Anand Nalya » python http://anandnalya.com blog Wed, 04 Jan 2012 06:55:44 +0000 en hourly 1 http://wordpress.org/?v= Curious case of Lewis Carrol, tournament runner ups and sorting http://anandnalya.com/2011/08/26/curious-case-of-lewis-carrol-tournament-runner-ups-and-sorting/?utm_source=rss&utm_medium=rss&utm_campaign=curious-case-of-lewis-carrol-tournament-runner-ups-and-sorting http://anandnalya.com/2011/08/26/curious-case-of-lewis-carrol-tournament-runner-ups-and-sorting/#comments Fri, 26 Aug 2011 10:18:57 +0000 anand http://anandnalya.com/?p=134 Continue reading →]]> No less than four grand slams are played every year to find the best tennis player in the world. These are knockout tournaments in which, at each stage half of the players lose and get out. Two [supposedly] best players clash in the finals and the winner of that game is declared the champion (the best player) and the loser the runner up (the second best player). All is fine with our champion but there is just a small problem with our runner up: He might not be the second best player of the tournament.

How?

Let us assume that there were 16 players in the beginning with seedings 1 to 16, 16 being the best. Consider the following results for the matches in the tournament

15
	15
1
		15
5
	9
9
			16
12
	16
16
		16
4
	4
3
				16
11
	11
6
		11
7
	10
10
			14
2
	8
8
		14
13
	14
14

As expected, 16 is the winner but the runner up is 14 not 15. 15 crashed out in the semi finals playing against the champion.

So what can we conclude from this?

  1. Runner up may not be the second best player of the tournament.
  2. log n matches are required to decide the best player in the tournament.
  3. We can find the second best player in the tournament looking at the match results of the winner which is a list of log n players. At some point he must have defeated the second best player.

Here is a program that gives you the second best player in (n - 1) + ((log n) - 1) = n + (log n) - 2 comparisons:

# Finding the second best player in a knockout tournament

defeatedListMap = {}

def fillMap(x,y):
        if x in defeatedListMap:
                defeatedListMap[x].add(y)
        else:
                defeatedListMap[x] = set([y])


def largest(array):
        if len(array) == 0:
                return array
        elif len(array) == 1:
                return array[0];
        elif len(array)== 2:
                fillMap(array[0], array[1])
                if(array[0]>array[1]):
                        fillMap(array[0],array[1])
                        return array[0]
                else:
                        fillMap(array[1], array[0])
                        return array[1]
        else:
                x = largest(array[:len(array)/2])
                y = largest(array[len(array)/2:])
                if x > y:
                        fillMap(x,y)
                        return x
                else:
                        fillMap(y,x)
                        return y


# generate a randomize draw for matches
import random
inputList = range(1,17)
random.shuffle(inputList)

#get the champion
champion  =  largest(inputList)

# look for the runner up in the list of players defeatee by champion
runnerUp = largest(list(defeatedListMap.get(champion)))

print champion, runnerUp

view raw tournament.py This Gist brought to you by GitHub.
]]> http://anandnalya.com/2011/08/26/curious-case-of-lewis-carrol-tournament-runner-ups-and-sorting/feed/ 0 Humanizing the time difference ( in django ) http://anandnalya.com/2009/05/20/humanizing-the-time-difference-in-django/?utm_source=rss&utm_medium=rss&utm_campaign=humanizing-the-time-difference-in-django http://anandnalya.com/2009/05/20/humanizing-the-time-difference-in-django/#comments Wed, 20 May 2009 10:02:35 +0000 anand http://anandnalya.com/?p=70 Continue reading →]]> django.contrib.humanize is a set of Django template filters that adds human touch to data. It provides naturalday filter that formats date to ‘yesterday’, ‘today’ or ‘tomorrow’ when applicable.

A similar requirement which the humanize pacakge does not address is to display time difference with this human touch. so here is a snippet that does so.

from django import template

register = template.Library()

MOMENT = 120    # duration in seconds within which the time difference 
                # will be rendered as 'a moment ago'

@register.filter
def naturalTimeDifference(value):
    """
    Finds the difference between the datetime value given and now()
    and returns appropriate humanize form
    """
    
    from datetime import datetime

    if isinstance(value, datetime):
        delta = datetime.now() - value
        if delta.days > 6:
            return value.strftime("%b %d")                    # May 15
        if delta.days > 1:
            return value.strftime("%A")                       # Wednesday
        elif delta.days == 1:
            return 'yesterday'                                # yesterday
        elif delta.seconds > 3600:
            return str(delta.seconds / 3600 ) + ' hours ago'  # 3 hours ago
        elif delta.seconds >  MOMENT:
            return str(delta.seconds/60) + ' minutes ago'     # 29 minutes ago
        else:
            return 'a moment ago'                             # a moment ago
        return defaultfilters.date(value)
    else:
        return str(value)

view raw humanizeTimeDifference.py This Gist brought to you by GitHub.
]]> http://anandnalya.com/2009/05/20/humanizing-the-time-difference-in-django/feed/ 1