Sunday, February 24, 2013

Selection Sort animated

Lately I bumped in the Wikipedia page dedicated to the Selection Sort algorithm and I found an interesting animation that shows its behavior. So I decided to write this post which shows how to recreate that animation using Python.
The idea behind the selection sort is straightforward: at each iteration the unsorted element with the smallest (or largest) value is moved to its proper position in the array. Assume that we wish to sort an array in increasing order. We begin by selecting the lowest element and moving it to the lowest index position. We can do this by swapping the element at the lowest index and the lowest element. We then reduce the effective size of the unsorted items by one element and repeat the process on the smaller unsorted (sub)array. The process stops when the effective number of the unsorted items becomes 1.
Let's see a Python implementation of the selection sort which is able to visualize with a graph the status of the sorting at each iteration:
import pylab

def selectionsort_anim(a):
 x = range(len(a)) 
 for j in range(len(a)-1):
  iMin = j
  for i in range(j+1,len(a)):
   if a[i] < a[iMin]: # find the smallest value
    iMin = i
  if iMin != j: # place the value into its proper location
   a[iMin], a[j] = a[j], a[iMin]
  # plotting
  pylab.plot(x,a,'k.',markersize=6)
  pylab.savefig("selectionsort/img" + '%04d' % j + ".png")
  pylab.clf() # figure clear

# running the algorithm
a = range(300) # initialization of the array
shuffle(a)     # shuffle!
selectionsort_anim(a) # sorting
At each iteration the status of the algorithm is visualized plotting the indexes of the array versus its values. Every plot is saved as an image and we can easily join them as a video using ffmpeg:
$ cd selectionsort # the directory where the images are
$ ffmpeg -qscale 5 -r 20 -b 9600 -i img%04d.png movie.mp4
The result should be as follows

At each frame of the video we can see that the elements on the left form a subset of items already sorted and the rest of the items remain to be sorted. It's nice to see that the number unsorted elements decrease at each iterations while the subset of sorted items grows forming a straight line.

This is just the first of a series of posts about the visualization of sorting algorithms. Stay tuned for the animations of other sorting algorithms!

5 comments:

  1. The video is marked private :(

    ReplyDelete
    Replies
    1. Hello Aaron, now the video is public. It's the first video I put on youtube and I thought the submissions were public by default.

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  2. Fun! Great image. Can't wait to see quick sort and bubble sort. Matplotlib + ffmpeg is such a great idea. I will try that sometime.

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  3. Very great ! Why not use Matplotlib's animation module ? It also uses ffmpeg I think, and it makes things simpler.

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    Replies
    1. I used the Matplotlib's animation module here :

      http://glowingpython.blogspot.com/2011/06/sierpinski-fractal.html

      I prefer to use ffmpeg because it gives me the video in the mpg format directly.

      Delete