organized

This commit is contained in:
Mari Wahl 2014-08-20 17:34:32 -04:00
parent 77731415d1
commit 5ed530430c
60 changed files with 439 additions and 563 deletions

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
@ -17,7 +18,6 @@ def binary_search(seq, key):
hi = mid
else:
lo = mid + 1
return None
def binary_search_rec(seq, key, lo=0, hi=None):

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Searches an element in a matrix where in every row, the values are increasing from left to right, but the last number in a row is smaller than the first number in the next row.

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@ -1,25 +1,11 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Given a sorted array that was rotated, find an item with binary search:
>>> l1 = [3, 4, 5, 6, 7, 1, 2]
>>> find_element_rot_array(l1, 7)
4
>>> find_element_rot_array(l1, 3)
0
>>> find_element_rot_array(l1, 4)
1
>>> find_element_rot_array(l1, 5)
2
>>> find_element_rot_array(l1, 6)
3
>>> find_element_rot_array(l1, 1)
5
>>> find_element_rot_array(l1, 2)
6
>>> find_element_rot_array(l1, 8)
'''
def find_element_rot_array(seq, key, lo=0, hi=None):
@ -47,10 +33,12 @@ def find_element_rot_array(seq, key, lo=0, hi=None):
return find_element_rot_array(seq, key, lo, mid)
def test_find_element_rot_array():
l1 = [3, 4, 5, 6, 7, 1, 2]
assert(find_element_rot_array(l1, 7) == 4 )
print("Tests passed!")
if __name__ == '__main__':
import doctest
doctest.testmod()
test_find_element_rot_array()

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
def find_max_unimodal_array(A):

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@ -1,6 +1,9 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"

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@ -1,21 +1,13 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Given a sorted an array with empty strings, we use binary search to find some string (since
the list is sorted):
--> we deal with the empty strings with strip and then run to left and right, or move
mid to the closed non-empty str (remember that the index must be conserved):
>>> l1 = ['acre', 'ball', '', 'coach', '', 'cut', '']
>>> find_str_array_with_empty_str(l1, l1[0])
0
>>> find_str_array_with_empty_str(l1, l1[1])
1
>>> find_str_array_with_empty_str(l1, l1[3])
3
>>> find_str_array_with_empty_str(l1, l1[5])
5
>>> find_str_array_with_empty_str(l1, 'bla')
'''
@ -46,7 +38,12 @@ def find_str_array_with_empty_str(seq, s1):
if __name__ == '__main__':
import doctest
doctest.testmod()
def test_find_str_array_with_empty_str():
seq = ['acre', 'ball', '', 'coach', '', 'cut', '']
key = seq[1]
assert(find_str_array_with_empty_str(seq, key) == 1)
print('Tests passed!')
if __name__ == '__main__':
test_find_str_array_with_empty_str()

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
def binary_serch_counting(lst1, k, lo=0, hi=None):

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@ -1,6 +1,9 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' using sets '''

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@ -1,6 +1,9 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
def ordered_sequential_search(seq, n):

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@ -1,6 +1,9 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
import numpy

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
def sequential_search(seq, n):
@ -29,4 +31,4 @@ if __name__ == '__main__':
Case Best Case Worst Case Average Case
item is present 1 n n2
item is not present n n n
""""
"""

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@ -1,112 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
''' A recursive and an iterative example of binary search in Python.
Remember: sequence must be sorted! You can return True/False or the index:
>>> l1 = [1, 2, 3, 4, 5, 6, 7]
>>> binary_search_rec(l1, 1)
0
>>> binary_search_rec(l1, 2)
1
>>> binary_search_rec(l1, 3)
2
>>> binary_search_rec(l1, 4)
3
>>> binary_search_rec(l1, 5)
4
>>> binary_search_rec(l1, 6)
5
>>> binary_search_rec(l1, 7)
6
>>> binary_search_rec(l1, 8)
>>> l1 = [1, 2, 3, 4, 5, 6]
>>> binary_search_rec(l1, 1)
0
>>> binary_search_rec(l1, 2)
1
>>> binary_search_rec(l1, 3)
2
>>> binary_search_rec(l1, 4)
3
>>> binary_search_rec(l1, 5)
4
>>> binary_search_rec(l1, 6)
5
>>> binary_search_rec(l1, 7)
>>> l1 = [1, 2, 3, 4, 5, 6, 7]
>>> binary_search_iter(l1, 1)
0
>>> binary_search_iter(l1, 2)
1
>>> binary_search_iter(l1, 3)
2
>>> binary_search_iter(l1, 4)
3
>>> binary_search_iter(l1, 5)
4
>>> binary_search_iter(l1, 6)
5
>>> binary_search_iter(l1, 7)
6
>>> binary_search_iter(l1, 8)
>>> l1 = [1, 2, 3, 4, 5, 6]
>>> binary_search_iter(l1, 1)
0
>>> binary_search_iter(l1, 2)
1
>>> binary_search_iter(l1, 3)
2
>>> binary_search_iter(l1, 4)
3
>>> binary_search_iter(l1, 5)
4
>>> binary_search_iter(l1, 6)
5
>>> binary_search_iter(l1, 7)
'''
def binary_search_iter(seq, key):
hi, lo = len(seq), 0
while lo < hi: # here is <!
mid = (hi+lo)//2
if key == seq[mid]: return mid
elif key < seq[mid]: hi = mid
else: lo = mid + 1
return None
def bool_binary_search_iter(seq, key):
hi, lo = len(seq), 0
while lo < hi:
mid = (hi+lo)//2
if key == seq[mid]: return True
elif key < seq[mid]: hi = mid
else: lo = mid + 1
return False
def binary_search_rec(seq, key, lo=0, hi=None):
hi = hi or len(seq)
if hi <= lo: return None # base case: <= for odd and even numbers!
mid = (hi + lo) // 2
if key == seq[mid]: return mid
elif key < seq[mid] : return binary_search_rec(seq, key, lo, mid) # include until mid-1
else: return binary_search_rec(seq, key, mid+1, hi)
def bool_binary_search_rec(seq, key, lo=0, hi=None):
hi = hi or len(seq)
if hi <= lo: return False # base case: <= for odd and even numbers!
mid = (hi + lo) // 2
if key == seq[mid]: return True
elif key < seq[mid] : return bool_binary_search_rec(seq, key, lo, mid)
else: return bool_binary_search_rec(seq, key, mid+1, hi)
if __name__ == '__main__':
import doctest
doctest.testmod()

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@ -1,16 +1,14 @@
#!/usr/bin/python3
#!/usr/bin/python
# Mari von Steinkirch @ 2013
# mari.wahl9@gmail.com
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
# Bernardo Sulzbach (mafagafo) @ 2014
# 1449441@gmail.com
def bubble_sort(seq):
"""
Implementation of bubble sort.
O(n²) and thus highly ineffective.
O(n2) and thus highly ineffective.
:param seq: the sequence to be sorted.
:return: the sorted sequence.
"""

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
from collections import defaultdict

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
import random
@ -54,6 +55,7 @@ def test_find_k_largest_seq_quickselect():
seq = [3, 10, 4, 5, 1, 8, 9, 11, 5]
k = 2
assert(find_k_largest_seq_quickselect(seq,k) == [10, 11])
print("Tests passed!")
if __name__ == '__main__':

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@ -1,11 +1,10 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
from do_benchmark import benchmark
@benchmark
def gnome_sort(seq):
''' sort a sequence using the gnome sort alg '''
i = 0

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
class Heap(object):
def __init__(self, data):

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@ -0,0 +1,85 @@
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Heapsort using Pythons libraries'''
import heapq
def heap_sort1(seq):
''' heap sort with Python's heapq '''
h = []
for value in seq:
heapq.heappush(h, value)
return [heapq.heappop(h) for i in range(len(h))]
def test_heap_sort1():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(heap_sort1(seq) == sorted(seq))
print('Tests passed!')
''' Heapsort using my Heap class '''
from heap import Heap
def heap_sort2(seq):
heap = Heap(seq)
res = []
for i in range(len(seq)):
res.insert(0, heap.extract_max())
return res
def test_heap_sort2():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
print heap_sort2(seq)
print('Tests passed!')
''' A third way of doing heap sort '''
def heap_sort3(seq):
for start in range((len(seq)-2)//2, -1, -1):
siftdown(seq, start, len(seq)-1)
for end in range(len(seq)-1, 0, -1):
seq[end], seq[0] = seq[0], seq[end]
siftdown(seq, 0, end - 1)
return seq
def siftdown(seq, start, end):
root = start
while True:
child = root * 2 + 1
if child > end: break
if child + 1 <= end and seq[child] < seq[child + 1]:
child += 1
if seq[root] < seq[child]:
seq[root], seq[child] = seq[child], seq[root]
root = child
else:
break
def test_heap_sort3():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(heap_sort3(seq) == sorted(seq))
print('Tests passed!')
if __name__ == '__main__':
test_heap_sort1()
test_heap_sort2()
test_heap_sort3()

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@ -1,23 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
import heapq
def heap_sort1(seq):
''' heap sort with Python's heapq '''
h = []
for value in seq:
heapq.heappush(h, value)
return [heapq.heappop(h) for i in range(len(h))]
def test_heap_sort1():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(heap_sort1(seq) == sorted(seq))
print('Tests passed!')
if __name__ == '__main__':
test_heap_sort1()

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@ -1,24 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
from heap import Heap
def heap_sort2(seq):
heap = Heap(seq)
res = []
for i in range(len(seq)):
res.insert(0, heap.extract_max())
return res
def test_heap_sort2():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(heap_sort2(seq) == sorted(seq))
print('Tests passed!')
if __name__ == '__main__':
test_heap_sort2()

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@ -1,36 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def heap_sort3(seq):
for start in range((len(seq)-2)//2, -1, -1):
siftdown(seq, start, len(seq)-1)
for end in range(len(seq)-1, 0, -1):
seq[end], seq[0] = seq[0], seq[end]
siftdown(seq, 0, end - 1)
return seq
def siftdown(seq, start, end):
root = start
while True:
child = root * 2 + 1
if child > end: break
if child + 1 <= end and seq[child] < seq[child + 1]:
child += 1
if seq[root] < seq[child]:
seq[root], seq[child] = seq[child], seq[root]
root = child
else:
break
def test_heap_sort():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(heap_sort3(seq) == sorted(seq))
print('Tests passed!')
if __name__ == '__main__':
test_heap_sort3()

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@ -1,6 +1,8 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"

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@ -1,7 +1,23 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Some examples of how to implement Merge Sort in Python
--> RUNTIME: WORST/BEST/AVERAGE Is O(nlogn)
--> space complexity is O(n) for arrays
--> not in place, good for large arrays
>>> seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
>>> merge_sort(seq) == sorted(seq)
True
>>> seq2 = [3, 3, 3, 3, 3, 3, 3, 3]
>>> merge_sort(seq2) == sorted(seq2)
True
>>> seq3 = []
>>> merge_sort(seq3) == sorted(seq3)
True
'''
def merge_sort(seq):
@ -22,12 +38,63 @@ def merge_sort(seq):
def test_merge_sort():
seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
assert(merge_sort(seq) == sorted(seq))
print('Tests passed!')
'''
We could also divide this sort into two parts, separating
the merge part in another function
'''
def merge_sort_sep(seq):
if len(seq) < 2 : return seq # base case
mid = len(seq)//2
left, right = None, None # we could have declared the arrays here,
# but this would allocate unecessary extra space
if seq[:mid]: left = merge_sort(seq[:mid])
if seq[mid:]: right = merge_sort(seq[mid:]) # notice that mid is included!
return merge(left, right) # merge iteratively
def merge(left, right):
if not left or not right: return left or right # nothing to be merged
result = []
i, j = 0, 0
while i < len(left) and j < len(right):
if left[i] <= right[j]:
result.append(left[i])
i += 1
else:
result.append(right[j])
j += 1
if left[i:] : result.extend(left[i:]) # REMEMBER TO TO ENXTEND NOT APPEND
if right[j:] : result.extend(right[j:])
return result
''' The two following merge functions are O(2n)=O(n) and O(n) respectively. They
illustrate many features in Python that '''
def merge_2n(left, right):
if not left or not right: return left or right # nothing to be merged
result = []
while left and right:
if left[-1] >= right[-1]:
result.append(left.pop())
else:
result.append(right.pop())
result.reverse()
return (left or right) + result
if __name__ == '__main__':
test_merge_sort()

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' --> In the case of two arrays: we can merge two arrays using the merge function from the merge sort
--> we can do this for files too, merging each two

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@ -1,6 +1,27 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' Some examples of how to implement Quick Sort in Python
--> RUNTIME: BEST/AVERAGE Is O(nlogn), WORST is O(n2)
--> the first example is not in place, the second is in place
--> test with two element arrays, identical values
Quick sort in place:
1) select pivot as the index = 0
2) start pointer1 at index = 1 and pointer2 in the last element
3) while pointer1 < pointer2:
if value in pointer1 <= pivot
swap value in pointer1 with value in pointer2 and advanced pointer2
else
advance pointer1
4) now the array is like this:
[pivot, larger than pivot, smaller than pivot]
5) swap the pivot where pointer 1 stop
6) do recursively for [smaller] + [pivot] + [larger]
'''
@ -13,6 +34,19 @@ def quick_sort(seq):
return left + [pivot] + right
''' slightly different in the way we get the pivot'''
def quick_sort(seq):
if len(seq) < 2 : return seq
mid = len(seq)//2
pi = seq[mid]
seq = seq[:mid] + seq[mid+1:]
left = quick_sort([x for x in seq if x <= pi]) # REMEMBER TO INCLUDE X (OR IN RIGHT)
right = quick_sort([x for x in seq if x > pi])
return left + [pi] + right
""" we can also divide them into two functions """
def partition(seq):
pi,seq = seq[0],seq[1:]
@ -26,6 +60,23 @@ def quick_sort_divided(seq):
return quick_sort_divided(lo) + [pi] + quick_sort_divided(hi)
''' quick_sort in place '''
def quick_sort_in(seq):
if len(seq) < 2 : return seq
if len(seq) == 2 and seq[0] > seq[1]:
seq[0], seq[1] = seq[1], seq[0] # problems when only 2 elements because of swap
pivot = seq[0] # start at the ends because we don't know how many elements
p1, p2 = 1, len(seq) -1 # set pointers at both ends
while p1 < p2: # must be < or out of range
if seq[p1] <= pivot: # must be <= because of pivot swap
seq[p1], seq[p2] = seq[p2], seq[p1]
p2 -= 1
else:
p1 += 1
seq[0], seq[p1] = seq[p1], pivot
return quick_sort_in(seq[p1+1:]) + [seq[p1]] + quick_sort_in(seq[:p1])
def test_quick_sort():

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
def selection_sort(seq):

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@ -1,6 +1,7 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
''' A method to sort an array so that all the anagrams are together. Since we only
want the anagrams to be grouped, we can use a dictionary for this task. This

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@ -1,70 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
''' Some examples of how to implement Merge Sort in Python
--> RUNTIME: WORST/BEST/AVERAGE Is O(nlogn)
--> space complexity is O(n) for arrays
--> not in place, good for large arrays
>>> seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
>>> merge_sort(seq) == sorted(seq)
True
>>> seq2 = [3, 3, 3, 3, 3, 3, 3, 3]
>>> merge_sort(seq2) == sorted(seq2)
True
>>> seq3 = []
>>> merge_sort(seq3) == sorted(seq3)
True
'''
''' This is the main function that keep dividing the seq '''
def merge_sort(seq):
if len(seq) < 2 : return seq # base case
mid = len(seq)//2
left, right = None, None # we could have declared the arrays here,
# but this would allocate unecessary extra space
if seq[:mid]: left = merge_sort(seq[:mid])
if seq[mid:]: right = merge_sort(seq[mid:]) # notice that mid is included!
return merge(left, right) # merge iteratively
''' The two following merge functions are O(2n)=O(n) and O(n) respectively. They
illustrate many features in Python that '''
def merge_2n(left, right):
if not left or not right: return left or right # nothing to be merged
result = []
while left and right:
if left[-1] >= right[-1]:
result.append(left.pop())
else:
result.append(right.pop())
result.reverse()
return (left or right) + result
def merge(left, right):
if not left or not right: return left or right # nothing to be merged
result = []
i, j = 0, 0
while i < len(left) and j < len(right):
if left[i] <= right[j]:
result.append(left[i])
i += 1
else:
result.append(right[j])
j += 1
if left[i:] : result.extend(left[i:]) # REMEMBER TO TO ENXTEND NOT APPEND
if right[j:] : result.extend(right[j:])
return result
if __name__ == '__main__':
import doctest
doctest.testmod()

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@ -1,74 +0,0 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
''' Some examples of how to implement Quick Sort in Python
--> RUNTIME: BEST/AVERAGE Is O(nlogn), WORST is O(n2)
--> the first example is not in place, the second is in place
--> test with two element arrays, identical values
Quick sort in place:
1) select pivot as the index = 0
2) start pointer1 at index = 1 and pointer2 in the last element
3) while pointer1 < pointer2:
if value in pointer1 <= pivot
swap value in pointer1 with value in pointer2 and advanced pointer2
else
advance pointer1
4) now the array is like this:
[pivot, larger than pivot, smaller than pivot]
5) swap the pivot where pointer 1 stop
6) do recursively for [smaller] + [pivot] + [larger]
>>> seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
>>> quick_sort(seq) == sorted(seq)
True
>>> quick_sort([3, 3, 3, 3, 3, 3]) == [3, 3, 3, 3, 3, 3]
True
>>> quick_sort([]) == []
True
>>> quick_sort([2,1]) == [1, 2]
True
>>> quick_sort_in(seq) == sorted(seq)
True
>>> quick_sort_in([3, 3, 3, 3, 3, 3]) == [3, 3, 3, 3, 3, 3]
True
>>> quick_sort_in([]) == []
True
>>> quick_sort_in([2,1]) == [1, 2]
True
'''
def quick_sort(seq):
if len(seq) < 2 : return seq
mid = len(seq)//2
pi = seq[mid]
seq = seq[:mid] + seq[mid+1:]
left = quick_sort([x for x in seq if x <= pi]) # REMEMBER TO INCLUDE X (OR IN RIGHT)
right = quick_sort([x for x in seq if x > pi])
return left + [pi] + right
def quick_sort_in(seq):
if len(seq) < 2 : return seq
if len(seq) == 2 and seq[0] > seq[1]:
seq[0], seq[1] = seq[1], seq[0] # problems when only 2 elements because of swap
pivot = seq[0] # start at the ends because we don't know how many elements
p1, p2 = 1, len(seq) -1 # set pointers at both ends
while p1 < p2: # must be < or out of range
if seq[p1] <= pivot: # must be <= because of pivot swap
seq[p1], seq[p2] = seq[p2], seq[p1]
p2 -= 1
else:
p1 += 1
seq[0], seq[p1] = seq[p1], pivot
return quick_sort_in(seq[p1+1:]) + [seq[p1]] + quick_sort_in(seq[:p1])
if __name__ == '__main__':
import doctest
doctest.testmod()