# Python Program to Sort Matrix by Sliced Row and Column Summation

• Last Updated : 18 Jul, 2021

Given a Matrix and a range of indices, the task is to write a python program that can sort a matrix on the basis of the sum of only given range of indices of each row and column i.e. the rows and columns are to sliced from a given start to end index, further, matrix are sorted using only those slices sum from each row or column.

Input : test_list = [[1, 4, 3, 1, 3], [3, 4, 5, 2, 4], [23, 5, 5, 3], [2, 3, 5, 1, 6]], i, j = 1, 3
Output : [[1, 4, 3, 1, 3], [2, 3, 5, 1, 6], [3, 4, 5, 2, 4], [23, 5, 5, 3]]
Explanation : 7 < 8 < 9 < 10, is summation of 1st and 2nd element.

Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning - Basic Level Course

Input : test_list = [[1, 4, 3, 1, 3], [23, 5, 5, 3], [2, 3, 5, 1, 6]], i, j = 1, 3
Output : [[1, 4, 3, 1, 3], [2, 3, 5, 1, 6], [23, 5, 5, 3]]
Explanation : 7 < 8 < 10, is summation of 1st and 2nd element.

### Summation on rows

Method 1 : Using sort(), slice and sum()

In this, we perform the task of in-place sorting using sort(), and summation is done using sum(), slice operation is done using list slicing, which together forms as key function for sorting.

Example:

## Python3

 `# get sliced summation``def` `get_sliced_sum(row):``    ``return` `sum``(row[i:j])`` ` ` ` `# initializing list``test_list ``=` `[[``1``, ``4``, ``3``, ``1``, ``3``], [``3``, ``4``, ``5``, ``2``, ``4``],``             ``[``23``, ``5``, ``5``, ``3``], [``2``, ``3``, ``5``, ``1``, ``6``]]`` ` `# printing original list``print``(``"The original list is : "` `+` `str``(test_list))`` ` `# initializing range``i, j ``=` `1``, ``3`` ` `# performing sort``test_list.sort(key``=``get_sliced_sum)`` ` `# printing result``print``(``"Sorted List : "` `+` `str``(test_list))`

Output:

The original list is : [[1, 4, 3, 1, 3], [3, 4, 5, 2, 4], [23, 5, 5, 3], [2, 3, 5, 1, 6]]

Sorted List : [[1, 4, 3, 1, 3], [2, 3, 5, 1, 6], [3, 4, 5, 2, 4], [23, 5, 5, 3]]

Method 2 : Using sorted(), lambda, sum() and slicing

In this, the task of performing sort is done using sorted() and lambda function is used to get a summation of sliced rendered using one-statement without external function call.

Example:

## Python3

 `# initializing list``test_list ``=` `[[``1``, ``4``, ``3``, ``1``, ``3``], [``3``, ``4``, ``5``, ``2``, ``4``],``             ``[``23``, ``5``, ``5``, ``3``], [``2``, ``3``, ``5``, ``1``, ``6``]]`` ` `# printing original list``print``(``"The original list is : "` `+` `str``(test_list))`` ` `# initializing range``i, j ``=` `1``, ``3`` ` `# performing sort using sorted()``# filter util. using lambda fnc.``res ``=` `sorted``(test_list, key``=``lambda` `row: ``sum``(row[i:j]))`` ` `# printing result``print``(``"Sorted List : "` `+` `str``(res))`

Output:

The original list is : [[1, 4, 3, 1, 3], [3, 4, 5, 2, 4], [23, 5, 5, 3], [2, 3, 5, 1, 6]]

Sorted List : [[1, 4, 3, 1, 3], [2, 3, 5, 1, 6], [3, 4, 5, 2, 4], [23, 5, 5, 3]]

### Summation on column

Method 1 : Using sort(), slice and sum()

In this, we perform transpose of a base matrix and then perform the usual task of getting slice using above method 1, after sorting, the matrix is again converted to its transposed format.

Example:

## Python3

 `# get sliced summation``def` `get_sliced_sum(row):``    ``return` `sum``(row[i:j])`` ` ` ` `# initializing list``test_list ``=` `[[``1``, ``4``, ``3``, ``1``], [``3``, ``4``, ``5``, ``2``],``             ``[``23``, ``5``, ``5``, ``3``], [``2``, ``3``, ``5``, ``1``]]`` ` `# printing original list``print``(``"The original list is : "` `+` `str``(test_list))`` ` `# initializing range``i, j ``=` `1``, ``3`` ` `# transposing matrix``test_list ``=` `list``(``zip``(``*``test_list))`` ` `# performing sort``test_list.sort(key``=``get_sliced_sum)`` ` `# performing transpose again to get ``# result.``test_list ``=` `zip``(``*``test_list)`` ` `# converting list of tuples to list of ``# lists``res ``=` `[``list``(sub) ``for` `sub ``in` `test_list]`` ` `# printing result``print``(``"Sorted List Columnwise : "` `+` `str``(res))`

Output:

The original list is : [[1, 4, 3, 1], [3, 4, 5, 2], [23, 5, 5, 3], [2, 3, 5, 1]]

Sorted List Columnwise : [[1, 4, 3, 1], [2, 4, 5, 3], [3, 5, 5, 23], [1, 3, 5, 2]]

Method 2 : Using sorted(), lambda, sum() and slicing

In this, we perform transpose of a base matrix and then perform the usual task of getting slice using above method 2, after sorting, the matrix is again converted to its transposed format.

Example:

## Python3

 `# initializing list``test_list ``=` `[[``1``, ``4``, ``3``, ``1``], [``3``, ``4``, ``5``, ``2``], ``             ``[``23``, ``5``, ``5``, ``3``], [``2``, ``3``, ``5``, ``1``]]`` ` `# printing original list``print``(``"The original list is : "` `+` `str``(test_list))`` ` `# initializing range``i, j ``=` `1``, ``3`` ` `# transposing matrix``test_list ``=` `zip``(``*``test_list)`` ` `# performing sort using sorted()``# filter util. using lambda fnc.``res ``=` `sorted``(test_list, key``=``lambda` `row: ``sum``(row[i:j]))`` ` `# performing transpose again to get result.``res ``=` `zip``(``*``res)`` ` `# converting list of tuples to list of lists``res ``=` `[``list``(sub) ``for` `sub ``in` `res]`` ` `# printing result``print``(``"Sorted List Columnwise : "` `+` `str``(``list``(res)))`

Output:

The original list is : [[1, 4, 3, 1], [3, 4, 5, 2], [23, 5, 5, 3], [2, 3, 5, 1]]

Sorted List Columnwise : [[1, 4, 3, 1], [2, 4, 5, 3], [3, 5, 5, 23], [1, 3, 5, 2]]

My Personal Notes arrow_drop_up