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Deterministic Selection (Median of Medians) Algorithm
def merge_tuple(a,b):
""" Function to merge two arrays of tuples """
c = []
while len(a) != 0 and len(b) != 0:
if a[0][0] < b[0][0]:
c.append(a[0])
a.remove(a[0])
else:
c.append(b[0])
b.remove(b[0])
if len(a) == 0:
c += b
else:
c += a
return c
def mergesort_tuple(x):
""" Function to sort an array using merge sort algorithm """
if len(x) == 0 or len(x) == 1:
return x
else:
middle = len(x)/2
a = mergesort_tuple(x[:middle])
b = mergesort_tuple(x[middle:])
return merge_tuple(a,b)
def lol(x,k):
""" Function to divide a list into a list of lists of size k each. """
return [x[i:i+k] for i in range(0,len(x),k)]
def preprocess(x):
""" Function to assign an index to each element of a list of integers, outputting a list of tuples"""
return zip(x,range(len(x)))
def partition(x, pivot_index = 0):
""" Function to partition an unsorted array around a pivot"""
i = 0
if pivot_index !=0: x[0],x[pivot_index] = x[pivot_index],x[0]
for j in range(len(x)-1):
if x[j+1] < x[0]:
x[j+1],x[i+1] = x[i+1],x[j+1]
i += 1
x[0],x[i] = x[i],x[0]
return x,i
def ChoosePivot(x):
""" Function to choose pivot element of an unsorted array using 'Median of Medians' method. """
if len(x) <= 5:
return mergesort_tuple(x)[middle_index(x)]
else:
lst = lol(x,5)
lst = [mergesort_tuple(el) for el in lst]
C = [el[middle_index(el)] for el in lst]
return ChoosePivot(C)
def DSelect(x,k):
""" Function to """
if len(x) == 1:
return x[0]
else:
xpart = partition(x,ChoosePivot(preprocess(x))[1])
x = xpart[0] # partitioned array
j = xpart[1] # pivot index
if j == k:
return x[j]
elif j > k:
return DSelect(x[:j],k)
else:
k = k - j - 1
return DSelect(x[(j+1):], k)
arr = range(100,0,-1)
print DSelect(arr,50)
%timeit DSelect(arr,50)
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