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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)

Merge Sort

Worst Case: 0(n(log(n)) Best Case: 0(n(log(n))

A divide and conquer algorithm invented by John von Neumann. Very good in linked list but clumsy with arrays, takes more memory.





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]

Quicksort

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