------
#  Tree max X.
#
#  $xmax = newick_max_X( $node )
#-------------------------------------------------------------------------------
sub newick_max_X {
    my ( $node, $not_root ) = @_;

    my $xmax = 0;
    foreach ( newick_desc_list( $node ) ) {
        my $x = newick_max_X( $_, 1 );
        if ( $x > $xmax ) { $xmax = $x }
    }

    my $x = $not_root ? newick_x( $node ) : 0;
    $xmax + ( defined( $x ) ? $x : 1 );           #  Convert undefined to 1
}


#-------------------------------------------------------------------------------
#  Most distant tip from root: distance and path.
#
#  ( $xmax, @path ) = newick_most_distant_tip_path( $tree )
#-------------------------------------------------------------------------------
sub newick_most_distant_tip_path {
    my ( $node, $not_root ) = @_;

    my $imax = newick_n_desc( $node );
    my $xmax = ( $imax > 0 ) ? -1 : 0;
    my @pmax = ();
    for ( my $i = 1; $i <= $imax; $i++ ) {
        my ( $x, @path ) = newick_most_distant_tip_path( newick_desc_i( $node, $i ), 1 );
        if ( $x > $xmax ) { $xmax = $x; @pmax = ( $i, @path ) }
    }

    my $x = $not_root ? newick_x( $node ) : 0;
    $xmax += defined( $x ) ? $x : 0;            #  Convert undefined to 1
    ( $xmax, $node, @pmax );
}


#-------------------------------------------------------------------------------
#  Most distant tip from root, and its distance.
#
#  ( $tipref, $xmax ) = newick_most_distant_tip_ref( $tree )
#-------------------------------------------------------------------------------
sub newick_most_distant_tip_ref {
    my ( $node, $not_root ) = @_;

    my $imax = newick_n_desc( $node );
    my $xmax = ( $imax > 0 ) ? -1 : 0;
    my $tmax = $node;
    foreach ( newick_desc_list( $node ) ) {
        my ( $t, $x ) = newick_most_distant_tip_ref( $_, 1 );
        if ( $x > $xmax ) { $xmax = $x; $tmax = $t }
    }

    my $x = $not_root ? newick_x( $node ) : 0;
    $xmax += defined( $x ) ? $x : 1;            #  Convert undefined to 1
    ( $tmax, $xmax );
}


#-------------------------------------------------------------------------------
#  Name of most distant tip from root, and its distance.
#
#  ( $tipname, $xmax ) = newick_most_distant_tip_name( $tree )
#-------------------------------------------------------------------------------
sub newick_most_distant_tip_name {
    my ( $tipref, $xmax ) = newick_most_distant_tip_ref( $_[0] );
    ( newick_lbl( $tipref ), $xmax )
}


#-------------------------------------------------------------------------------
#  Standard node name:
#     Tip label if at a tip
#     Three sorted tip labels intersecting at node, each being smallest
#           of all the tips of their subtrees
#
#  @TipOrTips = std_node_name( $Tree, $Node )
#-------------------------------------------------------------------------------
sub std_node_name {
    my $tree = $_[0];

    #  Node reference is last element of path to node

    my $noderef = ( path_to_node( @_ ) )[-1];
    defined( $noderef ) || return ();

    if ( node_is_tip( $noderef ) || $noderef eq $tree ) {  # Is it a tip?
        return newick_lbl( $noderef );
    }

    #  Work through lists of tips in descendant subtrees, removing them from
    #  @rest, and keeping the best tip for each subtree.

    my @rest = tips_in_newick( $tree );
    my @best = map {
            my @tips = sort { lc $a cmp lc $b } tips_in_newick( $_ );
            @rest = set_difference( \@rest, \@tips );
            $tips[0];
        } newick_desc_list( $noderef );

    # Best of the rest of the tree
    push @best, ( sort { lc $a cmp lc $b } @rest )[0];

    # Take the top 3, in order:

    ( @best >= 3 ) ? ( sort { lc $a cmp lc $b } @best )[0 .. 2] : ();
}


#===============================================================================
#  Functions to find paths in trees.
#
#  Path descriptions are of form:
#      ( $node0, $i0, $node1, $i1, $node2, $i2, ..., $nodeN )   # Always odd
#      () is returned upon failure
#
#  Numbering of descendants is 1-based.
#===============================================================================
#  Path to tip:
#
#  @path = path_to_tip( $treenode, $tipname )
#-------------------------------------------------------------------------------
sub path_to_tip {
    my ( $node, $tip, @path0 ) = @_;

    push @path0, $node;
    my $imax = newick_n_desc( $node );
    if ( $imax < 1 ) { return ( newick_lbl( $node ) eq $tip ) ? @path0 : () }

    #  Special case for tree rooted on tip

    if ( ( $imax  == 1 )                  #  One descendant
      && ( @path0 == 1 )                  #  First step in path
      && ( newick_lbl( $node ) eq $tip )  #  Label matches
       ) { return @path0 }

    my @path;
    for (my $i = 1; $i <= $imax; $i++ ) {
       @path = path_to_tip( newick_desc_i( $node, $i ), $tip, ( @path0, $i ) );
       if ( @path ) { return @path }
    }

    ();  #  Not found
}


#-------------------------------------------------------------------------------
#  Path to named node.
#  Like path to tip, but will find named internal nodes as well.
#
#  @path = path_to_named_node( $treenode, $name )
#-------------------------------------------------------------------------------
sub path_to_named_node {
    my ( $node, $name, @path0 ) = @_;

    push @path0, $node;
    if ( newick_lbl( $node ) eq $name ) { return @path0 }

    my @path;
    my $imax = newick_n_desc( $node );
    for ( my $i = 1; $i <= $imax; $i++ ) {
       @path = path_to_named_node( newick_desc_i( $node, $i ), $name, ( @path0, $i ) );
       if ( @path ) { return @path }
    }

    ();  #  Not found
}


#-------------------------------------------------------------------------------
#  Path to node reference.
#
#  @path = path_to_node_ref( $treenode, $noderef )
#-------------------------------------------------------------------------------
sub path_to_node_ref {
    my ( $node, $noderef, @path0 ) = @_;

    push @path0, $node;
    if ( $node eq $noderef ) { return @path0 }

    my @path;
    my $imax = newick_n_desc( $node );
    for ( my $i = 1; $i <= $imax; $i++ ) {
       @path = path_to_node_ref( newick_desc_i( $node, $i ), $noderef, ( @path0, $i ) );
       if ( @path ) { return @path }
    }

    ();  #  Not found
}


#-------------------------------------------------------------------------------
#  Path to node, as defined by 1 or 3 tips.
#
#  @path = path_to_node( $node,   $tip1, $tip2, $tip3   )  #  3 tip names
#  @path = path_to_node( $node, [ $tip1, $tip2, $tip3 ] )  #  Allow array ref
#  @path = path_to_node( $node,   $tip1                 )  #  Use path_to_tip
#  @path = path_to_node( $node, [ $tip1 ]               )  #  Use path_to_tip
#-------------------------------------------------------------------------------
sub path_to_node {
    my ( $node, $tip1, $tip2, $tip3 ) = @_;
    array_ref( $node ) && defined( $tip1 ) || return ();

    # Allow arg 2 to be an array reference
    if ( array_ref( $tip1 ) ) { ( $tip1, $tip2, $tip3 ) = @$tip1 }

    my @p1 = path_to_tip( $node, $tip1 );                #  Path to first tip
    @p1 || return ();                                    #  Was the tip found?
    defined( $tip2 ) && defined( $tip3 ) || return @p1;  #  Two more defined?

    my @p2 = path_to_tip( $node, $tip2 );
    my @p3 = path_to_tip( $node, $tip3 );
    @p2 && @p3 || return ();                             #  Were they found?

    # Find the common prefix for each pair of paths
    my @p12 = common_prefix( \@p1, \@p2 );
    my @p13 = common_prefix( \@p1, \@p3 );
    my @p23 = common_prefix( \@p2, \@p3 );

    # Return the longest common prefix of any two paths
    ( @p12 >= @p13 && @p12 >= @p23 ) ? @p12 :
    ( @p13 >= @p23 )                 ? @p13 :
                                       @p23 ;
}


#-------------------------------------------------------------------------------
#  Distance along path.
#
#  $distance = newick_path_length( @path )
#-------------------------------------------------------------------------------
sub newick_path_length {
    my $node = shift;      #  Discard the first node
    array_ref( $node ) || return undef;
    @_ ? distance_along_path_2( @_ ) : 0;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  This expects to get path minus root node:
#
#  $distance = distance_along_path_2( @path )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub distance_along_path_2 {
    shift;                 #  Discard descendant number
    my $node = shift;
    array_ref( $node ) || return undef;
    my $d1 = newick_x( $node );
    my $d2 = @_ ? distance_along_path_2(@_) : 0;
    defined( $d1 ) && defined( $d2 ) ? $d1 + $d2 : undef;
}


#-------------------------------------------------------------------------------
#  Tip-to-tip distance.
#
#  $distance = tip_to_tip_distance( $tree, $tip1, $tip2 )
#-------------------------------------------------------------------------------
sub tip_to_tip_distance {
    my ( $node, $tip1, $tip2 ) = @_;

    array_ref( $node ) && defined( $tip1 )
                       && defined( $tip2 ) || return undef;
    my @p1 = path_to_tip( $node, $tip1 );
    my @p2 = path_to_tip( $node, $tip2 );
    @p1 && @p2 || return undef;                          # Were they found?

    # Find the unique suffixes of the two paths
    my ( $suf1, $suf2 ) = unique_suffixes( \@p1, \@p2 ); # Common node is lost
    my $d1 = @$suf1 ? distance_along_path_2( @$suf1 ) : 0;
    my $d2 = @$suf2 ? distance_along_path_2( @$suf2 ) : 0;

    defined( $d1 ) && defined( $d2 ) ? $d1 + $d2 : undef;
}


#-------------------------------------------------------------------------------
#  Node-to-node distance.
#  Nodes can be:   $tipname
#                [ $tipname ]
#                [ $tipname1, $tipname2, $tipname3 ]
#
#  $distance = node_to_node_distance( $tree, $node1, $node2 )
#-------------------------------------------------------------------------------
sub node_to_node_distance {
    my ( $node, $node1, $node2 ) = @_;

    array_ref( $node ) && defined( $node1 )
                       && defined( $node2 ) || return undef;
    my @p1 = path_to_node( $node, $node1 );
    my @p2 = path_to_node( $node, $node2 );
    @p1 && @p2 || return undef;                          # Were they found?

    # Find the unique suffixes of the two paths
    my ( $suf1, $suf2 ) = unique_suffixes( \@p1, \@p2 ); # Common node is lost
    my $d1 = @$suf1 ? distance_along_path_2( @$suf1 ) : 0;
    my $d2 = @$suf2 ? distance_along_path_2( @$suf2 ) : 0;

    defined( $d1 ) && defined( $d2 ) ? $d1 + $d2 : undef;
}


#===============================================================================
#  Tree manipulations:
#===============================================================================
#  Copy tree.
#  Lists are copied, except that references to empty lists go to undef.
#  Only defined fields are added, so tree list may be shorter than 8 fields.
#
#  $treecopy = copy_newick_tree( $tree )
#-------------------------------------------------------------------------------
sub copy_newick_tree {
    my ( $node ) = @_;
    array_ref( $node ) || return undef;

    my $nn = [];  #  Reference to a new node structure
    #  Build a new descendant list, if not empty
    my @dl = newick_desc_list( $node );
    set_newick_desc_ref( $nn, @dl ? [ map { copy_newick_tree( $_ ) } @dl ]
                                  : undef
                       );

    #  Copy label and x, if defined
    my ( $l, $x );
    if ( defined( $l = newick_lbl( $node ) ) ) { set_newick_lbl( $nn, $l ) }
    if ( defined( $x = newick_x(   $node ) ) ) { set_newick_x(   $nn, $x ) }

    #  Build new comment lists, when not empty ( does not extend array unless
    #  necessary)
    my $c;
    if ( $c = newick_c1( $node ) and @$c ) { set_newick_c1( $nn, [ @$c ] ) }
    if ( $c = newick_c2( $node ) and @$c ) { set_newick_c2( $nn, [ @$c ] ) }
    if ( $c = newick_c3( $node ) and @$c ) { set_newick_c3( $nn, [ @$c ] ) }
    if ( $c = newick_c4( $node ) and @$c ) { set_newick_c4( $nn, [ @$c ] ) }
    if ( $c = newick_c5( $node ) and @$c ) { set_newick_c5( $nn, [ @$c ] ) }

    $nn;
}


#-------------------------------------------------------------------------------
#  Use a hash to relabel the nodes in a newick tree.
#
#  $newtree = newick_relabel_nodes( $node, \%new_name )
#-------------------------------------------------------------------------------
sub newick_relabel_nodes {
    my ( $node, $new_name ) = @_;

    my ( $lbl, $new );
    if ( defined( $lbl = newick_lbl( $node ) )
      && ( $lbl ne "" )
      && defined( $new = $new_name->{ $lbl } )
       ) {
        set_newick_lbl( $node, $new );
    }

    foreach ( newick_desc_list( $node ) ) {
        newick_relabel_nodes( $_, $new_name );
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Use a hash to relabel the nodes in a newick tree (case insensitive).
#
#  $newtree = newick_relabel_nodes_i( $node, \%new_name )
#-------------------------------------------------------------------------------
sub newick_relabel_nodes_i {
    my ( $node, $new_name ) = @_;

    #  Add any necessary lowercase keys to the hash:

    my $lc_lbl;
    foreach ( keys %$new_name ) {
        $lc_lbl = lc $_;
        ( $lc_lbl eq $_ ) or ( $new_name->{ $lc_lbl } = $new_name->{ $_ } );
    }

    newick_relabel_nodes_i2( $node, $new_name );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Do the actual relabeling
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub newick_relabel_nodes_i2 {
    my ( $node, $new_name ) = @_;

    my ( $lbl, $new );
    if ( defined( $lbl = newick_lbl( $node ) )
      && ( $lbl ne "" )
      && defined( $new = $new_name->{ lc $lbl } )
       ) {
        set_newick_lbl( $node, $new );
    }

    foreach ( newick_desc_list( $node ) ) {
        newick_relabel_nodes_i2( $_, $new_name );
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Use a hash to relabel the tips in a newick tree.
#
#  $newtree = newick_relabel_tips( $node, \%new_name )
#-------------------------------------------------------------------------------
sub newick_relabel_tips {
    my ( $node, $new_name ) = @_;

    my @desc = newick_desc_list( $node );

    if ( @desc ) {
        foreach ( @desc ) { newick_relabel_tips( $_, $new_name ) }
    }
    else {
        my ( $lbl, $new );
        if ( defined( $lbl = newick_lbl( $node ) )
          && ( $lbl ne "" )
          && defined( $new = $new_name->{ $lbl } )
           ) {
            set_newick_lbl( $node, $new );
        }
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Use a hash to relabel the tips in a newick tree (case insensitive).
#
#  $newtree = newick_relabel_tips_i( $node, \%new_name )
#-------------------------------------------------------------------------------
sub newick_relabel_tips_i {
    my ( $node, $new_name ) = @_;

    #  Add any necessary lowercase keys to the hash:

    my $lc_lbl;
    foreach ( keys %$new_name ) {
        $lc_lbl = lc $_;
        ( $lc_lbl eq $_ ) or ( $new_name->{ $lc_lbl } = $new_name->{ $_ } );
    }

    newick_relabel_tips_i2( $node, $new_name );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Do the actual relabeling
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub newick_relabel_tips_i2 {
    my ( $node, $new_name ) = @_;

    my @desc = newick_desc_list( $node );

    if ( @desc ) {
        foreach ( @desc ) { newick_relabel_tips_i2( $_, $new_name ) }
    }
    else {
        my ( $lbl, $new );
        if ( defined( $lbl = newick_lbl( $node ) )
          && ( $lbl ne "" )
          && defined( $new = $new_name->{ lc $lbl } )
           ) {
            set_newick_lbl( $node, $new );
        }
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Set undefined branch lenghts (except root) to length x.
#
#  $n_changed = newick_set_undefined_branches( $node, $x )
#-------------------------------------------------------------------------------
sub newick_set_undefined_branches {
    my ( $node, $x, $not_root ) = @_;

    my $n = 0;
    if ( $not_root && ! defined( newick_x( $node ) ) ) {
        set_newick_x( $node, $x );
        $n++;
    }

    foreach ( newick_desc_list( $node ) ) {
        $n += newick_set_undefined_branches( $_, $x, 1 );
    }

    $n;
}


#-------------------------------------------------------------------------------
#  Set all branch lenghts (except root) to length x.
#
#  $n_changed = newick_set_all_branches( $node, $x )
#-------------------------------------------------------------------------------
sub newick_set_all_branches {
    my ( $node, $x, $not_root ) = @_;

    my $n = 0;
    if ( $not_root ) {
        set_newick_x( $node, $x );
        $n++;
    }

    foreach ( newick_desc_list( $node ) ) {
        $n += newick_set_all_branches( $_, $x, 1 );
    }

    $n;
}


#-------------------------------------------------------------------------------
#  Set negative branches to zero.  The original tree is modfied.
#
#  $n_changed = newick_fix_negative_branches( $tree )
#-------------------------------------------------------------------------------
sub newick_fix_negative_branches {
    my ( $tree ) = @_;
    array_ref( $tree ) or return undef;
    my $n_changed = 0;
    my $x = newick_x( $tree );
    if ( defined( $x ) and $x < 0 )
    {
        set_newick_x( $tree, 0 );
        $n_changed++;
    }

    foreach ( newick_desc_list( $tree ) )
    {
        $n_changed += newick_fix_negative_branches( $_ );
    }

    $n_changed;
}


#-------------------------------------------------------------------------------
#  Normalize tree order (in place).
#
#  ( $tree, $label1 ) = normalize_newick_tree( $tree )
#-------------------------------------------------------------------------------
sub normalize_newick_tree {
    my ( $node ) = @_;

    my @descends = newick_desc_list( $node );
    if ( @descends == 0 ) { return ( $node, lc newick_lbl( $node ) ) }

    my %hash = map { (normalize_newick_tree( $_ ))[1] => $_ } @descends;
    my @keylist = sort { $a cmp $b } keys %hash;
    set_newick_desc_list( $node, map { $hash{$_} } @keylist );

    ( $node, $keylist[0] );
}


#-------------------------------------------------------------------------------
#  Reverse tree order (in place).
#
#  $tree = reverse_newick_tree( $tree )
#-------------------------------------------------------------------------------
sub reverse_newick_tree {
    my ( $node ) = @_;

    my @descends = newick_desc_list( $node );
    if ( @descends ) {
        set_newick_desc_list( $node, reverse @descends );
        foreach ( @descends ) { reverse_newick_tree( $_ ) }
    }
    $node;
}


#-------------------------------------------------------------------------------
#  Standard unrooted tree (in place).
#
#  $stdtree = std_unrooted_newick( $tree )
#-------------------------------------------------------------------------------
sub std_unrooted_newick {
    my ( $tree ) = @_;

    my ( $mintip ) = sort { lc $a cmp lc $b } newick_tip_list( $tree );
    ( normalize_newick_tree( reroot_newick_next_to_tip( $tree, $mintip ) ) )[0];
}


#-------------------------------------------------------------------------------
#  Move largest groups to periphery of tree (in place).
#
#      dir  <= -2 for up-sweeping tree (big groups always first),
#            = -1 for big group first, balanced tree,
#            =  0 for balanced tree,
#            =  1 for small group first, balanced tree, and
#           >=  2 for down-sweeping tree (small groups always top)
#
#  $tree = aesthetic_newick_tree( $treeref, $dir )
#-------------------------------------------------------------------------------
sub aesthetic_newick_tree {
    my ( $tree, $dir ) = @_;
    my %cnt;

    $dir = ! $dir       ?        0 :  #  Undefined or zero
             $dir <= -2 ? -1000000 :
             $dir <   0 ?       -1 :
             $dir >=  2 ?  1000000 :
                                 1 ;
    build_tip_count_hash( $tree, \%cnt );
    reorder_by_tip_count( $tree, \%cnt, $dir );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Build a hash to look up the number of descendants of each node.
#  Access count with $cntref->{$noderef}
#
#  $count = build_tip_count_hash( $node, $cnt_hash_ref )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub build_tip_count_hash {
    my ( $node, $cntref ) = @_;
    my ( $i, $cnt );

    if ( newick_n_desc( $node ) < 1 ) { $cnt = 1 }
    else {
        $cnt = 0;
        foreach ( newick_desc_list( $node ) ) {
            $cnt += build_tip_count_hash( $_, $cntref );
        }
    }

    $cntref->{$node} = $cnt;
    $cnt;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $node = reorder_by_tip_count( $node, $cntref, $dir )
#      dir  < 0 for upward branch (big group first),
#           = 0 for no change, and
#           > 0 for downward branch (small group first).
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub reorder_by_tip_count {
    my ( $node, $cntref, $dir ) = @_;

    my $nd = newick_n_desc( $node );
    if ( $nd <  1 ) { return $node }       #  Do nothing to a tip

    #  Reorder this subtree:

    my $dl_ref = newick_desc_ref( $node );
    if    ( $dir < 0 ) {                   #  Big group first
        @$dl_ref = sort { $cntref->{$b} <=> $cntref->{$a} } @$dl_ref;
    }
    elsif ( $dir > 0 ) {                   #  Small group first
        @$dl_ref = sort { $cntref->{$a} <=> $cntref->{$b} } @$dl_ref;
    }

    #  Reorder within descendant subtrees:

    my $step = 0;
    if ( abs( $dir ) < 1e5 ) {
        $dir = 1 - $nd;                              #  Midgroup => as is
    #   $dir = 1 - $nd + ( $dir < 0 ? -0.5 : 0.5 );  #  Midgroup => outward
        $step = 2;
    }

    for ( my $i = 0; $i < $nd; $i++ ) {
        reorder_by_tip_count( $dl_ref->[$i], $cntref, $dir );
        $dir += $step;
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Move smallest groups to periphery of tree (in place).
#
#      dir  <= -2 for up-sweeping tree (big groups always first),
#            = -1 for big group first, balanced tree,
#            =  0 for balanced tree,
#            =  1 for small group first, balanced tree, and
#           >=  2 for down-sweeping tree (small groups always top)
#
#  $tree = unaesthetic_newick_tree( $treeref, $dir )
#-------------------------------------------------------------------------------
sub unaesthetic_newick_tree {
    my ( $tree, $dir ) = @_;
    my %cnt;

    $dir = ! $dir       ?        0 :  #  Undefined or zero
             $dir <= -2 ? -1000000 :
             $dir <   0 ?       -1 :
             $dir >=  2 ?  1000000 :
                                 1 ;
    build_tip_count_hash( $tree, \%cnt );
    reorder_against_tip_count( $tree, \%cnt, $dir );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $node = reorder_by_tip_count( $node, $cntref, $dir )
#      dir  < 0 for upward branch (big group first),
#           = 0 for no change, and
#           > 0 for downward branch (small group first).
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub reorder_against_tip_count {
    my ( $node, $cntref, $dir ) = @_;

    my $nd = newick_n_desc( $node );
    if ( $nd <  1 ) { return $node }       #  Do nothing to a tip

    #  Reorder this subtree:

    my $dl_ref = newick_desc_ref( $node );
    if    ( $dir > 0 ) {                   #  Big group first
        @$dl_ref = sort { $cntref->{$b} <=> $cntref->{$a} } @$dl_ref;
    }
    elsif ( $dir < 0 ) {                   #  Small group first
        @$dl_ref = sort { $cntref->{$a} <=> $cntref->{$b} } @$dl_ref;
    }

    #  Reorder within descendant subtrees:

    my $step = 0;
    if (abs( $dir ) < 1e5) {
        $dir = 1 - $nd;                              #  Midgroup => as is
    #   $dir = 1 - $nd + ( $dir < 0 ? -0.5 : 0.5 );  #  Midgroup => outward
        $step = 2;
    }

    for ( my $i = 0; $i < $nd; $i++ ) {
        reorder_by_tip_count( $dl_ref->[$i], $cntref, $dir );
        $dir += $step;
    }

    $node;
}


#-------------------------------------------------------------------------------
#  Randomize descendant order at each node (in place).
#
#  $tree = random_order_newick_tree( $tree )
#-------------------------------------------------------------------------------
sub random_order_newick_tree {
    my ( $node ) = @_;

    my $nd = newick_n_desc( $node );
    if ( $nd <  1 ) { return $node }       #  Do nothing to a tip

    #  Reorder this subtree:

    my $dl_ref = newick_desc_ref( $node );
    @$dl_ref = random_order( @$dl_ref );

    #  Reorder descendants:

    foreach ( @$dl_ref ) { random_order_newick_tree( $_ ) }

    $node;
}


#-------------------------------------------------------------------------------
#  Reroot a tree to the node that lies at the end of a path.
#
#  $newtree = reroot_newick_by_path( @path )
#-------------------------------------------------------------------------------
sub reroot_newick_by_path {
    my ( $node1, $path1, @rest ) = @_;
    array_ref( $node1 ) || return undef;      #  Always expect a node

    defined( $path1 ) && @rest || return $node1;  #  If no path, we're done

    my $node2 = $rest[0];                     #  Next element in path is node 2
    newick_desc_i( $node1, $path1 ) eq $node2 || return undef;  #  Check link

    #  Remove node 2 from node 1 descendant list.  Could use a simple splice:
    #
    #      splice( @$dl1, $path1-1, 1 );
    #
    #  But this maintains the cyclic order of the nodes:

    my $dl1 = newick_desc_ref( $node1 );
    my $nd1 = @$dl1;
    if    ( $path1 == 1    ) { shift @$dl1 }
    elsif ( $path1 == $nd1 ) { pop   @$dl1 }
    else                     { @$dl1 = ( @$dl1[ $path1 .. $nd1-1   ]
                                       , @$dl1[ 0      .. $path1-2 ]
                                       )
    }

    #  Append node 1 to node 2 descendant list (does not alter numbering):

    my $dl2 = newick_desc_ref( $node2 );
    if ( array_ref( $dl2 ) ) { push @$dl2, $node1 }
    else                     { set_newick_desc_list( $node2, [ $node1 ] ) }

    #  Move c1 comments from node 1 to node 2:

    my $C11 = newick_c1( $node1 );
    my $C12 = newick_c1( $node2 );
    ! defined( $C11 ) || set_newick_c1( $node1, undef ); #  Remove them from node 1
    if ( $C12 && @$C12 ) {                      #  If node 2 comments and
        if ( $C11 && @$C11 ) { unshift @$C12, @$C11 } #  Node 1, prefix 1 to 2
    }
    elsif ( $C11 && @$C11 ) { set_newick_c1( $node2, $C11 ) }     #  Otherwise move node 1 link

    #  Swap branch lengths and comments for reversal of link direction:

    my $x1 = newick_x( $node1 );
    my $x2 = newick_x( $node2 );
    ! defined( $x1 ) && ! defined ( $x2 ) || set_newick_x( $node1, $x2 );
    ! defined( $x1 ) && ! defined ( $x2 ) || set_newick_x( $node2, $x1 );

    my $c41 = newick_c4( $node1 );
    my $c42 = newick_c4( $node2 );
    ! defined( $c42 ) || ! @$c42 || set_newick_c4( $node1, $c42 );
    ! defined( $c41 ) || ! @$c41 || set_newick_c4( $node2, $c41 );

    my $c51 = newick_c5( $node1 );
    my $c52 = newick_c5( $node2 );
    ! defined( $c52 ) || ! @$c52 || set_newick_c5( $node1, $c52 );
    ! defined( $c51 ) || ! @$c51 || set_newick_c5( $node2, $c51 );

    reroot_newick_by_path( @rest );           #  Node 2 is first element of rest
}


#-------------------------------------------------------------------------------
#  Move root of tree to named tip.
#
#  $newtree = reroot_newick_to_tip( $tree, $tip )
#-------------------------------------------------------------------------------
sub reroot_newick_to_tip {
    my ( $tree, $tipname ) = @_;
    reroot_newick_by_path( path_to_tip( $tree, $tipname ) );
}


#-------------------------------------------------------------------------------
#  Move root of tree to be node adjacent to a named tip.
#
#  $newtree = reroot_newick_next_to_tip( $tree, $tip )
#-------------------------------------------------------------------------------
sub reroot_newick_next_to_tip {
    my ( $tree, $tipname ) = @_;
    my @path = path_to_tip( $tree, $tipname );
    @path || return undef;
    @path == 1 ? reroot_newick_by_path( $tree, 1, newick_desc_i( $tree, 1 ) )
               : reroot_newick_by_path( @path[0 .. @path-3] );
}


#-------------------------------------------------------------------------------
#  Move root of tree to a node, defined by 1 or 3 tip names.
#
#  $newtree = reroot_newick_to_node( $tree, @node )
#-------------------------------------------------------------------------------
sub reroot_newick_to_node {
    reroot_newick_by_path( path_to_node( @_ ) );
}


#-------------------------------------------------------------------------------
#  Move root of tree to a node, defined by reference.
#
#  $newtree = reroot_newick_to_node_ref( $tree, $noderef )
#-------------------------------------------------------------------------------
sub reroot_newick_to_node_ref {
    my ( $tree, $node ) = @_;
    reroot_newick_by_path( path_to_node_ref( $tree, $node ) );
}


#-------------------------------------------------------------------------------
#  Move root of tree to an approximate midpoint.
#
#  $newtree = reroot_newick_to_approx_midpoint( $tree )
#-------------------------------------------------------------------------------
sub reroot_newick_to_approx_midpoint {
    my ( $tree ) = @_;

    #  Compile average tip to node distances assending

    my $dists1 = average_to_tips_1( $tree );

    #  Compile average tip to node distances descending, returning midpoint node

    my $node = average_to_tips_2( $dists1, undef, undef );

    #  Reroot

    $node ? reroot_newick_to_node_ref( $tree, $node ) : $tree
}


sub average_to_tips_1 {
    my ( $node ) = @_;

    my @desc_dists = map { average_to_tips_1( $_ ) } newick_desc_list( $node );
    my $x_below = 0;
    if ( @desc_dists )
    {
        foreach ( @desc_dists ) { $x_below += $_->[0] }
        $x_below /= @desc_dists;
    }
    my $x = newick_x( $node ) || 0;
    my $x_net = $x_below + $x;

    [ $x_net, $x, $x_below, [ @desc_dists ], $node ]
}

    
sub average_to_tips_2 {
    my ( $dists1, $x_above, $anc_node ) = @_;
    my ( undef, $x, $x_below, $desc_list, $node ) = @$dists1;

    #  Are we done?  Root is in this node's branch, or "above"?

    # defined( $x_above ) and print STDERR "x_above = $x_above\n";
    # print STDERR "x       = $x\n";
    # print STDERR "x_below = $x_below\n";
    # print STDERR "n_desc  = ", scalar @$desc_list, "\n\n";

    if ( defined( $x_above ) && ( ( $x_above + $x ) >= $x_below ) )
    {
        #  At this point the root can only be in this node's branch,
        #  or "above" it in the current rooting of the tree (which
        #  would mean that the midpoint is actually down a different
        #  path from the root of the current tree).
        #
        #  Is the root in the current branch?

        if ( ( $x_below + $x ) >= $x_above )
        {
            return ( $x_above >= $x_below ) ? $anc_node : $node;
        }
        else
        {
            return undef;
        }
    }

    #  The root must be somewhere below this node:

    my $n_1      =   @$desc_list - ( $anc_node ? 0 : 1 );
    my $ttl_dist = ( @$desc_list * $x_below ) + ( defined( $x_above ) ? ( $x_above + $x ) : 0 );

    foreach ( @$desc_list )
    {
        #  If input tree is tip_rooted, $n-1 can be 0, so:

        my $above2 = $n_1 ? ( ( $ttl_dist - $_->[0] ) / $n_1 ) : 0;
        my $root = average_to_tips_2( $_, $above2, $node );
        if ( $root ) { return $root }
    }

    #  Was not anywhere below this node (oh-oh):

    return undef;
}

    
#-------------------------------------------------------------------------------
#  Move root of tree to an approximate midpoint.  Weight by tips.
#
#  $newtree = reroot_newick_to_approx_midpoint_w( $tree )
#-------------------------------------------------------------------------------
sub reroot_newick_to_approx_midpoint_w {
    my ( $tree ) = @_;

    #  Compile average tip to node distances assending

    my $dists1 = average_to_tips_1_w( $tree );

    #  Compile average tip to node distances descending, returning midpoint node

    my $node = average_to_tips_2_w( $dists1, undef, undef, undef );

    #  Reroot

    $node ? reroot_newick_to_node_ref( $tree, $node ) : $tree
}


sub average_to_tips_1_w {
    my ( $node ) = @_;

    my @desc_dists = map { average_to_tips_1_w( $_ ) } newick_desc_list( $node );
    my $x_below = 0;
    my $n_below = 1;
    if ( @desc_dists )
    {
        $n_below = 0;
        my $n;
        foreach ( @desc_dists )
        {
            $n_below += $n = $_->[1];
            $x_below += $n * $_->[0];
        }
        $x_below /= $n_below;
    }
    my $x = newick_x( $node ) || 0;
    my $x_net = $x_below + $x;

    [ $x_net, $n_below, $x, $x_below, [ @desc_dists ], $node ]
}


sub average_to_tips_2_w {
    my ( $dists1, $x_above, $n_above, $anc_node ) = @_;
    my ( undef, $n_below, $x, $x_below, $desc_list, $node ) = @$dists1;

    #  Are we done?  Root is in this node's branch, or "above"?

    # defined( $x_above ) and print STDERR "x_above = $x_above\n";
    # print STDERR "x       = $x\n";
    # print STDERR "x_below = $x_below\n";
    # print STDERR "n_desc  = ", scalar @$desc_list, "\n\n";

    if ( defined( $x_above ) && ( ( $x_above + $x ) >= $x_below ) )
    {
        #  At this point the root can only be in this node's branch,
        #  or "above" it in the current rooting of the tree (which
        #  would mean that the midpoint is actually down a different
        #  path from the root of the current tree).
        #
        #  Is the root in the current branch?

        if ( ( $x_below + $x ) >= $x_above )
        {
            return ( $x_above >= $x_below ) ? $anc_node : $node;
        }
        else
        {
            return undef;
        }
    }

    #  The root must be some where below this node:

    $n_above ||= 0;
    my $n = $n_above + $n_below;
    my $ttl_w_dist = ( $n_below * $x_below )
                   + ( defined( $x_above ) ? $n_above * ( $x_above + $x ) : 0 );

    foreach ( @$desc_list )
    {
        my $n_2      = $_->[1];    # n in subtree
        my $n_above2 = $n - $n_2;  # tip rooted has 1 above

        #  If input tree is tip_rooted, $n_above2 can be 0, so:

        my $x_above2 = $n_above2 ? ( ( $ttl_w_dist - $n_2 * $_->[0] ) / $n_above2 )
                                 : 0;
        my $root = average_to_tips_2_w( $_, $x_above2, $n_above2 || 1, $node );
        if ( $root ) { return $root }
    }

    #  Was not anywhere below this node (oh-oh):

    return undef;
}

    
#-------------------------------------------------------------------------------
#  Move root of tree from tip to adjacent node.
#
#  $newtree = uproot_tip_rooted_newick( $tree )
#-------------------------------------------------------------------------------
sub uproot_tip_rooted_newick {
    my ( $node ) = @_;
    newick_is_tip_rooted( $node ) || return $node;

    #  Path to the sole descendant:

    reroot_newick_by_path( $node, 1, newick_desc_i( $node, 1 ) );
}


#-------------------------------------------------------------------------------
#  Remove root bifurcation.
#
#  Root node label, label comment and descendant list comment are discarded.
#
#  $newtree = uproot_newick( $tree )
#-------------------------------------------------------------------------------
sub uproot_newick {
    my ( $node0 ) = @_;
    newick_is_rooted( $node0 ) || return $node0;

    my ( $node1, $node2 ) = newick_desc_list( $node0 );

    #  Ensure that node1 has at least 1 descendant

    if    ( newick_n_desc( $node1 ) ) {
        push @{ newick_desc_ref( $node1 ) }, $node2;    #  Add node2 to descend list
    }

    #  Or node2 has at least 1 descendant

    elsif ( newick_n_desc( $node2 ) ) {
        unshift @{ newick_desc_ref( $node2 ) }, $node1;   #  Add node1 to descend list
        ( $node1, $node2 ) = ( $node2, $node1 );        #  And reverse labels
    }

    #  We could make this into a tip rooted tree, but for now:

    else { return $node0 }

    #  Prefix node1 branch to that of node2:

    add_to_newick_branch( $node2, $node1 );
    set_newick_x( $node1, undef );

    #  Tree prefix comment lists (as references):

    my $C10 = newick_c1( $node0 );
    my $C11 = newick_c1( $node1 );
    if ( $C11 && @$C11 ) { 
        if ( $C10 && @$C10 ) { unshift @$C11, @$C10 } #  Prefix to node1 comments
    }
    elsif ( $C10 && @$C10 ) {
        set_newick_c1( $node1, $C10 )          #  Or move node0 comments to node1
    }

    $node1;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Prefix branch of node2 to that of node1:
#
#  $node1 = add_to_newick_branch( $node1, $node2 )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub add_to_newick_branch {
    my ( $node1, $node2 ) = @_;
    array_ref( $node1 ) || die "add_to_newick_branch: arg 1 not array ref\n";
    array_ref( $node2 ) || die "add_to_newick_branch: arg 2 not array ref\n";

    #  Node structure template:
    #     my ( $DL, $L, $X, $C1, $C2, $C3, $C4, $C5 ) = @$node;

    #  Fix branch lengths for joining of two branches:

    set_newick_x( $node1, newick_x( $node1 ) + newick_x( $node2 ) );

    #  Merge branch length comments:

    my $C41 = newick_c4( $node1 );  #  Ref to node1 C4
    my $C42 = newick_c4( $node2 );  #  Ref to node2 C4
    if ( $C41 && @$C41 ) {
        if ( $C42 && @$C42 ) { unshift @$C41, @$C42 }         #  Add node2 comment
    }
    elsif ( $C42 && @$C42 ) { set_newick_c4( $node1, $C42 ) } #  Or move node1 comment

    my $C51 = newick_c5( $node1 );  #  Ref to node1 C5
    my $C52 = newick_c5( $node2 );  #  Ref to node2 C5
    if ( $C51 && @$C51 ) {
        if ( $C52 && @$C52 ) { unshift @$C51, @$C52 }         #  Add node2 comment
    }
    elsif ( $C52 && @$C52 ) { set_newick_c5( $node1, $C52 ) } #  Or move node1 comment

    $node1;
}


#-------------------------------------------------------------------------------
#  Collapse zero-length branches to make multifurcation.  The original tree
#  is modified.
#
#  $tree = collapse_zero_length_branches( $tree )
#  $tree = collapse_zero_length_branches( $tree, $not_root )
#-------------------------------------------------------------------------------
sub collapse_zero_length_branches {
    my ( $tree, $not_root ) = @_;
    array_ref( $tree ) || return undef;

    my @desc = newick_desc_list( $tree );
    @desc or return ( $tree );              # Cannot collapse terminal branch

    #  Analyze descendants:

    $not_root ||= 0;
    my @new_desc = ();
    my $changed = 0;
    foreach ( @desc )
    {
        my ( undef, @to_add ) = collapse_zero_length_branches( $_, $not_root+1 );
        if ( @to_add )
        {
            push @new_desc, @to_add;
            $changed = 1;
        }
        else
        {
            push @new_desc, $_;
        }
    }
    set_newick_desc_ref( $tree, [ @new_desc ] ) if $changed;

    #  Collapse if not root, not tip and zero (or negative) branch:

    my $collapse = $not_root && @new_desc && ( newick_x( $tree ) <= 0 ) ? 1 : 0;
    ( $tree, ( $collapse ? @new_desc : () ) );
}


#-------------------------------------------------------------------------------
#  Prune one or more tips from a tree:
#     Caveat:  if one tip is listed, the original tree is modified.
#              if more than one tip is listed, a copy of the tree is returned
#                   (even if it is just listing the same tip twice!).
#
#  $newtree = prune_from_newick( $tree,  $tip  )
#  $newtree = prune_from_newick( $tree,  @tips )
#  $newtree = prune_from_newick( $tree, \@tips )
#-------------------------------------------------------------------------------
sub prune_from_newick {
    my ( $tr, @tips ) = @_;
    if ( @tips == 1 && ref( $tips[0] ) eq "ARRAY" ) { @tips = @{ $tips[0] } }
    
    if ( @tips == 0 ) { return $tr }
    if ( @tips == 1 ) { return prune_1_from_newick( $tr, @tips ) }

    my %del  = map  { ( $_, 1 ) } @tips;
    my @keep = grep { ! $del{ $_ } } newick_tip_list( $tr );
    newick_subtree( $tr, @keep );
}


#-------------------------------------------------------------------------------
#  Prune a tip from a tree:
#
#  $newtree = prune_1_from_newick( $tree, $tip )
#-------------------------------------------------------------------------------
sub prune_1_from_newick {
    my ( $tr, $tip ) = @_;
    my @path = path_to_tip( $tr, $tip );
    if ( @path < 3 ) { return $tr }

    my $node = $path[-1];  #  Node with the tip
    my $i1   = $path[-2];  #  Descendant number of node in ancestor desc list
    my $anc1 = $path[-3];  #  Ancestor of node
    my $nd1  = newick_n_desc( $anc1 );  #  Number of descendants of ancestor
    my $anc2 = ( @path >= 5 ) ? $path[-5] : undef; # Ancestor of anc1

    # dump_tree( $node );
    # print STDERR "i1 = $i1\n";
    # dump_tree( $anc1 );
    # print STDERR "nd1 = $nd1\n";
    # defined( $anc2 ) && dump_tree( $anc2 );

    if ( $nd1 > 3 || ( $anc2 && $nd1 > 2 ) ) {   # Tip joins at multifurcation
        splice( @{ $anc1->[0] }, $i1-1, 1 );     #    delete the descendant
    }

    elsif ( $anc2 ) {                            # Tip joins at internal bifurcation
        my $sis = newick_desc_i( $anc1, 3-$i1 );     # find sister node
        add_to_newick_branch( $sis, $anc1 );         # combine internal branches
        set_newick_desc_i( $anc2, $path[-4], $sis ); # remove $anc1
    }

    elsif ( $nd1 == 2) {                         # Tip joins bifurcating root node
        my $sis = newick_desc_i( $anc1, 3-$i1 ); #    find sister node
        $sis->[1] = $anc1->[1] if ! $sis->[1] && $anc1->[1];  # root label
        $sis->[2] = undef;                                    # root branch len
        $sis->[3] = $anc1->[3] if ! $sis->[3] && $anc1->[3];  # tree comment
        $sis->[4] = $anc1->[4] if ! $sis->[4] && $anc1->[4];  # desc list comment
        $sis->[5] = $anc1->[5] if ! $sis->[5] && $anc1->[5];  # label comment 
        $sis->[6] = undef      if   $sis->[6];   #    root branch comment
        $sis->[7] = undef      if   $sis->[7];   #    root branch comment
        $tr = $sis;                              #    sister is new root
    }

    elsif ( $nd1 == 3 ) {                        # Tip joins trifurcating root:
        splice( @{ $anc1->[0] }, $i1-1, 1 );     #    delete the descendant, and
        $tr = uproot_newick( $tr );              #    fix the rooting
    }

    else {
        return undef;
    }

    return $tr;
}


#-------------------------------------------------------------------------------
#  Produce a subtree with the desired tips:
#
#     Except for (some) tip nodes, the tree produced is a copy.
#     There is no check that requested tips exist.
#
#  $newtree = newick_subtree( $tree,  @tips )
#  $newtree = newick_subtree( $tree, \@tips )
#-------------------------------------------------------------------------------
sub newick_subtree {
    my ( $tr, @tips ) = @_;
    if ( @tips == 1 && ref( $tips[0] ) eq "ARRAY" ) { @tips = @{ $tips[0] } }

    if ( @tips < 2 ) { return undef }
    my $was_rooted = newick_is_rooted( $tr );
    my $keephash = { map { ( $_, 1 ) } @tips };
    my $tr2 = subtree1( $tr, $keephash );
    $tr2 = uproot_newick( $tr2 ) if ! $was_rooted && newick_is_rooted( $tr2 );
    $tr2->[2] = undef if $tr2;                   # undef root branch length
    $tr2;
}


sub subtree1 {
    my ( $tr, $keep ) = @_;
    my @desc1 = newick_desc_list( $tr );

    #  Is this a tip, and is it in the keep list?

    if ( @desc1 < 1 ) {
        return ( $keep->{ newick_lbl( $tr ) } ) ? $tr : undef;
    }

    #  Internal node: analyze the descendants:

    my @desc2 = ();
    foreach ( @desc1 ) {
        my $desc = subtree1( $_, $keep );
        if ( $desc && @$desc ) { push @desc2, $desc }
    }

    if ( @desc2 == 0 ) { return undef }
    if ( @desc2 >  1 ) { return [ \@desc2, @$tr[ 1 .. @$tr - 1 ] ] }

    #  Exactly 1 descendant

    my $desc = $desc2[ 0 ];
    my @nn = ( $desc->[0],
               $desc->[1] ? $desc->[1] : $tr->[1],
               defined( $tr->[2] ) ? $desc->[2] + $tr->[2] : undef
             );

    #  Merge comments (only recreating the ones that existed):

    if ( $tr->[3] && @{$tr->[3]} || $desc->[3] && @{$desc->[3]} ) {
        $nn[3] = [ $tr->[3] ? @{$tr->[3]} : (), $desc->[3] ? @{$desc->[3]} : () ];
    }
    if ( $tr->[4] && @{$tr->[4]} || $desc->[4] && @{$desc->[4]} ) {
        $nn[4] = [ $tr->[4] ? @{$tr->[4]} : (), $desc->[4] ? @{$desc->[4]} : () ];
    }
    if ( $tr->[5] && @{$tr->[5]} || $desc->[5] && @{$desc->[5]} ) {
        $nn[5] = [ $tr->[5] ? @{$tr->[5]} : (), $desc->[5] ? @{$desc->[5]} : () ];
    }
    if ( $tr->[6] && @{$tr->[6]} || $desc->[6] && @{$desc->[6]} ) {
        $nn[6] = [ $tr->[6] ? @{$tr->[6]} : (), $desc->[6] ? @{$desc->[6]} : () ];
    }
    if ( $tr->[7] && @{$tr->[7]} || $desc->[7] && @{$desc->[7]} ) {
        $nn[7] = [ $tr->[7] ? @{$tr->[7]} : (), $desc->[7] ? @{$desc->[7]} : () ];
    }

    return \@nn;
}


#===============================================================================
#
#  Tree writing and reading
#
#===============================================================================
#  writeNewickTree( $tree [, $file ] )
#-------------------------------------------------------------------------------
sub writeNewickTree {
    my ( $tree, $file ) = @_;
    $file || ( $file = \*STDOUT );
    print  $file  ( strNewickTree( $tree ), "\n" );
}


#-------------------------------------------------------------------------------
#  fwriteNewickTree( $file, $tree )     #  Args reversed to writeNewickTree
#-------------------------------------------------------------------------------
sub fwriteNewickTree { writeNewickTree( $_[1], $_[0] ) }


#-------------------------------------------------------------------------------
#  $treestring = strNewickTree( $tree )
#-------------------------------------------------------------------------------
sub strNewickTree {
    my $node = shift @_;
    strNewickSubtree( $node, "" ) . ";";
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $string = strNewickSubtree( $node, $prefix )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub strNewickSubtree {
    my ( $node, $prefix ) = @_;
    my  $s;

    $s = strNewickComments( newick_c1( $node ), $prefix );
    if ( $s ) { $prefix = " " }

    my $ndesc;
    if ( $ndesc = newick_n_desc( $node ) ) {
        for (my $d = 1; $d <= $ndesc; $d++) {
            $s .= ( ( $d == 1 )  ?  $prefix . "("  :  "," )
               .  strNewickSubtree( newick_desc_i( $node, $d ), " " );
        }

        $s .= ")" . strNewickComments( newick_c2( $node ), " " );
        $prefix = " ";
    }

    if ( defined( newick_lbl( $node ) ) && newick_lbl( $node ) ) {
        $s .= $prefix
           .  q_newick_lbl( $node )
           .  strNewickComments( newick_c3( $node ), " " );
    }

    if ( defined( newick_x( $node ) ) ) {
        $s .= ":"
           .   strNewickComments( newick_c4( $node ), " " )
           .   sprintf( " %.6f", newick_x( $node ) )
           .   strNewickComments( newick_c5( $node ), " " );
    }

    $s;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $string = strNewickComments( $clist, $prefix )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub strNewickComments {
    my ( $clist, $prefix ) = @_;
    array_ref( $clist ) && ( @$clist > 0 ) || return  "";
    $prefix . "[" . join( "] [", @$clist ) . "]";
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $quoted_label = q_newick_lbl( $label )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub q_newick_lbl {
    my $lbl = newick_lbl( $_[0] );
    defined( $lbl ) && ( $lbl ne "" ) || return undef;

    if ( $lbl =~ m/^[^][()_:;,]+$/        #  Anything but []()_:;,
      && $lbl !~ m/^'/  ) {               #     and does not start with '
        $lbl =~ s/ /_/g;                  #  Recode blanks as _
        return $lbl;
    }

    else {
        $lbl =~ s/'/''/g;                 #  Double existing single quote marks
        return  q(') . $lbl . q(');       #  Wrap in single quote marks
    }
}


#===============================================================================
#  $treestring = formatNewickTree( $tree )
#===============================================================================
sub formatNewickTree {
    formatNewickSubtree( $_[0], "", "" ) . ";";
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $string = formatNewickSubtree( $node, $prefix, $indent )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub formatNewickSubtree {
    my ( $node, $prefix, $indent ) = @_;
    my  $s;

    $s = formatNewickComments( newick_c1( $node ), $prefix, $indent );
    if ( $s ) { $prefix = "\n$indent" }

    if ( my $ndesc = newick_n_desc( $node ) ) {
        for (my $d = 1; $d <= $ndesc; $d++) {
            $s .= ( ( $d == 1 )  ?  $prefix . "("  :  ",\n$indent " )
               .  formatNewickSubtree( newick_desc_i( $node, $d ), " ", $indent . "  " );
        }

        $s .= "\n$indent)" . formatNewickComments( newick_c2( $node ), " ", $indent );
        $prefix = " ";
    }

    if ( defined( newick_lbl( $node ) ) && newick_lbl( $node ) ) {
        $s .= $prefix
           .  q_newick_lbl( $node )
           .  formatNewickComments( newick_c3( $node ), " ", $indent );
    }

    if ( defined( newick_x( $node ) ) ) {
        $s .= ":"
           .   formatNewickComments( newick_c4( $node ), " ", $indent )
           .   sprintf(" %.6f", newick_x( $node ) )
           .   formatNewickComments( newick_c5( $node ), " ", $indent );
    }

    $s;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $string = formatNewickComments( $clist, $prefix, $indent )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub formatNewickComments {
    my ( $clist, $prefix, $indent ) = @_;
    array_ref( $clist ) && @$clist || return  "";
    $prefix . "[" . join( "] [", @$clist ) . "]";
}


#===============================================================================
#  Tree reader adapted from the C language reader in fastDNAml
#
#  $tree = parse_newick_tree_str( $string )
#===============================================================================
sub parse_newick_tree_str {
    my $s = shift @_;

    my ( $ind, $rootnode ) = parse_newick_subtree( $s, 0 );
    if ( substr( $s, $ind, 1 ) ne ";") { warn "warning: tree missing ';'\n" }
    $rootnode;
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Read a subtrees recursively (everything of tree but a semicolon)
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub parse_newick_subtree {
    my ( $s, $ind ) = @_;

    my $newnode = [];
    my @dlist   = ();
    my ( $lbl, $x, $c1, $c2, $c3, $c4, $c5 );
 
    ( $ind, $c1 ) = getNextTreeChar( $s, $ind );       #  Comment 1
    if ( ! defined( $ind ) ) { treeParseError( "missing subtree" ) }
    if ( $c1 && @$c1 ) { set_newick_c1( $newnode, $c1 ) }

    if ( substr( $s, $ind, 1 ) eq "(" ) {                #  New internal node
        while ( ! @dlist || ( substr( $s, $ind, 1 ) eq "," ) ) {
            my $desc;
            ( $ind, $desc ) = parse_newick_subtree( $s, $ind+1 );
            if (! $ind) { return () }
            push @dlist, $desc;
        }
        if ( substr( $s, $ind, 1 ) ne ")" ) { treeParseError( "missing ')'" ) }

        ( $ind, $c2 ) = getNextTreeChar( $s, $ind+1 );   #  Comment 2
        if ( $c2 && @$c2 ) { set_newick_c2( $newnode, $c2 ) }
        ( $ind, $lbl ) = parseTreeNodeLabel( $s, $ind ); #  Node label
    }

    elsif ( substr( $s, $ind, 1 ) =~ /[^][(,):;]/ ) {    #  New tip
        ( $ind, $lbl ) = parseTreeNodeLabel( $s, $ind ); #  Tip label
        if (! $ind) { return () }
    }

    @dlist || $lbl || treeParseError( "no descendant list or label" );

    if ( @dlist ) { set_newick_desc_ref( $newnode, \@dlist ) }
    if ( $lbl   ) { set_newick_lbl( $newnode, $lbl ) }

    ( $ind, $c3 ) = getNextTreeChar( $s, $ind );         #  Comment 3
    if ( $c3 && @$c3 ) { set_newick_c3( $newnode, $c3 ) }

    if (substr( $s, $ind, 1 ) eq ":") {                  #  Branch length
        ( $ind, $c4 ) = getNextTreeChar( $s, $ind+1 );   #  Comment 4
        if ( $c4 && @$c4 ) { set_newick_c4( $newnode, $c4 ) }
        ( $ind, $x ) = parseBranchLength( $s, $ind );
        if ( defined( $x ) ) { set_newick_x( $newnode, $x ) }
        ( $ind, $c5 ) = getNextTreeChar( $s, $ind );     #  Comment 5
        if ( $c5 && @$c5 ) { set_newick_c5( $newnode, $c5 ) }
    }

    ( $ind, $newnode );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Read a Newick tree label
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub parseTreeNodeLabel {  #  Empty string is permitted
    my ( $s, $ind ) = @_;
    my ( $lbl, $c );

    if ( substr( $s, $ind, 1 ) eq "'") {
        my $ind1 = ++$ind;

        while ( ) {
            if ( ! defined( $c = substr( $s, $ind, 1 ) ) || $c eq "" ) {
                treeParseError( "missing close quote on label '" . substr( $s, $ind1 ) . "'" )
            }
            elsif ( $c ne "'"  )                  { $ind++ }
            elsif ( substr( $s, $ind, 2 ) eq "''" ) { $ind += 2 }
            else                                    { last }
        }

        $lbl = substr( $s, $ind1, $ind-$ind1 );
        $lbl =~ s/''/'/g;
        $ind++;
    }

    else {
        my $ind1 = $ind;
        while ( defined( $c = substr($s, $ind, 1) ) && $c ne "" && $c !~ /[][\s(,):;]/ ) { $ind++ }
        $lbl = substr( $s, $ind1, $ind-$ind1 );
        $lbl =~ s/_/ /g;
    }

    ( $ind, $lbl );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Read a Newick tree branch length
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub parseBranchLength {
    my ( $s, $ind ) = @_;

    my $c = substr( $s, $ind, 1 );

    my $sign = ( $c ne "-" ) ? 1 : -1;      #  Sign
    if ( $c =~ /[-+]/ ) { $c = substr( $s, ++$ind, 1 ) }

    if ( $c !~ /^[.0-9]$/ ) {   #  Allows starting with decimal
        treeParseError( "invalid branch length character '$c'" )
    }

    my $v = 0;
    while ( $c =~ /[0-9]/ ) {               #  Whole number
        $v = 10 * $v + $c;
        $c = substr( $s, ++$ind, 1 );
    }

    if ( $c eq "." ) {                      #  Fraction
        my $f = 0.1;
        $c = substr( $s, ++$ind, 1 );
        while ( $c =~ /[0-9]/ ) {
            $v += $f * $c;
            $f *= 0.1;
            $c  = substr( $s, ++$ind, 1 );
        }
    }

    $v *= $sign;

    if ( $c =~ /[dDeEgG]/ ) {                 #  Exponent
        $c = substr( $s, ++$ind, 1 );
        my $esign = ( $c ne "-" ) ? 1 : -1;
        if ( $c =~ /^[-+]$/ ) { $c = substr( $s, ++$ind, 1 ) }
        if ( $c !~ /^[0-9]$/ ) {
            treeParseError( "missing branch length exponent '$c'" )
        }

        my $e = 0;
        while ( $c =~ /[0-9]/ ) {
            $e = 10 * $e + $c;
            $c = substr( $s, ++$ind, 1 );
        }
        $e *= $esign;
        $v *= 10**$e;
    }

    ( $ind, $v );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  ( $index, /@commentlist ) = getNextTreeChar( $string, $index )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub getNextTreeChar {       #  Move to next nonblank, noncomment character
    my ( $s, $ind ) = @_;

    my @clist = ();

    #  Skip white space
    if ( substr( $s, $ind ) =~ /^(\s+)/ ) { $ind += length( $1 ) }

    #  Loop while it is a comment:
    while ( substr( $s, $ind, 1 ) eq "[" ) {
        $ind++;

        #  Find end
        if ( substr( $s, $ind ) !~ /^([^]]*)\]/ ) {
            treeParseError( "comment missing closing bracket '["
                           . substr( $s, $ind ) . "'" )
        }
        my $comment = $1;

        #  Save if it includes any "text"
        if ( $comment =~ m/\S/ ) { push @clist, $comment }

        $ind += length( $comment ) + 1;     #  Comment plus closing bracket

        #  Skip white space
        if ( substr( $s, $ind ) =~ /^(\s+)/ ) { $ind += length( $1 ) }
    }

    ( $ind, @clist ? \@clist : undef )
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  treeParseError( $message )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub treeParseError { die "Error: parse_newick_subtree: " . $_[0] . "\n" }


#===============================================================================
#  Make a printer plot of a tree:
#
#     $node   newick tree root node
#     $file   undef (= \*STDOUT), \*STDOUT, \*STDERR, or a file name.
#     $width  the approximate characters for the tree without labels
#     $min_dx the minimum horizontal branch length
#     $dy     the vertical space per taxon
#
#  printer_plot_newick( $node, $file (D=\*STDOUT), $width (D=68), $min_dx (D=2), $dy (D=1) )
#===============================================================================
sub printer_plot_newick {
    my ( $node, $file, $width, $min_dx, $dy ) = @_;

    my ( $fh, $close );
    if ( ! defined( $file ) ) {
        $fh = \*STDOUT;
    }
    elsif ( $file =~ /^\*/ ) {
        $fh = $file;
    }
    else {
        open $fh, ">$file" or die "Could not open $file for writing printer_plot_newick\n";
        $close = 1;
    }

    print $fh join( "\n", text_plot_newick( $node, $width, $min_dx, $dy ) ), "\n";
    if ( $close ) { close $fh }
}


#===============================================================================
#  Make a text plot of a tree:
#
#     $node   newick tree root node
#     $width  the approximate characters for the tree without labels
#     $min_dx the minimum horizontal branch length
#     $dy     the vertical space per taxon
#
#  @textlines = text_plot_newick( $node, $width (D=68), $min_dx (D=2), $dy (D=1) )
#===============================================================================
sub text_plot_newick {
    my ( $node, $width, $min_dx, $dy ) = @_;
    array_ref( $node ) || die "Bad node passed to text_plot_newick\n";
    defined( $min_dx ) and ( $min_dx >=  0 ) or $min_dx =  2;
    defined(     $dy ) and (     $dy >=  1 ) or     $dy =  1;
    defined( $width  )                       or  $width = 68;

    $min_dx = int( $min_dx );
    $dy     = int( $dy );
    my $x_scale = $width / ( newick_max_X( $node ) || 1 );  # Div by zero caught by RAE

    my $hash = {};
    layout_printer_plot( $node, $hash, 0, -0.5 * $dy, $x_scale, $min_dx, $dy );

    # dump_tree_hash( $node, $hash ); exit;

    #  Generate the lines of the tree one by one:

    my ( $y1, $y2 ) = @{ $hash->{ $node } };
    map { text_tree_row( $node, $hash, $_, "", "+" ) } ( $y1 .. $y2 );
}

#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  ( $xmax, $ymax, $root_y ) = layout_printer_plot( $node, $hash, $x0, $y0, $x_scale, $min_dx, $dy )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub layout_printer_plot {
    my ( $node, $hash, $x0, $y0, $x_scale, $min_dx, $dy ) = @_;
    array_ref( $node ) || die "Bad node ref passed to layout_printer_plot\n";
    hash_ref(  $hash ) || die "Bad hash ref passed to layout_printer_plot\n";

    my $dx = newick_x( $node );
    if ( defined( $dx ) ) {
        $dx *= $x_scale;
        $dx >= $min_dx or $dx = $min_dx;
    }
    else {
        $dx = ( $x0 > 0 ) ? $min_dx : 0;
    }
    $dx = int( $dx + 0.4999 );

    my ( $x, $xmax, $y, $ymax, $y1, $y2, $yn1, $yn2 );

    $x = $x0 + $dx;
    $y1 = int( $y0 + 0.5 * $dy + 0.4999 );
    my @dl = newick_desc_list( $node );

    if ( ! @dl ) {               #  A tip
        $xmax  = $x;
        $y = $yn1 = $yn2 = $y2 = $y1;
        $ymax  = $y + 0.5 * $dy;
    }

    else {                       #  A subtree
        $xmax = -1;
        my $xmaxi;
        my $yi;
        my @ylist = ();
        $ymax = $y0;

        foreach ( @dl ) {
            ( $xmaxi, $ymax, $yi ) = layout_printer_plot( $_, $hash, $x, $ymax, $x_scale, $min_dx, $dy );
            push @ylist, $yi;
            if ( $xmaxi > $xmax ) { $xmax = $xmaxi }
        }

        #  Use of y-list is overkill for saving first and last values,
        #  but eases implimentation of alternative y-value calculations.

        $yn1 = $ylist[ 0];
        $yn2 = $ylist[-1];
        $y = int( 0.5 * ( $yn1 + $yn2 ) + 0.4999 );
    }

    $y2 = int( $ymax - 0.5 * $dy + 0.4999 );

    $hash->{ $node } = [ $y1, $y2, $x0, $x, $y, $yn1, $yn2 ];
    ( $xmax, $ymax, $y );
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Debug routine
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub dump_tree {
    my ( $node, $prefix ) = @_;
    defined( $prefix ) or $prefix = "";
    print STDERR $prefix, join(", ", @$node), "\n";
    my @dl = $node->[0] ? @{$node->[0]} : ();
    foreach ( @dl ) { dump_tree( $_, $prefix . "  " ) }
    $prefix or print STDERR "\n";
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  Debug routine
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub dump_tree_hash {
    my ( $node, $hash, $prefix ) = @_;
    defined( $prefix ) or print STDERR "node; [ y1, y2, x0, x, y, yn1, yn2 ]\n" and $prefix = "";
    print STDERR $prefix, join(", ", @$node), "; ", join(", ", @{ $hash->{ $node } } ), "\n";
    my @dl = $node->[0] ? @{$node->[0]} : ();
    foreach (@dl) { dump_tree_hash( $_, $hash, $prefix . "  " ) }
}


#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#  $line = text_tree_row( $node, $hash, $row, $line, $symb )
#- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
sub text_tree_row {
    my ( $node, $hash, $row, $line, $symb ) = @_;

    my ( $y1, $y2, $x0, $x, $y, $yn1, $yn2 ) = @{ $hash->{ $node } };
    if ( $row < $y1 || $row > $y2 ) { return $line }

    if ( length( $line ) < $x0 ) { $line .= " " x ( $x0 - length( $line ) ) }

    if ( $row == $y ) {
        $line = substr( $line, 0, $x0 ) . $symb . (( $x > $x0 ) ? "-" x ($x - $x0) : "");
    }

    elsif ( $row > $yn1 && $row < $yn2 ) {
        if ( length( $line ) < $x ) { $line .= " " x ( $x - length( $line ) ) . "|" }
        else { substr( $line, $x ) = "|" }
    }

    my @dl = newick_desc_list( $node );

    if ( @dl < 1 ) {
        $line .= " " . $node->[1];
    }

    else {
        my @list = map { [ $_, "+" ] } @dl;  #  Print symbol for line
        $list[ 0]->[1] = "/";
        $list[-1]->[1] = "\\";

        foreach ( @list ) {
            my ( $n, $s ) = @$_;
            if ( $row >= $hash->{ $n }->[0] && $row <= $hash->{ $n }->[1] ) {
                $line = text_tree_row( $n, $hash, $row, $line, $s );
            }
         }

        if ( $row == $y ) { substr( $line, $x, 1 ) = "+" }
    }

    return $line;
}


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