Python Program to test whether the length of rows are in increasing order

Given a Matrix, the following program is used to test if length all rows of a matrix are in increasing order or not. If yes, it returns True, otherwise False.

Input : test_list = [[3], [1, 7], [10, 2, 4], [8, 6, 5, 1, 4]] 
Output : True 
Explanation : 1 < 2 < 3 < 5, increasing lengths of rows, hence True.
Input : test_list = [[3], [1, 7], [10], [8, 6, 5, 1, 4]] 
Output : False 
Explanation : 1 <2 >1 < 5, Non-increasing lengths of rows, hence False.

Method 1: Using loop and len()

In this, we are using loop to check whether the length of next row is greater than the present row, if not, result is flagged off.

Python3

# Initializing list
test_list = [[3], [1, 7], [10, 2, 4], [8, 6, 5, 1, 4]]

# Printing original list
print("The original list is : " + str(test_list))

res = True
for idx in range(len(test_list) - 1) :

    # flag off in case next length is not greater
    # than current
    if len(test_list[idx + 1]) <= len(test_list[idx]):
        res = False
        break

# Printing result
print("Are rows of increasing lengths ? : " + str(res))

Output:

The original list is : [[3], [1, 7], [10, 2, 4], [8, 6, 5, 1, 4]]

Are rows of increasing lengths ? : True

Time Complexity: O(n)
Auxiliary Space: O(n)

Method 2 : Using all() and list comprehension

In this, we test for next length being greater than the current length using len() and all() is used to check for all the rows.

Python3

# initializing list
test_list = [[3], [1, 7], [10, 2, 4], [8, 6, 5, 1, 4]]

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

# checking for truth for all rows in matrix
res = all(len(test_list[idx + 1]) > len(test_list[idx]) for idx in range(len(test_list) - 1))

# printing result
print("Are rows of increasing lengths ? : " + str(res))

Output:

The original list is : [[3], [1, 7], [10, 2, 4], [8, 6, 5, 1, 4]]

Are rows of increasing lengths ? : True

Time Complexity: O(n), where n is the length of the input list. This is because we’re using the built-in all() and list comprehension which all has a time complexity of O(n) in the worst case.
Auxiliary Space: O(1), as we’re not using additional space other than the input list itself. 

Method 3: Using len() and sort()

In this we will append length of each row to a new list, later we will check whether the initial list and  list after sorting are same or not.If same the length of rows are in increasing manner

Python3

# initializing list
test_list = [[3], [1, 7], [10], [8, 6, 5, 1, 4]]

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

res = False
x=[]
for i in test_list:
    x.append(len(i))
a=x
x=x.sort()
if(a==x):
    res=True
# printing result
print("Are rows of increasing lengths ? : " + str(res))

Output

The original list is : [[3], [1, 7], [10], [8, 6, 5, 1, 4]]
Are rows of increasing lengths ? : False

Method 4: Using map() and sorted() function

1. Initialize the list lengths with the lengths of each sublist in test_list.
2. Sort the list lengths in ascending order using the sorted() function.
3. Compare the sorted list lengths with the original list lengths using the == operator to check if the rows are of increasing lengths.
4. Return the result as a boolean value.

Python3

# initializing list
test_list = [[3], [1, 7], [10], [8, 6, 5, 1, 4]]

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

# Method 4: Using map() and sorted()
lengths = list(map(len, test_list))
res = lengths == sorted(lengths)

# printing result
print("Are rows of increasing lengths ? : " + str(res))

Output

The original list is : [[3], [1, 7], [10], [8, 6, 5, 1, 4]]
Are rows of increasing lengths ? : False

Time complexity: O(n log n), where n is the number of sublists in test_list. 
Auxiliary space: O(n), where n is the number of sublists in test_list.