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Answer to Question #240532 in Python for sai krishna

given an MxN integer matrix write a program to

Find all zeros and replace them with the sum of their neighboring elements.

After replacing the zeros set all other elements the corresponding row and column with zeros (excluding the elements which where previously zeros)

Note: consider the upper ,lower,right and left elements as neighboring elements

The first line of input is two space seperated integeres M and N

The next M lines of input contain N space seperated integers

the output should be an MxN matrix

sample input 1

sample output 1

sample input 2

sample output 2

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Python Matrices and NumPy Arrays

A matrix is a two-dimensional data structure where numbers are arranged into rows and columns. For example:

This matrix is a 3x4 (pronounced "three by four") matrix because it has 3 rows and 4 columns.

• Python Matrix

Python doesn't have a built-in type for matrices. However, we can treat a list of a list as a matrix. For example:

We can treat this list of a list as a matrix having 2 rows and 3 columns.

Be sure to learn about Python lists before proceed this article.

Let's see how to work with a nested list.

When we run the program, the output will be:

Here are few more examples related to Python matrices using nested lists.

• Add two matrices
• Transpose a Matrix
• Multiply two matrices

Using nested lists as a matrix works for simple computational tasks, however, there is a better way of working with matrices in Python using NumPy package.

• NumPy Array

NumPy is a package for scientific computing which has support for a powerful N-dimensional array object. Before you can use NumPy, you need to install it. For more info,

• Visit: How to install NumPy?
• If you are on Windows, download and install anaconda distribution of Python. It comes with NumPy and other several packages related to data science and machine learning.

Once NumPy is installed, you can import and use it.

NumPy provides multidimensional array of numbers (which is actually an object). Let's take an example:

As you can see, NumPy's array class is called ndarray .

How to create a NumPy array?

There are several ways to create NumPy arrays.

1. Array of integers, floats and complex Numbers

When you run the program, the output will be:

2. Array of zeros and ones

Here, we have specified dtype to 32 bits (4 bytes). Hence, this array can take values from -2 -31 to 2 -31 -1 .

3. Using arange() and shape()

Learn more about other ways of creating a NumPy array .

Matrix Operations

Above, we gave you 3 examples: addition of two matrices, multiplication of two matrices and transpose of a matrix. We used nested lists before to write those programs. Let's see how we can do the same task using NumPy array.

Addition of Two Matrices

We use + operator to add corresponding elements of two NumPy matrices.

Multiplication of Two Matrices

To multiply two matrices, we use dot() method. Learn more about how numpy.dot works.

Note: * is used for array multiplication (multiplication of corresponding elements of two arrays) not matrix multiplication.

Transpose of a Matrix

We use numpy.transpose to compute transpose of a matrix.

As you can see, NumPy made our task much easier.

Access matrix elements, rows and columns

Access matrix elements

Similar like lists, we can access matrix elements using index. Let's start with a one-dimensional NumPy array.

Now, let's see how we can access elements of a two-dimensional array (which is basically a matrix).

Access rows of a Matrix

Access columns of a Matrix

If you don't know how this above code works, read slicing of a matrix section of this article.

Slicing of a Matrix

Slicing of a one-dimensional NumPy array is similar to a list. If you don't know how slicing for a list works, visit Understanding Python's slice notation .

Let's take an example:

Now, let's see how we can slice a matrix.

As you can see, using NumPy (instead of nested lists) makes it a lot easier to work with matrices, and we haven't even scratched the basics. We suggest you to explore NumPy package in detail especially if you trying to use Python for data science/analytics.

NumPy Resources you might find helpful:

• NumPy Tutorial
• NumPy Reference

Table of Contents

• What is a matrix?
• Numbers(integers, float, complex etc.) Array
• Zeros and Ones Array
• Array Using arange() and shape()
• Multiplication
• Access elements
• Access rows
• Access columns
• Slicing of Matrix
• Useful Resources

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5 Best Ways to Explain Python Matrix with Examples

💡 Problem Formulation: Matrices are fundamental for a multitude of operations in software development, data analysis, and scientific computing. In Python, a matrix can be represented and manipulated in various ways. This article solves the problem of how to create, modify, and perform operations on Python matrices with practical examples. Imagine you want to represent 2D data like pixel values in an image or distances between cities; such tasks require creating and managing a matrix efficiently.

Method 1: Using Nested Lists

In Python, one of the most straightforward ways to represent a matrix is using nested lists. Each inner list represents a row in the matrix, and the elements of these lists are the matrix elements. Accessing, updating, and iterating over these matrices is intuitive and requires no additional libraries.

Here’s an example:

The code snippet creates a 3×3 matrix with nested lists. It then accesses and prints the element on the second row and third column, which is the number 6. This method is easy to understand and works well without additional dependencies, but can become inefficient for large matrices or complex operations.

Method 2: Using NumPy Arrays

NumPy is a powerful library for numerical computing in Python. Its array object is more efficient and convenient for large matrices and supports a wide range of mathematical operations. NumPy arrays are homogeneous, which can lead to better performance compared to nested lists.

This example demonstrates creating a NumPy array to represent a matrix and performing an element-wise addition with another matrix. NumPy arrays offer more efficient storage and better functionality for large-scale operations than lists.

Method 3: Using pandas DataFrame

pandas is another library that’s extremely useful for data analysis, and it provides the DataFrame object which can be thought of as a matrix with more functionality like labeled rows and columns. DataFrames are great for handling tabular data and can be created from lists, dicts, or even reading from files like CSV.

This code snippet creates a 3×3 matrix as a pandas DataFrame with labeled rows and columns. It selects and prints the element from row labeled ‘Y’ and column labeled ‘B’. pandas DataFrames are ideal for complex data manipulation but may be an overkill for simple matrix operations.

Method 4: Using List Comprehensions

List comprehensions provide a concise way to create lists including matrices. They are elegant and can be used to initialize, transform, and even transpose matrices with readable and compact code. List comprehensions are a Pythonic way to operate with matrices represented by lists.

The given code uses a list comprehension to create a 3×3 identity matrix, a matrix with 1s on the diagonal and 0s elsewhere. List comprehensions are a compact and readable method to create matrices, but can become less readable for very complex operations.

Bonus One-Liner Method 5: Using zip() and * Operator

Transposing a matrix, which is flipping it over its diagonal, can be elegantly achieved in Python by using the zip() function in conjunction with the star operator * . This one-liner is very readable and takes advantage of Python’s unpacking feature.

The code takes a 3×2 matrix and transposes it to a 2×3 matrix using the zip() function. The star operator unpacks the rows of the original matrix such that they are passed as separate arguments to zip() , which pairs elements of the same index from these arguments. This is a short and efficient one-liner for transposing matrices but may be less obvious to beginners.

Summary/Discussion

• Method 1: Nested Lists. Easily understandable. Not as efficient for large or complex matrices.
• Method 2: Using NumPy Arrays. Highly efficient and versatile. Requires additional knowledge of NumPy.
• Method 3: Using pandas DataFrames. Great for complex data manipulations with labeled axes. Overly powerful for simple tasks.
• Method 4: List Comprehensions. Elegant and Pythonic. Can become unwieldy for complex operations.
• Bonus Method 5: Using zip() and * Operator. Succinct for transposing. Less intuitive for those unfamiliar with argument unpacking.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.

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Solving Assignment Problem using Linear Programming in Python

Learn how to use Python PuLP to solve Assignment problems using Linear Programming.

In earlier articles, we have seen various applications of Linear programming such as transportation, transshipment problem, Cargo Loading problem, and shift-scheduling problem. Now In this tutorial, we will focus on another model that comes under the class of linear programming model known as the Assignment problem. Its objective function is similar to transportation problems. Here we minimize the objective function time or cost of manufacturing the products by allocating one job to one machine.

If we want to solve the maximization problem assignment problem then we subtract all the elements of the matrix from the highest element in the matrix or multiply the entire matrix by –1 and continue with the procedure. For solving the assignment problem, we use the Assignment technique or Hungarian method, or Flood’s technique.

The transportation problem is a special case of the linear programming model and the assignment problem is a special case of transportation problem, therefore it is also a special case of the linear programming problem.

In this tutorial, we are going to cover the following topics:

Assignment Problem

A problem that requires pairing two sets of items given a set of paired costs or profit in such a way that the total cost of the pairings is minimized or maximized. The assignment problem is a special case of linear programming.

For example, an operation manager needs to assign four jobs to four machines. The project manager needs to assign four projects to four staff members. Similarly, the marketing manager needs to assign the 4 salespersons to 4 territories. The manager’s goal is to minimize the total time or cost.

Problem Formulation

A manager has prepared a table that shows the cost of performing each of four jobs by each of four employees. The manager has stated his goal is to develop a set of job assignments that will minimize the total cost of getting all 4 jobs.  

Initialize LP Model

In this step, we will import all the classes and functions of pulp module and create a Minimization LP problem using LpProblem class.

Define Decision Variable

In this step, we will define the decision variables. In our problem, we have two variable lists: workers and jobs. Let’s create them using  LpVariable.dicts()  class.  LpVariable.dicts()  used with Python’s list comprehension.  LpVariable.dicts()  will take the following four values:

• First, prefix name of what this variable represents.
• Second is the list of all the variables.
• Third is the lower bound on this variable.
• Fourth variable is the upper bound.
• Fourth is essentially the type of data (discrete or continuous). The options for the fourth parameter are  LpContinuous  or  LpInteger .

Let’s first create a list route for the route between warehouse and project site and create the decision variables using LpVariable.dicts() the method.

Define Objective Function

In this step, we will define the minimum objective function by adding it to the LpProblem  object. lpSum(vector)is used here to define multiple linear expressions. It also used list comprehension to add multiple variables.

Define the Constraints

Here, we are adding two types of constraints: Each job can be assigned to only one employee constraint and Each employee can be assigned to only one job. We have added the 2 constraints defined in the problem by adding them to the LpProblem  object.

Solve Model

In this step, we will solve the LP problem by calling solve() method. We can print the final value by using the following for loop.

From the above results, we can infer that Worker-1 will be assigned to Job-1, Worker-2 will be assigned to job-3, Worker-3 will be assigned to Job-2, and Worker-4 will assign with job-4.

In this article, we have learned about Assignment problems, Problem Formulation, and implementation using the python PuLp library. We have solved the Assignment problem using a Linear programming problem in Python. Of course, this is just a simple case study, we can add more constraints to it and make it more complicated. You can also run other case studies on Cargo Loading problems , Staff scheduling problems . In upcoming articles, we will write more on different optimization problems such as transshipment problem, balanced diet problem. You can revise the basics of mathematical concepts in  this article  and learn about Linear Programming  in this article .

• Solving Blending Problem in Python using Gurobi
• Transshipment Problem in Python Using PuLP

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Python – Matrix

Here we will discuss different ways how we can form a matrix using Python within this tutorial we will also discuss the various operation that can be performed on a matrix. we will also cover the external module Numpy to form a matrix and its operations in Python .

What is the matrix?

A matrix is a collection of numbers arranged in a rectangular array in rows and columns. In the fields of engineering, physics, statistics, and graphics, matrices are widely used to express picture rotations and other types of transformations. The matrix is referred to as an m by n matrix, denoted by the symbol “m x n” if there are m rows and n columns.

Creating a simple matrix using Python

Method 1: creating a matrix with a list of list.

Here, we are going to create a matrix using the list of lists.

Method 2: Take Matrix input from user in Python

Here, we are taking a number of rows and columns from the user and printing the Matrix.

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

Method 3: Create a matrix using list comprehension

List comprehension is an elegant way to define and create a list in Python, we are using the range function for printing 4 rows and 4 columns.

Assigning Value in a matrix

Method 1: assign value to an individual cell in matrix.

Here we are replacing and assigning value to an individual cell (1 row and 1 column = 11) in the Matrix.

Method 2: Assign a value to an individual cell using negative indexing in Matrix

Here we are replacing and assigning value to an individual cell (-2 row and -1 column = 21) in the Matrix.

Accessing Value in a matrix

Method 1: accessing matrix values.

Here, we are accessing elements of a Matrix by passing its row and column.

Method 2: Accessing Matrix values using negative indexing

Here, we are accessing elements of a Matrix by passing its row and column on negative indexing.

Mathematical Operations with Matrix in Python

Example 1: adding values to a matrix with a for loop in python.

Here, we are adding two matrices using the Python for-loop.

Example 2: Adding and subtracting values to a matrix with list comprehension

Performing the Basic addition and subtraction using list comprehension.

Example 3: Python program to multiply and divide two matrices

Performing the Basic multiplication and division using Python loop.

Transpose in matrix

Example: python program to transpose a matrix using loop.

Transpose of a matrix is obtained by changing rows to columns and columns to rows. In other words, transpose of A[][] is obtained by changing A[i][j] to A[j][i].

Matrix using Numpy

Create a matrix using numpy .

Here we are creating a Numpy array using numpy.random and a random module .

Matrix mathematical operations in Python Using Numpy

Here we are covering different mathematical operations such as addition subtraction, multiplication, and division using Numpy.

Dot and cross product with Matrix

Here, we will find the inner, outer, and cross products of matrices and vectors using NumPy in Python.

Matrix transpose in Python using Numpy

To perform transpose operation in matrix we can use the numpy.transpose() method.

Create an empty matrix with NumPy in Python

Initializing an empty array, using the np.zeros() .

Slicing in Matrix using Numpy

Slicing is the process of choosing specific rows and columns from a matrix and then creating a new matrix by removing all of the non-selected elements. In the first example, we are printing the whole matrix, in the second we are passing 2 as an initial index, 3 as the last index, and index jump as 1. The same is used in the next print we have just changed the index jump to 2.

Delete rows and columns using Numpy

Here, we are trying to delete rows using the np.delete() function . In the code, we first tried to delete the 0 th row, then we tried to delete the 2 nd row, and then the 3 rd row.

Add row/columns in the Numpy array

We added one more column at the 4 th position using np.hstack . 

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Ordered Matrix in Python

Problem statement:.

In the ordered matrix in python, we are given a matrix of integers. We need to convert the given matrix to an ordered matrix and print it. An ordered matrix is a matrix that is sorted row-wise.

Code for Ordered Matrix in Python:

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