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CountInversions.py
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CountInversions.py
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# Merge two sorted sublists A[low .. mid] and A[mid + 1 .. high]
def Merge(arr, temporary_arr, low_point, mid_point, high_point):
i = k = low_point
j = mid_point + 1
inversion_count = 0
# Conditions are checked to make sure that
# i and j don't exceed their
# subarray limits.
while i <= mid_point and j <= high_point:
if arr[i] < arr[j]:
temporary_arr[k] = arr[i]
i += 1
elif arr[j] < arr[i]:
temporary_arr[k] = arr[j]
j += 1
inversion_count += mid_point - i + 1
k += 1
# Copy the remaining of left and right (in the case we run out of elements in one of our copies)
while i <= mid_point:
temporary_arr[k] = arr[i]
k += 1
i += 1
while j <= high_point:
temporary_arr[k] = arr[j]
k += 1
j += 1
# Copy the temporary to the original array
for index in range(low_point, high_point + 1):
arr[index] = temporary_arr[index]
return inversion_count
def Merge_and_count (arr, temporary_arr, low_point, high_point):
inversion_count = 0
if high_point > low_point:
mid_point = (low_point + high_point) // 2
# recursively split runs into two halves until run size == 1,
inversion_count += Merge_and_count(arr, temporary_arr, low_point, mid_point) # split / merge left half
inversion_count += Merge_and_count(arr, temporary_arr, mid_point + 1, high_point) # split / merge right half
# then merge them and return back up the call chain
inversion_count += Merge(arr, temporary_arr, low_point, mid_point, high_point) # merge the two half runs, through three variables low, high, mid
return inversion_count
my_list = [1, 3, 5, 2, 4, 6, 12, 67, 19, 54, 100, 96, 7]
temp = [0] * len(my_list)
print(Merge_and_count(my_list, my_list.copy(), 0, len(my_list) - 1))