```
In [ ]:
```

```
In [ ]:
```'''
Find Kth permutation
Memory: O(n)
Runtime: O(n)
The way this works is that we compute the size of the block-
the amount of permutations that will start with that value at
this level of a tree of permutations, we determine the index of
the value at that level by subtracting 1 and dividing by the block
size. Use that index from the array, append it, and then delete it
Pass on the new k by subtrating the selected index times the block
size
'''
def factorial(n):
if n == 0 or n == 1:
return 1
return n * factorial(n -1 )
def find_kth_permutation(v, k, result):
if not v:
return
n = len(v)
# block_size is number of permutations starting with first digit
block_size = factorial(n - 1)
ith_block_digit = (k - 1) / block_size
result += str(v[ith_block_digit])
del v[ ith_block_digit]
k = k - (block_size * ith_block_digit)
find_kth_permutation(v, k, result)

```
In [10]:
```def sort(array):
if len(array) <= 1:
return array
else:
pivot = len(array) // 2
arr1 = sort(array[:pivot])
arr2 = sort(array[pivot:])
return merge(arr1, arr2)
def merge(left, right):
l_index, r_index = 0, 0
result = []
while l_index < len(left) and r_index < len(right):
if left[l_index] < right[r_index]:
result.append(left[l_index])
l_index += 1
else:
result.append(right[r_index])
r_index += 1
# while l_index< len(left):
# result.append(left[l_index])
# l_index += 1
# while r_index < len(right):
# result.append(right[r_index])
# r_index += 1
result += left[l_index:]
result += right[r_index:]
return result
test1 = [54,26,93,17,77,31,44,55,20]
test2 = []
test3 = [89,34, 23, 342,234,67, 1, 4]
print(sort(test1))
print(sort(test2))
print(sort(test3))

```
```[17, 20, 26, 31, 44, 54, 55, 77, 93]
[]
[1, 4, 23, 34, 67, 89, 234, 342]

Worst Case: 0(n^2) when the worst pivot is chosen

Average Performance: 0(nlog(n))

Choosing the pivot is the most important, chosing the wrong pivot can be disastorous. The best case is random, there is also the best of three rule but this only pays off in very large lists. Quicksort is a great inplace sort.

There are two kinds of parition schemes, Hoare, and Lomuto. Hoare is the more efficient partition scheme because it does three times fewer swaps on average. Hoare's performs particularly well with duplicate values but Lomuto is easier to implement.

```
In [22]:
```def quickSort(alist, left= 0, right= len(alist) - 1):
pivot = partitionHoare(alist, left, right)
if left < pivot- 1:
quickSort(alist, left, pivot)
if right > pivot:
quickSort(alist, pivot, right)
return alist
def swap(alist, i, j):
temp = alist[i]
alist[i] = alist[j]
alist[j] = temp
return alist
def partitionLomuto(alist, left, right):
pivot = right
partition = left
for idx in range(left, right):
if alist[idx] <= alist[pivot]:
swap(alist, partition, idx)
partition += 1
swap(alist, partition, left) #j in js original
return partition
def partitionHoare(alist, left, right):
pivot = (left + right) // 2
while left <= right:
print("pivot: %s, list: %s" % (pivot, alist))
while alist[left] < alist[pivot]:
left += 1
while alist[right] > alist[pivot]:
right -= 1
if left <= right:
alist = swap(alist, left, right)
left += 1
right -= 1
return pivot
test1 = [54,26,93,17,77,31,44,55,20]
test2 = []
test3 = [89,34, 23, 342,234,67, 1, 4]
print(quickSort(test1))
#print(quickSort(test2))
print(quickSort(test3))

```
```pivot: 4, list: [54, 26, 93, 17, 77, 31, 44, 55, 20]
pivot: 4, list: [54, 26, 20, 17, 77, 31, 44, 55, 93]
pivot: 4, list: [54, 26, 20, 17, 55, 31, 44, 77, 93]
pivot: 2, list: [54, 26, 20, 17, 55, 31, 44, 77, 93]
pivot: 2, list: [17, 26, 20, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
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pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]
pivot: 1, list: [17, 20, 26, 54, 55, 31, 44, 77, 93]

---------------------------------------------------------------------------
RecursionError Traceback (most recent call last)
<ipython-input-22-2af90829acc8> in <module>()
48 test3 = [89,34, 23, 342,234,67, 1, 4]
49
---> 50 print(quickSort(test1))
51 #print(quickSort(test2))
52 print(quickSort(test3))
<ipython-input-22-2af90829acc8> in quickSort(alist, left, right)
4
5 if left < pivot- 1:
----> 6 quickSort(alist, left, pivot)
7 if right > pivot:
8 quickSort(alist, pivot, right)
<ipython-input-22-2af90829acc8> in quickSort(alist, left, right)
4
5 if left < pivot- 1:
----> 6 quickSort(alist, left, pivot)
7 if right > pivot:
8 quickSort(alist, pivot, right)
<ipython-input-22-2af90829acc8> in quickSort(alist, left, right)
6 quickSort(alist, left, pivot)
7 if right > pivot:
----> 8 quickSort(alist, pivot, right)
9 return alist
10
... last 1 frames repeated, from the frame below ...
<ipython-input-22-2af90829acc8> in quickSort(alist, left, right)
6 quickSort(alist, left, pivot)
7 if right > pivot:
----> 8 quickSort(alist, pivot, right)
9 return alist
10
RecursionError: maximum recursion depth exceeded in comparison

```
In [26]:
```def quickSort(alist):
quickSortHelper(alist,0,len(alist)-1)
def quickSortHelper(alist,first,last):
if first<last:
splitpoint = partition(alist,first,last)
quickSortHelper(alist,first,splitpoint-1)
quickSortHelper(alist,splitpoint+1,last)
def partition(alist,first,last):
pivotvalue = alist[first]
leftmark = first+1
rightmark = last
done = False
while not done:
while leftmark <= rightmark and alist[leftmark] <= pivotvalue:
leftmark = leftmark + 1
while alist[rightmark] >= pivotvalue and rightmark >= leftmark:
rightmark = rightmark -1
if rightmark < leftmark:
done = True
else:
temp = alist[leftmark]
alist[leftmark] = alist[rightmark]
alist[rightmark] = temp
temp = alist[first]
alist[first] = alist[rightmark]
alist[rightmark] = temp
return rightmark
alist = [54,26,93,17,77,31,44,55,20]
quickSort(alist)
print(alist)

```
```[17, 20, 26, 31, 44, 54, 55, 77, 93]

```
In [ ]:
```'''
Binary Search
Runtime Complexity - nlog(n)
Memory Complexity - 1
'''
def binary_search(a, key):
low = 0
high = len(a) -1
while low <= high:
mid = low + (high -low)//2
if a[mid] == key:
return mid
elif a[mid] > key:
high = mid -1
elif a[mid] < key:
low = mid + 1
else:
return -1
return -1

Content source: nohmapp/acme-for-now

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