Python | Check for Descending Sorted List

The sorted operation of list is essential operation in many application. But it takes best of O(nlogn) time complexity, hence one hopes to avoid this. So, to check if this is required or not, knowing if list is by default reverse sorted or not, one can check if list is sorted or not. Lets discuss various ways this can be achieved. 

Method #1 : Naive method The simplest way to check this is run a loop for first element and check if we could find any larger element than it after that element, if yes, the list is not reverse sorted. 

Python3

# Python3 code to demonstrate
# Check for Descending Sorted List
# using naive method

# initializing list
test_list = [10, 8, 4, 3, 1]

# printing original list
print ("Original list : " + str(test_list))

# using naive method to
# Check for Descending Sorted List
flag = 0
i = 1
while i < len(test_list):
    if(test_list[i] > test_list[i - 1]):
        flag = 1
    i += 1

# printing result
if (not flag) :
    print ("Yes, List is reverse sorted.")
else :
    print ("No, List is not reverse sorted.")

Output : 

Original list : [10, 8, 4, 3, 1]
Yes, List is reverse sorted.

Time Complexity: O(n), where n is the length of the list test_list 
Auxiliary Space: O(1) additional space is not needed

Method #2 : Using sort() + reverse The new list can be made as a copy of the original list, sorting the new list and comparing with the old list will give us the result if sorting was required to get reverse sorted list or not. 

Python3

# Python3 code to demonstrate
# Check for Descending Sorted List
# using sort() + reverse

# initializing list
test_list = [10, 5, 4, 3, 1]

# printing original list
print ("Original list : " + str(test_list))

# using sort() + reverse to
# Check for Descending Sorted List
flag = 0
test_list1 = test_list[:]
test_list1.sort(reverse = True)
if (test_list1 == test_list):
    flag = 1

# printing result
if (flag) :
    print ("Yes, List is reverse sorted.")
else :
    print ("No, List is not reverse sorted.")

Output : 

Original list : [10, 8, 4, 3, 1]
Yes, List is reverse sorted.

Time Complexity: O(nlogn), where n is the number of elements in the list “test_list”.
Auxiliary Space: O(1), constant extra space is required

Method #3 : Using all() function
The all() function returns True if all elements of the iterable are True. Hence, by comparing each element with its next, we can find if the list is reverse sorted or not.

Python3

# Python3 code to demonstrate
# Check for Descending Sorted List
# using all() function

# initializing list
test_list = [10, 8, 4, 3, 1]

# printing original list
print ("Original list : " + str(test_list))

# using all() function to
# Check for Descending Sorted List
if all(test_list[i] >= test_list[i+1] for i in range(len(test_list)-1)):
    print ("Yes, List is reverse sorted.")
else:
    print ("No, List is not reverse sorted.")
 #This code is contributed by Edula Vinay Kumar Reddy

Output

Original list : [10, 8, 4, 3, 1]
Yes, List is reverse sorted.

Time complexity: O(n)

Auxiliary Space: O(n)