I try to find cycles by comparing the list to sorted array. i check forwards and backwards and find which one has the min. O(n log n) space, 0(n) space ` def lilysHomework(arr): # Write your code here sorted_arr = arr.copy() sorted_arr.sort() arr_map = {v: k for k, v in enumerate(sorted_arr)} visited = [0] * len(arr)

swaps = 0
r_swaps = 0
# print(arr_map)
for i in range(len(arr)):
    if arr[i] != sorted_arr[i]:
        k = i
        if not visited[k]:
            swaps -= 1
        while not visited[k]:
            # print("visiting", k)
            visited[k] = 1
            k = arr_map[arr[k]]
            swaps += 1

sorted_arr.reverse()
arr_map = {v: k for k, v in enumerate(sorted_arr)}
visited = [0] * len(arr)

for i in range(len(arr)):
    if arr[i] != sorted_arr[i]:
        k = i
        if not visited[k]:
            r_swaps -= 1
        while not visited[k]:
            # print("r visiting", k)
            visited[k] = 1
            k = arr_map[arr[k]]
            r_swaps += 1

return min(swaps, r_swaps)