| Andrew Cooke | Contents | Latest | RSS | Twitter | Previous | Next


Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

Personal Projects

Lepl parser for Python.

Colorless Green.

Photography around Santiago.

SVG experiment.

Professional Portfolio

Calibration of seismometers.

Data access via web services.

Cache rewrite.

Extending OpenSSH.

Last 100 entries

Brandalism; Table of Shifter, Cassette and Derailleur Compatability; Lenovo Demonstrates How Bad HTTPS Is; Telegraph Owned by HSBC; Smaptop - Sunrise (Music); Equation Group (NSA); UK Torture in NI; And - A Natural Extension To Regexps; This Is The Future Of Religion; The Shazam (Music Matching) Algorithm; Tributes To Lesbian Community From AIDS Survivors; Nice Rust Summary; List of Good Fiction Books; Constructing JSON From Postgres (Part 2); Constructing JSON From Postgres (Part 1); Postgres in Docker; Why Poor Places Are More Diverse; Smart Writing on Graceland; Satire in France; Free Speech in France; MTB Cornering - Where Should We Point Our Thrusters?; Secure Secure Shell; Java Generics over Primitives; 2014 (Charlie Brooker); How I am 7; Neural Nets Applied to Go; Programming, Business, Social Contracts; Distributed Systems for Fun and Profit; XML and Scheme; Internet Radio Stations (Curated List); Solid Data About Placebos; Half of Americans Think Climate Change Is a Sign of the Apocalypse; Saturday Surf Sessions With Juvenile Delinquents; Ssh, tty, stdout and stderr; Feathers falling in a vacuum; Santiago 30m Bike Route; Mapa de Ciclovias en Santiago; How Unreliable is UDP?; SE Santiago 20m Bike Route; Cameron's Rap; Configuring libxml with Eclipse; Reducing Combinatorial Complexity With Occam - AI; Sentidos Comunes (Chilean Online Magazine); Hilary Mantel: The Assassination of Margaret Thatcher - August 6th 1983; NSA Interceptng Gmail During Delivery; General IIR Filters; What's happening with Scala?; Interesting (But Largely Illegible) Typeface; Retiring Essentialism; Poorest in UK, Poorest in N Europe; I Want To Be A Redneck!; Reverse Racism; The Lost Art Of Nomography; IBM Data Center (Photo); Interesting Account Of Gamma Hack; The Most Interesting Audiophile In The World; How did the first world war actually end?; Ky - Restaurant Santiago; The Black Dork Lives!; The UN Requires Unaninmous Decisions; LPIR - Steganography in Practice; How I Am 6; Clear Explanation of Verizon / Level 3 / Netflix; Teenage Girls; Formalising NSA Attacks; Switching Brakes (Tektro Hydraulic); Naim NAP 100 (Power Amp); AKG 550 First Impressions; Facebook manipulates emotions (no really); Map Reduce "No Longer Used" At Google; Removing RAID metadata; New Bike (Good Bike Shop, Santiago Chile); Removing APE Tags in Linux; Compiling Python 3.0 With GCC 4.8; Maven is Amazing; Generating Docs from a GitHub Wiki; Modular Shelves; Bash Best Practices; Good Emergency Gasfiter (Santiago, Chile); Readings in Recent Architecture; Roger Casement; Integrated Information Theory (Or Not); Possibly undefined macro AC_ENABLE_SHARED; Update on Charges; Sunburst Visualisation; Spectral Embeddings (Distances -> Coordinates); Introduction to Causality; Filtering To Help Colour-Blindness; ASUS 1015E-DS02 Too; Ready Player One; Writing Clear, Fast Julia Code; List of LatAm Novels; Running (for women); Building a Jenkins Plugin and a Jar (for Command Line use); Headphone Test Recordings; Causal Consistency; The Quest for Randomness; Chat Wars; Real-life Financial Co Without ACID Database...; Flexible Muscle-Based Locomotion for Bipedal Creatures; SQL Performance Explained

© 2006-2013 Andrew Cooke (site) / post authors (content).

Printing binary trees sideways

From: andrew cooke <andrew@...>

Date: Mon, 13 May 2013 11:16:42 -0400

This was preliminary work for the StackOverflow answer at
- I did it while on holiday (installed Python on Mum's laptop :o) and then
posted the answer when I got home.  I have modified these posts since first
writing them to improve the code and explanation a little.

To be honest, it's not very exciting code - just careful bookkeeping and the
kind of recursive approach you'd expect, merging results from sub-trees.

Here are some results (I've named the leaves according to their location,
which helps understand what is happening, I hope):

 5 nodes
  / /lrr

 20 nodes
	/  \rrll
       /   /rlrrr
      /\  /\/rlrrlr
     /  \/\ \rlrrll
    /    \ \rlrl
   /      \/rllr
  /        \rlll
  \        /lrrrr
   \      /\lrrrl
    \    /\lrrl
     \  / /lrlr
      \/\/ /lrllrr
       \ \/\lrllrl
	\ \lrlll

And the code follows.



from itertools import chain
from random import randint

# first, some support routines.  these assume that a tree is either a string
# leaf value, or a tuple (pair) of subnodes.

def leaf(t):
    '''is the given node a leaf?'''
    return isinstance(t, str)

def random(n):
    '''generate a random tree with n nodes (n > 1)'''
    def extend(t):
        if leaf(t):
            return (t+'l', t+'r')
            l, r = t
            if randint(0, 1): return (l, extend(r))
            else: return (extend(l), r)
    t = ''
    for _ in range(n-1): t = extend(t)
    return t

# next, the formatting itself.  this is not that exciting - a recursive 
# descent to the leaves and then a merging of sub-trees on the returns.
# the hard part is just the book-keeping.

def format(t):
    '''format the tree (returns a multi-line string reprn)'''

    def pad(label, prefix, spaces, previous):
        '''add spaces between / (or \) and the previous line contents.
           change ' ' to label to see what logic is used where'''
        return prefix + (' ' * spaces) + previous

    def merge(l, r):
        '''merges the two sub-trees to generate the fragment for the
           combined node.  a fragment is (above, below, lines) where
           above is number of lines above root, below below root, and
           lines is an iterator over each partial line.'''
        l_above, l_below, l_lines = l
        r_above, r_below, r_lines = r
        gap = r_below + l_above
        gap_above = l_above  # this balances the result (see post text)
        gap_below = gap - gap_above

        def lines():
            '''the actual mergin of lines.  there are six different cases,
               handled in turn.'''
            for (i, line) in enumerate(chain(r_lines, l_lines)):
                if i < r_above:
                    # we already have 'sloped' data above where we are joining
                    yield line
                elif i - r_above < gap_above:
                    # we are in the upper branch region, joined by a / symbol
                    if i < r_above + r_below:
                        # are we filling the increasing gap between the new 
                        # / branch and the existing tree that has a \ shaped 
                        # boundary?
                        yield pad('A', '/', 2 * (i - r_above), line)
                        # or are we in the constant sized gap between the 
                        # new / branch and the upper / shaped boundary of the 
                        # lower sub-node?
                        yield pad('B', '/', 2 * gap_below - 1, line)
                elif i - r_above - gap_above < gap_below:
                    # we are in the lower branch region, joined by a \ symbol
                    if i < r_above + r_below:
                        # are we overlapping the \ shaped boundary of the 
                        # upper sub-node?
                        yield pad('C', '\\', 2 * gap_above - 1, line)
                        # or are we in the gap between the new \ and the 
                        # / shaped edge of the lower sub-node?
                        spaces = 2 * (r_above + gap_above + gap_below - i - 1)
                        yield pad('D', '\\', spaces, line)
                    # we already ave 'sloped' data below where we are joining
                    yield line
        return (r_above + gap_above, gap_below + l_below, lines())

    def descend(left, t):
        '''descend to leaf nodes, where we know what the fragments are
           (just the leaf contents) and then merge nodes on return.'''
        if leaf(t):
            if left:
                return (1, 0, [t])
                return (0, 1, [t])
            l, r = t
            return merge(descend(True, l), descend(False, r))

    def flatten(t):
        '''add left-hand spacing to the final tree.'''
        above, below, lines = t
        for (i, line) in enumerate(lines):
            if i < above: yield (' ' * (above - i - 1)) + line
            else: yield (' ' * (i - above)) + line

    # put it all together...
    return '\n'.join(flatten(descend(True, t)))

if __name__ == '__main__':
    for n in range(1,20,3):
        tree = random(n)

Some explanation

From: andrew cooke <andrew@...>

Date: Mon, 13 May 2013 11:45:05 -0400

[This post has also been edited since first posting]

The tree is formatted in three steps.

First, there's a recursive descent to the nodes, in the function descent.
This tracks whether the immediately preceding branch was left or right, so
that we know how to start the node (effectively, with a / or a \).

Second, as that function returns for each pair of nodes, we call "merge" to
combine the formatting information for the two sub-nodes.  To understand merge
you need to first understand what the formatting information is: a tuple
containing (above, below, lines) where above is the number of lines above the
root (of this sub-tree) and below is the number of lines below (note that a
root is always between lines).  Then lines is a sequence of strings containing
the existing information for each line.

The only unusual thing here, really, is that the lines are stored without
initial padding (that's what "flatten" adds, right at the end).  We need to do
this because if we stored them as padded blocks then we'd need to modify the
existing contents - storing without padding avoids needing to mutate data.

Here's an example.  Consider the tree


That would be stored as (1, 2, ['/r', '\/lr', '\ll']) (I am not escaping
backslashes here!).  There is no whitespace padding to the left of those

Then merge is simply patching together the lines from the two subtrees while
adding some extra / and \ characters and spaces.  It's only complicated
because of fiddly details - there's no deep magic.  See the comments in the

You can get an idea of which logic is used where by changing the "pad" routine
to print labels instead of spaces:


Compare the letters A-D with those in the merge routine.

Third, flatten adds space padding as needed for the final result (see above).

If you work through the code you'll see that there's an arbitrary decision
about exactly how to join the two subtrees - you get to choose the relative
number of / and \ characters (their sum is fixed).  The current code uses more
characters to get to the smaller subtree, so that the final result is
compact.  The line is:

  gap_above = l_above

And I'll try show what that means in this diagram:

   X  \rll
  X   Ylrrr
  \  Y\lrrl

Here X is "gap_above" and Y is "labove".  The "gap" is the number of lines
between the two sub-node roots that are being merged.  "gap_above" is the
upper branch (the / shaped part).  "l" identifies the lefthand sub-node and
"above" is the number of lines above the root.  So I choose the number of Xs
to match the number of Ys.

Also, for trees with data in the nodes (as well as the leaves) see


Comment on this post