Python – Sort Matrix by Number of elements greater than its previous element

When it is required to sort a matrix based on the number of elements that is greater than the previous element, a list comprehension and the len() method is used with a custom function as the sorting key.

Example

Here's how to sort a matrix by counting ascending pairs in each row ?

def fetch_greater_freq(row):
    return len([row[idx] for idx in range(0, len(row) - 1) if row[idx] < row[idx + 1]])

my_list = [[11, 3, 25, 99, 10], [5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25]]

print("The list is :")
print(my_list)

my_list.sort(key=fetch_greater_freq)

print("The resultant list is :")
print(my_list)

The output of the above code is ?

The list is :
[[11, 3, 25, 99, 10], [5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25]]
The resultant list is :
[[5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25], [11, 3, 25, 99, 10]]

How It Works

Let's break down how the sorting works for each row ?

def fetch_greater_freq(row):
    return len([row[idx] for idx in range(0, len(row) - 1) if row[idx] < row[idx + 1]])

rows = [
    [11, 3, 25, 99, 10],  # 3<25, 25<99 = 2 ascending pairs
    [5, 3, 25, 4],        # 3<25 = 1 ascending pair  
    [77, 11, 5, 3, 77, 77], # 3<77 = 1 ascending pair
    [11, 3, 25]           # 3<25 = 1 ascending pair, but comes later
]

for row in rows:
    count = fetch_greater_freq(row)
    print(f"{row} has {count} ascending pairs")

[11, 3, 25, 99, 10] has 2 ascending pairs
[5, 3, 25, 4] has 1 ascending pairs
[77, 11, 5, 3, 77, 77] has 1 ascending pairs
[11, 3, 25] has 1 ascending pairs

Alternative Implementation

You can also implement this using a simple loop instead of list comprehension ?

def count_ascending_pairs(row):
    count = 0
    for i in range(len(row) - 1):
        if row[i] < row[i + 1]:
            count += 1
    return count

matrix = [[11, 3, 25, 99, 10], [5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25]]

print("Original matrix:")
print(matrix)

matrix.sort(key=count_ascending_pairs)

print("Sorted matrix:")
print(matrix)

Original matrix:
[[11, 3, 25, 99, 10], [5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25]]
Sorted matrix:
[[5, 3, 25, 4], [77, 11, 5, 3, 77, 77], [11, 3, 25], [11, 3, 25, 99, 10]]

Key Points

• The fetch_greater_freq() function counts pairs where row[i] < row[i+1]

• The sort() method uses this function as a key to determine sorting order

• Rows with fewer ascending pairs appear first in the sorted result

• When counts are equal, Python's stable sort preserves the original order

Conclusion

This approach effectively sorts matrix rows by counting ascending adjacent pairs. The custom key function with sort() provides a clean solution for complex sorting criteria in Python.