Compare sorting algorithms' performance: Difference between revisions
m (Quick sort -> Quicksort) |
(couple examples of sorting routine) |
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Consider at least two different sorting function (different algorithms or/and different implementation of the same algorithm). |
Consider at least two different sorting function (different algorithms or/and different implementation of the same algorithm). |
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For example, consider [[Bubble Sort]], [[Insertion sort]], [[Quicksort]] or/and implementations of [[ |
For example, consider [[Bubble Sort]], [[Insertion sort]], [[Quicksort]] or/and implementations of [[Quicksort]] with different pivot selection mechanisms. |
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Where possible, use existing implementations. |
Where possible, use existing implementations. |
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'''Interpreter:''' [[Python]] 2.5 |
'''Interpreter:''' [[Python]] 2.5 |
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[[Category:Python]] |
[[Category:Python]] |
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===A couple examples of sorting routines=== |
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def builtinsort(x): |
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x.sort() |
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def partition(seq, pivot): |
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low, middle, up = [], [], [] |
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for x in seq: |
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if x < pivot: |
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low.append(x) |
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elif x == pivot: |
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middle.append(x) |
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else: |
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up.append(x) |
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return low, middle, up |
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# |
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def qsortranpart(seq): |
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size = len(seq) |
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if size < 2: return seq |
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low, middle, up = partition(seq, seq[random.randrange(size)]) |
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return qsortranpart(low) + middle + qsortranpart(up) |
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===Sequence generators=== |
===Sequence generators=== |
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Ns, Ts) |
Ns, Ts) |
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</code> |
</code> |
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Where ''writedat()'' is defined in the [[Write float arrays to a text file]] |
Where ''writedat()'' is defined in the [[Write float arrays to a text file]], ''usec()'' - [[Query Performance]], ''insertion_sort()'' - [[Insertion sort]], ''qsort'' - [[Quicksort]] subtasks correspondingly. |
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===Plot timings=== |
===Plot timings=== |
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{{library|matplotlib}} |
{{library|matplotlib}} |
Revision as of 07:47, 24 December 2007
You are encouraged to solve this task according to the task description, using any language you may know.
Measure a relative performance of sorting algorithms implementations.
Plot execution time vs. input sequence length dependencies for various implementation of sorting algorithm and different input sequence types.
Consider three type of input sequences:
- ones: sequence of all 1's. Example: {1, 1, 1, 1, 1}
- range: ascending sequence, i.e. already sorted. Example: {1, 2, 3, 10, 15}
- shuffledrange: sequence with elements randomly distributed. Example: {5, 3, 9, 6, 8}
Consider at least two different sorting function (different algorithms or/and different implementation of the same algorithm). For example, consider Bubble Sort, Insertion sort, Quicksort or/and implementations of Quicksort with different pivot selection mechanisms. Where possible, use existing implementations.
Preliminary subtask:
- Bubble Sort, Insertion sort, Quicksort, Radix sort, Shell sort
- Query Performance
- Write float arrays to a text file
- Plot x, y arrays
- Polynomial Fitting
General steps:
- Define sorting routines to be considered.
- Define appropriate sequence generators and write timings.
- Plot timings.
- What conclusions about relative performance of the sorting routines could be made based on the plots?
Python
Interpreter: Python 2.5
A couple examples of sorting routines
def builtinsort(x): x.sort()
def partition(seq, pivot): low, middle, up = [], [], [] for x in seq: if x < pivot: low.append(x) elif x == pivot: middle.append(x) else: up.append(x) return low, middle, up # def qsortranpart(seq): size = len(seq) if size < 2: return seq low, middle, up = partition(seq, seq[random.randrange(size)]) return qsortranpart(low) + middle + qsortranpart(up)
Sequence generators
def ones(n): return [1]*n
def reversedrange(n): x = range(n) x.reverse() return x
def shuffledrange(n): x = range(n) random.shuffle(x) return x
Write timings
def write_timings(npoints=10, maxN=10**4, sort_functions=(builtinsort,insertion_sort, qsort), sequence_creators = (ones, range, shuffledrange)):
"""`npoints' and `maxN' are recomendations that may be ignored by implementation"""
Ns = range(2, maxN, maxN//npoints)
for sort in sort_functions:
for make_seq in sequence_creators:
Ts = map(lambda n: usec(sort, (make_seq(n),)), Ns)
writedat('%s-%s-%d-%d.xy' % (sort.__name__, make_seq.__name__, len(Ns), max(Ns)),
Ns, Ts)
Where writedat() is defined in the Write float arrays to a text file, usec() - Query Performance, insertion_sort() - Insertion sort, qsort - Quicksort subtasks correspondingly.
Plot timings
This is an example of a library. You may see a list of other libraries used on Rosetta Code at Category:Solutions by Library.
import pylab
def plotdd(dictplotdict):
"""See ``plot_timings()`` below."""
symbols = ('o', '^', 'v', '<', '>', 's', '+', 'x', 'D', 'd',
'1', '2', '3', '4', 'h', 'H', 'p', '|', '_')
colors = map(None, 'bgrcmyk')
for npoints, plotdict in dictplotdict.iteritems():
for ttle, lst in plotdict.iteritems():
pylab.hold(False)
for i, (label, polynom, x, y) in enumerate(sorted(lst,key=operator.itemgetter(0))):
pylab.plot(x, y, colors[i % len(colors)] + symbols[i % len(symbols)],
label='%s %s' % (polynom, label))
pylab.hold(True)
y = numpy.polyval(polynom, x)
pylab.plot(x, y, colors[i % len(colors)], label= '_nolegend_')
pylab.legend(loc='upper left')
pylab.xlabel(p.variable)
pylab.ylabel('log2( time in microseconds )')
pylab.title(ttle, verticalalignment='bottom')
figname = '_%(npoints)03d%(ttle)s' % vars()
pylab.savefig(figname+'.png')
pylab.savefig(figname+'.pdf')
print figname
See Plot x, y arrays and Polynomial Fitting subtask for basic usage of pylab.plot() and numpy.polyfit().
This is an example of a library. You may see a list of other libraries used on Rosetta Code at Category:Solutions by Library.
import numpy
def plot_timings():
makedict = lambda: collections.defaultdict(lambda: collections.defaultdict(list))
df = makedict()
ds = makedict()
# populate plot dictionaries
for filename in glob.glob('*.xy'):
m = re.match(r'([^-]+)-([^-]+)-(\d+)-(\d+)\.xy', filename)
print filename
assert m, filename
funcname, seqname, npoints, maxN = m.groups()
npoints, maxN = int(npoints), int(maxN)
a = numpy.fromiter(itertools.imap(float, open(filename).read().split()), dtype='f')
Ns = a[::2] # sequences lengths
Ts = a[1::2] # corresponding times
assert len(Ns) == len(Ts) == npoints
assert max(Ns) <= maxN
#
logsafe = logical_and(Ns>0, Ts>0)
Ts = numpy.log2(Ts[logsafe])
Ns = numpy.log2(Ns[logsafe])
coeffs = numpy.polyfit(Ns, Ts, deg=1)
poly = numpy.poly1d(coeffs, variable='log2(N)')
#
df[npoints][funcname].append((seqname, poly, Ns, Ts))
ds[npoints][seqname].append((funcname, poly, Ns, Ts))
# actual plotting
plotdd(df)
plotdd(ds) # see ``plotdd()`` above