assignment problem in python

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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 .

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quadratic_assignment #

Approximates solution to the quadratic assignment problem and the graph matching problem.

Quadratic assignment solves problems of the following form:

where \(\mathcal{P}\) is the set of all permutation matrices, and \(A\) and \(B\) are square matrices.

Graph matching tries to maximize the same objective function. This algorithm can be thought of as finding the alignment of the nodes of two graphs that minimizes the number of induced edge disagreements, or, in the case of weighted graphs, the sum of squared edge weight differences.

Note that the quadratic assignment problem is NP-hard. The results given here are approximations and are not guaranteed to be optimal.

The square matrix \(A\) in the objective function above.

The square matrix \(B\) in the objective function above.

The algorithm used to solve the problem. ‘faq’ (default) and ‘2opt’ are available.

A dictionary of solver options. All solvers support the following:

Maximizes the objective function if True .

Fixes part of the matching. Also known as a “seed” [2] .

Each row of partial_match specifies a pair of matched nodes: node partial_match[i, 0] of A is matched to node partial_match[i, 1] of B . The array has shape (m, 2) , where m is not greater than the number of nodes, \(n\) .

numpy.random.RandomState }, optional

If seed is None (or np.random ), the numpy.random.RandomState singleton is used. If seed is an int, a new RandomState instance is used, seeded with seed . If seed is already a Generator or RandomState instance then that instance is used.

For method-specific options, see show_options('quadratic_assignment') .

OptimizeResult containing the following fields.

Column indices corresponding to the best permutation found of the nodes of B .

The objective value of the solution.

The number of iterations performed during optimization.

The default method ‘faq’ uses the Fast Approximate QAP algorithm [1] ; it typically offers the best combination of speed and accuracy. Method ‘2opt’ can be computationally expensive, but may be a useful alternative, or it can be used to refine the solution returned by another method.

J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik, S.G. Kratzer, E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and C.E. Priebe, “Fast approximate quadratic programming for graph matching,” PLOS one, vol. 10, no. 4, p. e0121002, 2015, DOI:10.1371/journal.pone.0121002

D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski, C. Priebe, “Seeded graph matching”, Pattern Recognit. 87 (2019): 203-215, DOI:10.1016/j.patcog.2018.09.014

“2-opt,” Wikipedia. https://en.wikipedia.org/wiki/2-opt

The see the relationship between the returned col_ind and fun , use col_ind to form the best permutation matrix found, then evaluate the objective function \(f(P) = trace(A^T P B P^T )\) .

Alternatively, to avoid constructing the permutation matrix explicitly, directly permute the rows and columns of the distance matrix.

Although not guaranteed in general, quadratic_assignment happens to have found the globally optimal solution.

Here is an example for which the default method, ‘faq’ , does not find the global optimum.

If accuracy is important, consider using ‘2opt’ to refine the solution.

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Job Assignment Problem using Branch And Bound

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Let there be N workers and N jobs. Any worker can be assigned to perform any job, incurring some cost that may vary depending on the work-job assignment. It is required to perform all jobs by assigning exactly one worker to each job and exactly one job to each agent in such a way that the total cost of the assignment is minimized.

Let us explore all approaches for this problem.

Solution 1: Brute Force  

We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O(n!).

Solution 2: Hungarian Algorithm  

The optimal assignment can be found using the Hungarian algorithm. The Hungarian algorithm has worst case run-time complexity of O(n^3).

Solution 3: DFS/BFS on state space tree  

A state space tree is a N-ary tree with property that any path from root to leaf node holds one of many solutions to given problem. We can perform depth-first search on state space tree and but successive moves can take us away from the goal rather than bringing closer. The search of state space tree follows leftmost path from the root regardless of initial state. An answer node may never be found in this approach. We can also perform a Breadth-first search on state space tree. But no matter what the initial state is, the algorithm attempts the same sequence of moves like DFS.

Solution 4: Finding Optimal Solution using Branch and Bound  

The selection rule for the next node in BFS and DFS is “blind”. i.e. the selection rule does not give any preference to a node that has a very good chance of getting the search to an answer node quickly. The search for an optimal solution can often be speeded by using an “intelligent” ranking function, also called an approximate cost function to avoid searching in sub-trees that do not contain an optimal solution. It is similar to BFS-like search but with one major optimization. Instead of following FIFO order, we choose a live node with least cost. We may not get optimal solution by following node with least promising cost, but it will provide very good chance of getting the search to an answer node quickly.

There are two approaches to calculate the cost function:  

• For each worker, we choose job with minimum cost from list of unassigned jobs (take minimum entry from each row).
• For each job, we choose a worker with lowest cost for that job from list of unassigned workers (take minimum entry from each column).

In this article, the first approach is followed.

Let’s take below example and try to calculate promising cost when Job 2 is assigned to worker A. 

Since Job 2 is assigned to worker A (marked in green), cost becomes 2 and Job 2 and worker A becomes unavailable (marked in red). 

Now we assign job 3 to worker B as it has minimum cost from list of unassigned jobs. Cost becomes 2 + 3 = 5 and Job 3 and worker B also becomes unavailable. 

Finally, job 1 gets assigned to worker C as it has minimum cost among unassigned jobs and job 4 gets assigned to worker D as it is only Job left. Total cost becomes 2 + 3 + 5 + 4 = 14. 

Below diagram shows complete search space diagram showing optimal solution path in green. 

Complete Algorithm:  

Below is the implementation of the above approach:

Time Complexity: O(M*N). This is because the algorithm uses a double for loop to iterate through the M x N matrix.  Auxiliary Space: O(M+N). This is because it uses two arrays of size M and N to track the applicants and jobs.

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Python's Assignment Operator: Write Robust Assignments

Table of Contents

The Assignment Statement Syntax

The assignment operator, assignments and variables, other assignment syntax, initializing and updating variables, making multiple variables refer to the same object, updating lists through indices and slices, adding and updating dictionary keys, doing parallel assignments, unpacking iterables, providing default argument values, augmented mathematical assignment operators, augmented assignments for concatenation and repetition, augmented bitwise assignment operators, annotated assignment statements, assignment expressions with the walrus operator, managed attribute assignments, define or call a function, work with classes, import modules and objects, use a decorator, access the control variable in a for loop or a comprehension, use the as keyword, access the _ special variable in an interactive session, built-in objects, named constants.

Python’s assignment operators allow you to define assignment statements . This type of statement lets you create, initialize, and update variables throughout your code. Variables are a fundamental cornerstone in every piece of code, and assignment statements give you complete control over variable creation and mutation.

Learning about the Python assignment operator and its use for writing assignment statements will arm you with powerful tools for writing better and more robust Python code.

In this tutorial, you’ll:

• Use Python’s assignment operator to write assignment statements
• Take advantage of augmented assignments in Python
• Explore assignment variants, like assignment expressions and managed attributes
• Become aware of illegal and dangerous assignments in Python

You’ll dive deep into Python’s assignment statements. To get the most out of this tutorial, you should be comfortable with several basic topics, including variables , built-in data types , comprehensions , functions , and Python keywords . Before diving into some of the later sections, you should also be familiar with intermediate topics, such as object-oriented programming , constants , imports , type hints , properties , descriptors , and decorators .

Free Source Code: Click here to download the free assignment operator source code that you’ll use to write assignment statements that allow you to create, initialize, and update variables in your code.

Assignment Statements and the Assignment Operator

One of the most powerful programming language features is the ability to create, access, and mutate variables . In Python, a variable is a name that refers to a concrete value or object, allowing you to reuse that value or object throughout your code.

To create a new variable or to update the value of an existing one in Python, you’ll use an assignment statement . This statement has the following three components:

• A left operand, which must be a variable
• The assignment operator ( = )
• A right operand, which can be a concrete value , an object , or an expression

Here’s how an assignment statement will generally look in Python:

Here, variable represents a generic Python variable, while expression represents any Python object that you can provide as a concrete value—also known as a literal —or an expression that evaluates to a value.

To execute an assignment statement like the above, Python runs the following steps:

• Evaluate the right-hand expression to produce a concrete value or object . This value will live at a specific memory address in your computer.
• Store the object’s memory address in the left-hand variable . This step creates a new variable if the current one doesn’t already exist or updates the value of an existing variable.

The second step shows that variables work differently in Python than in other programming languages. In Python, variables aren’t containers for objects. Python variables point to a value or object through its memory address. They store memory addresses rather than objects.

This behavior difference directly impacts how data moves around in Python, which is always by reference . In most cases, this difference is irrelevant in your day-to-day coding, but it’s still good to know.

The central component of an assignment statement is the assignment operator . This operator is represented by the = symbol, which separates two operands:

• A value or an expression that evaluates to a concrete value

Operators are special symbols that perform mathematical , logical , and bitwise operations in a programming language. The objects (or object) on which an operator operates are called operands .

Unary operators, like the not Boolean operator, operate on a single object or operand, while binary operators act on two. That means the assignment operator is a binary operator.

Note: Like C , Python uses == for equality comparisons and = for assignments. Unlike C, Python doesn’t allow you to accidentally use the assignment operator ( = ) in an equality comparison.

Equality is a symmetrical relationship, and assignment is not. For example, the expression a == 42 is equivalent to 42 == a . In contrast, the statement a = 42 is correct and legal, while 42 = a isn’t allowed. You’ll learn more about illegal assignments later on.

The right-hand operand in an assignment statement can be any Python object, such as a number , list , string , dictionary , or even a user-defined object. It can also be an expression. In the end, expressions always evaluate to concrete objects, which is their return value.

Here are a few examples of assignments in Python:

The first two sample assignments in this code snippet use concrete values, also known as literals , to create and initialize number and greeting . The third example assigns the result of a math expression to the total variable, while the last example uses a Boolean expression.

Note: You can use the built-in id() function to inspect the memory address stored in a given variable.

Here’s a short example of how this function works:

The number in your output represents the memory address stored in number . Through this address, Python can access the content of number , which is the integer 42 in this example.

If you run this code on your computer, then you’ll get a different memory address because this value varies from execution to execution and computer to computer.

Unlike expressions, assignment statements don’t have a return value because their purpose is to make the association between the variable and its value. That’s why the Python interpreter doesn’t issue any output in the above examples.

Now that you know the basics of how to write an assignment statement, it’s time to tackle why you would want to use one.

The assignment statement is the explicit way for you to associate a name with an object in Python. You can use this statement for two main purposes:

• Creating and initializing new variables
• Updating the values of existing variables

When you use a variable name as the left operand in an assignment statement for the first time, you’re creating a new variable. At the same time, you’re initializing the variable to point to the value of the right operand.

On the other hand, when you use an existing variable in a new assignment, you’re updating or mutating the variable’s value. Strictly speaking, every new assignment will make the variable refer to a new value and stop referring to the old one. Python will garbage-collect all the values that are no longer referenced by any existing variable.

Assignment statements not only assign a value to a variable but also determine the data type of the variable at hand. This additional behavior is another important detail to consider in this kind of statement.

Because Python is a dynamically typed language, successive assignments to a given variable can change the variable’s data type. Changing the data type of a variable during a program’s execution is considered bad practice and highly discouraged. It can lead to subtle bugs that can be difficult to track down.

Unlike in math equations, in Python assignments, the left operand must be a variable rather than an expression or a value. For example, the following construct is illegal, and Python flags it as invalid syntax:

In this example, you have expressions on both sides of the = sign, and this isn’t allowed in Python code. The error message suggests that you may be confusing the equality operator with the assignment one, but that’s not the case. You’re really running an invalid assignment.

To correct this construct and convert it into a valid assignment, you’ll have to do something like the following:

In this code snippet, you first import the sqrt() function from the math module. Then you isolate the hypotenuse variable in the original equation by using the sqrt() function. Now your code works correctly.

Now you know what kind of syntax is invalid. But don’t get the idea that assignment statements are rigid and inflexible. In fact, they offer lots of room for customization, as you’ll learn next.

Python’s assignment statements are pretty flexible and versatile. You can write them in several ways, depending on your specific needs and preferences. Here’s a quick summary of the main ways to write assignments in Python:

Up to this point, you’ve mostly learned about the base assignment syntax in the above code snippet. In the following sections, you’ll learn about multiple, parallel, and augmented assignments. You’ll also learn about assignments with iterable unpacking.

Read on to see the assignment statements in action!

Assignment Statements in Action

You’ll find and use assignment statements everywhere in your Python code. They’re a fundamental part of the language, providing an explicit way to create, initialize, and mutate variables.

You can use assignment statements with plain names, like number or counter . You can also use assignments in more complicated scenarios, such as with:

• Qualified attribute names , like user.name
• Indices and slices of mutable sequences, like a_list[i] and a_list[i:j]
• Dictionary keys , like a_dict[key]

This list isn’t exhaustive. However, it gives you some idea of how flexible these statements are. You can even assign multiple values to an equal number of variables in a single line, commonly known as parallel assignment . Additionally, you can simultaneously assign the values in an iterable to a comma-separated group of variables in what’s known as an iterable unpacking operation.

In the following sections, you’ll dive deeper into all these topics and a few other exciting things that you can do with assignment statements in Python.

The most elementary use case of an assignment statement is to create a new variable and initialize it using a particular value or expression:

All these statements create new variables, assigning them initial values or expressions. For an initial value, you should always use the most sensible and least surprising value that you can think of. For example, initializing a counter to something different from 0 may be confusing and unexpected because counters almost always start having counted no objects.

Updating a variable’s current value or state is another common use case of assignment statements. In Python, assigning a new value to an existing variable doesn’t modify the variable’s current value. Instead, it causes the variable to refer to a different value. The previous value will be garbage-collected if no other variable refers to it.

Consider the following examples:

These examples run two consecutive assignments on the same variable. The first one assigns the string "Hello, World!" to a new variable named greeting .

The second assignment updates the value of greeting by reassigning it the "Hi, Pythonistas!" string. In this example, the original value of greeting —the "Hello, World!" string— is lost and garbage-collected. From this point on, you can’t access the old "Hello, World!" string.

Even though running multiple assignments on the same variable during a program’s execution is common practice, you should use this feature with caution. Changing the value of a variable can make your code difficult to read, understand, and debug. To comprehend the code fully, you’ll have to remember all the places where the variable was changed and the sequential order of those changes.

Because assignments also define the data type of their target variables, it’s also possible for your code to accidentally change the type of a given variable at runtime. A change like this can lead to breaking errors, like AttributeError exceptions. Remember that strings don’t have the same methods and attributes as lists or dictionaries, for example.

In Python, you can make several variables reference the same object in a multiple-assignment line. This can be useful when you want to initialize several similar variables using the same initial value:

In this example, you chain two assignment operators in a single line. This way, your two variables refer to the same initial value of 0 . Note how both variables hold the same memory address, so they point to the same instance of 0 .

When it comes to integer variables, Python exhibits a curious behavior. It provides a numeric interval where multiple assignments behave the same as independent assignments. Consider the following examples:

To create n and m , you use independent assignments. Therefore, they should point to different instances of the number 42 . However, both variables hold the same object, which you confirm by comparing their corresponding memory addresses.

Now check what happens when you use a greater initial value:

Now n and m hold different memory addresses, which means they point to different instances of the integer number 300 . In contrast, when you use multiple assignments, both variables refer to the same object. This tiny difference can save you small bits of memory if you frequently initialize integer variables in your code.

The implicit behavior of making independent assignments point to the same integer number is actually an optimization called interning . It consists of globally caching the most commonly used integer values in day-to-day programming.

Under the hood, Python defines a numeric interval in which interning takes place. That’s the interning interval for integer numbers. You can determine this interval using a small script like the following:

This script helps you determine the interning interval by comparing integer numbers from -10 to 500 . If you run the script from your command line, then you’ll get an output like the following:

This output means that if you use a single number between -5 and 256 to initialize several variables in independent statements, then all these variables will point to the same object, which will help you save small bits of memory in your code.

In contrast, if you use a number that falls outside of the interning interval, then your variables will point to different objects instead. Each of these objects will occupy a different memory spot.

You can use the assignment operator to mutate the value stored at a given index in a Python list. The operator also works with list slices . The syntax to write these types of assignment statements is the following:

In the first construct, expression can return any Python object, including another list. In the second construct, expression must return a series of values as a list, tuple, or any other sequence. You’ll get a TypeError if expression returns a single value.

Note: When creating slice objects, you can use up to three arguments. These arguments are start , stop , and step . They define the number that starts the slice, the number at which the slicing must stop retrieving values, and the step between values.

Here’s an example of updating an individual value in a list:

In this example, you update the value at index 2 using an assignment statement. The original number at that index was 7 , and after the assignment, the number is 3 .

Note: Using indices and the assignment operator to update a value in a tuple or a character in a string isn’t possible because tuples and strings are immutable data types in Python.

Their immutability means that you can’t change their items in place :

You can’t use the assignment operator to change individual items in tuples or strings. These data types are immutable and don’t support item assignments.

It’s important to note that you can’t add new values to a list by using indices that don’t exist in the target list:

In this example, you try to add a new value to the end of numbers by using an index that doesn’t exist. This assignment isn’t allowed because there’s no way to guarantee that new indices will be consecutive. If you ever want to add a single value to the end of a list, then use the .append() method.

If you want to update several consecutive values in a list, then you can use slicing and an assignment statement:

In the first example, you update the letters between indices 1 and 3 without including the letter at 3 . The second example updates the letters from index 3 until the end of the list. Note that this slicing appends a new value to the list because the target slice is shorter than the assigned values.

Also note that the new values were provided through a tuple, which means that this type of assignment allows you to use other types of sequences to update your target list.

The third example updates a single value using a slice where both indices are equal. In this example, the assignment inserts a new item into your target list.

In the final example, you use a step of 2 to replace alternating letters with their lowercase counterparts. This slicing starts at index 1 and runs through the whole list, stepping by two items each time.

Updating the value of an existing key or adding new key-value pairs to a dictionary is another common use case of assignment statements. To do these operations, you can use the following syntax:

The first construct helps you update the current value of an existing key, while the second construct allows you to add a new key-value pair to the dictionary.

For example, to update an existing key, you can do something like this:

In this example, you update the current inventory of oranges in your store using an assignment. The left operand is the existing dictionary key, and the right operand is the desired new value.

While you can’t add new values to a list by assignment, dictionaries do allow you to add new key-value pairs using the assignment operator. In the example below, you add a lemon key to inventory :

In this example, you successfully add a new key-value pair to your inventory with 100 units. This addition is possible because dictionaries don’t have consecutive indices but unique keys, which are safe to add by assignment.

The assignment statement does more than assign the result of a single expression to a single variable. It can also cope nicely with assigning multiple values to multiple variables simultaneously in what’s known as a parallel assignment .

Here’s the general syntax for parallel assignments in Python:

Note that the left side of the statement can be either a tuple or a list of variables. Remember that to create a tuple, you just need a series of comma-separated elements. In this case, these elements must be variables.

The right side of the statement must be a sequence or iterable of values or expressions. In any case, the number of elements in the right operand must match the number of variables on the left. Otherwise, you’ll get a ValueError exception.

In the following example, you compute the two solutions of a quadratic equation using a parallel assignment:

In this example, you first import sqrt() from the math module. Then you initialize the equation’s coefficients in a parallel assignment.

The equation’s solution is computed in another parallel assignment. The left operand contains a tuple of two variables, x1 and x2 . The right operand consists of a tuple of expressions that compute the solutions for the equation. Note how each result is assigned to each variable by position.

A classical use case of parallel assignment is to swap values between variables:

The highlighted line does the magic and swaps the values of previous_value and next_value at the same time. Note that in a programming language that doesn’t support this kind of assignment, you’d have to use a temporary variable to produce the same effect:

In this example, instead of using parallel assignment to swap values between variables, you use a new variable to temporarily store the value of previous_value to avoid losing its reference.

For a concrete example of when you’d need to swap values between variables, say you’re learning how to implement the bubble sort algorithm , and you come up with the following function:

In the highlighted line, you use a parallel assignment to swap values in place if the current value is less than the next value in the input list. To dive deeper into the bubble sort algorithm and into sorting algorithms in general, check out Sorting Algorithms in Python .

You can use assignment statements for iterable unpacking in Python. Unpacking an iterable means assigning its values to a series of variables one by one. The iterable must be the right operand in the assignment, while the variables must be the left operand.

Like in parallel assignments, the variables must come as a tuple or list. The number of variables must match the number of values in the iterable. Alternatively, you can use the unpacking operator ( * ) to grab several values in a variable if the number of variables doesn’t match the iterable length.

Here’s the general syntax for iterable unpacking in Python:

Iterable unpacking is a powerful feature that you can use all around your code. It can help you write more readable and concise code. For example, you may find yourself doing something like this:

Whenever you do something like this in your code, go ahead and replace it with a more readable iterable unpacking using a single and elegant assignment, like in the following code snippet:

The numbers list on the right side contains four values. The assignment operator unpacks these values into the four variables on the left side of the statement. The values in numbers get assigned to variables in the same order that they appear in the iterable. The assignment is done by position.

Note: Because Python sets are also iterables, you can use them in an iterable unpacking operation. However, it won’t be clear which value goes to which variable because sets are unordered data structures.

The above example shows the most common form of iterable unpacking in Python. The main condition for the example to work is that the number of variables matches the number of values in the iterable.

What if you don’t know the iterable length upfront? Will the unpacking work? It’ll work if you use the * operator to pack several values into one of your target variables.

For example, say that you want to unpack the first and second values in numbers into two different variables. Additionally, you would like to pack the rest of the values in a single variable conveniently called rest . In this case, you can use the unpacking operator like in the following code:

In this example, first and second hold the first and second values in numbers , respectively. These values are assigned by position. The * operator packs all the remaining values in the input iterable into rest .

The unpacking operator ( * ) can appear at any position in your series of target variables. However, you can only use one instance of the operator:

The iterable unpacking operator works in any position in your list of variables. Note that you can only use one unpacking operator per assignment. Using more than one unpacking operator isn’t allowed and raises a SyntaxError .

Dropping away unwanted values from the iterable is a common use case for the iterable unpacking operator. Consider the following example:

In Python, if you want to signal that a variable won’t be used, then you use an underscore ( _ ) as the variable’s name. In this example, useful holds the only value that you need to use from the input iterable. The _ variable is a placeholder that guarantees that the unpacking works correctly. You won’t use the values that end up in this disposable variable.

Note: In the example above, if your target iterable is a sequence data type, such as a list or tuple, then it’s best to access its last item directly.

To do this, you can use the -1 index:

Using -1 gives you access to the last item of any sequence data type. In contrast, if you’re dealing with iterators , then you won’t be able to use indices. That’s when the *_ syntax comes to your rescue.

The pattern used in the above example comes in handy when you have a function that returns multiple values, and you only need a few of these values in your code. The os.walk() function may provide a good example of this situation.

This function allows you to iterate over the content of a directory recursively. The function returns a generator object that yields three-item tuples. Each tuple contains the following items:

• The path to the current directory as a string
• The names of all the immediate subdirectories as a list of strings
• The names of all the files in the current directory as a list of strings

Now say that you want to iterate over your home directory and list only the files. You can do something like this:

This code will issue a long output depending on the current content of your home directory. Note that you need to provide a string with the path to your user folder for the example to work. The _ placeholder variable will hold the unwanted data.

In contrast, the filenames variable will hold the list of files in the current directory, which is the data that you need. The code will print the list of filenames. Go ahead and give it a try!

The assignment operator also comes in handy when you need to provide default argument values in your functions and methods. Default argument values allow you to define functions that take arguments with sensible defaults. These defaults allow you to call the function with specific values or to simply rely on the defaults.

As an example, consider the following function:

This function takes one argument, called name . This argument has a sensible default value that’ll be used when you call the function without arguments. To provide this sensible default value, you use an assignment.

Note: According to PEP 8 , the style guide for Python code, you shouldn’t use spaces around the assignment operator when providing default argument values in function definitions.

Here’s how the function works:

If you don’t provide a name during the call to greet() , then the function uses the default value provided in the definition. If you provide a name, then the function uses it instead of the default one.

Up to this point, you’ve learned a lot about the Python assignment operator and how to use it for writing different types of assignment statements. In the following sections, you’ll dive into a great feature of assignment statements in Python. You’ll learn about augmented assignments .

Augmented Assignment Operators in Python

Python supports what are known as augmented assignments . An augmented assignment combines the assignment operator with another operator to make the statement more concise. Most Python math and bitwise operators have an augmented assignment variation that looks something like this:

Note that $ isn’t a valid Python operator. In this example, it’s a placeholder for a generic operator. This statement works as follows:

• Evaluate expression to produce a value.
• Run the operation defined by the operator that prefixes the = sign, using the previous value of variable and the return value of expression as operands.
• Assign the resulting value back to variable .

In practice, an augmented assignment like the above is equivalent to the following statement:

As you can conclude, augmented assignments are syntactic sugar . They provide a shorthand notation for a specific and popular kind of assignment.

For example, say that you need to define a counter variable to count some stuff in your code. You can use the += operator to increment counter by 1 using the following code:

In this example, the += operator, known as augmented addition , adds 1 to the previous value in counter each time you run the statement counter += 1 .

It’s important to note that unlike regular assignments, augmented assignments don’t create new variables. They only allow you to update existing variables. If you use an augmented assignment with an undefined variable, then you get a NameError :

Python evaluates the right side of the statement before assigning the resulting value back to the target variable. In this specific example, when Python tries to compute x + 1 , it finds that x isn’t defined.

Great! You now know that an augmented assignment consists of combining the assignment operator with another operator, like a math or bitwise operator. To continue this discussion, you’ll learn which math operators have an augmented variation in Python.

An equation like x = x + b doesn’t make sense in math. But in programming, a statement like x = x + b is perfectly valid and can be extremely useful. It adds b to x and reassigns the result back to x .

As you already learned, Python provides an operator to shorten x = x + b . Yes, the += operator allows you to write x += b instead. Python also offers augmented assignment operators for most math operators. Here’s a summary:

The Example column provides generic examples of how to use the operators in actual code. Note that x must be previously defined for the operators to work correctly. On the other hand, y can be either a concrete value or an expression that returns a value.

Note: The matrix multiplication operator ( @ ) doesn’t support augmented assignments yet.

Consider the following example of matrix multiplication using NumPy arrays:

Note that the exception traceback indicates that the operation isn’t supported yet.

To illustrate how augmented assignment operators work, say that you need to create a function that takes an iterable of numeric values and returns their sum. You can write this function like in the code below:

In this function, you first initialize total to 0 . In each iteration, the loop adds a new number to total using the augmented addition operator ( += ). When the loop terminates, total holds the sum of all the input numbers. Variables like total are known as accumulators . The += operator is typically used to update accumulators.

Note: Computing the sum of a series of numeric values is a common operation in programming. Python provides the built-in sum() function for this specific computation.

Another interesting example of using an augmented assignment is when you need to implement a countdown while loop to reverse an iterable. In this case, you can use the -= operator:

In this example, custom_reversed() is a generator function because it uses yield . Calling the function creates an iterator that yields items from the input iterable in reverse order. To decrement the control variable, index , you use an augmented subtraction statement that subtracts 1 from the variable in every iteration.

Note: Similar to summing the values in an iterable, reversing an iterable is also a common requirement. Python provides the built-in reversed() function for this specific computation, so you don’t have to implement your own. The above example only intends to show the -= operator in action.

Finally, counters are a special type of accumulators that allow you to count objects. Here’s an example of a letter counter:

To create this counter, you use a Python dictionary. The keys store the letters. The values store the counts. Again, to increment the counter, you use an augmented addition.

Counters are so common in programming that Python provides a tool specially designed to facilitate the task of counting. Check out Python’s Counter: The Pythonic Way to Count Objects for a complete guide on how to use this tool.

The += and *= augmented assignment operators also work with sequences , such as lists, tuples, and strings. The += operator performs augmented concatenations , while the *= operator performs augmented repetition .

These operators behave differently with mutable and immutable data types:

Note that the augmented concatenation operator operates on two sequences, while the augmented repetition operator works on a sequence and an integer number.

Consider the following examples and pay attention to the result of calling the id() function:

Mutable sequences like lists support the += augmented assignment operator through the .__iadd__() method, which performs an in-place addition. This method mutates the underlying list, appending new values to its end.

Note: If the left operand is mutable, then x += y may not be completely equivalent to x = x + y . For example, if you do list_1 = list_1 + list_2 instead of list_1 += list_2 above, then you’ll create a new list instead of mutating the existing one. This may be important if other variables refer to the same list.

Immutable sequences, such as tuples and strings, don’t provide an .__iadd__() method. Therefore, augmented concatenations fall back to the .__add__() method, which doesn’t modify the sequence in place but returns a new sequence.

There’s another difference between mutable and immutable sequences when you use them in an augmented concatenation. Consider the following examples:

With mutable sequences, the data to be concatenated can come as a list, tuple, string, or any other iterable. In contrast, with immutable sequences, the data can only come as objects of the same type. You can concatenate tuples to tuples and strings to strings, for example.

Again, the augmented repetition operator works with a sequence on the left side of the operator and an integer on the right side. This integer value represents the number of repetitions to get in the resulting sequence:

When the *= operator operates on a mutable sequence, it falls back to the .__imul__() method, which performs the operation in place, modifying the underlying sequence. In contrast, if *= operates on an immutable sequence, then .__mul__() is called, returning a new sequence of the same type.

Note: Values of n less than 0 are treated as 0 , which returns an empty sequence of the same data type as the target sequence on the left side of the *= operand.

Note that a_list[0] is a_list[3] returns True . This is because the *= operator doesn’t make a copy of the repeated data. It only reflects the data. This behavior can be a source of issues when you use the operator with mutable values.

For example, say that you want to create a list of lists to represent a matrix, and you need to initialize the list with n empty lists, like in the following code:

In this example, you use the *= operator to populate matrix with three empty lists. Now check out what happens when you try to populate the first sublist in matrix :

The appended values are reflected in the three sublists. This happens because the *= operator doesn’t make copies of the data that you want to repeat. It only reflects the data. Therefore, every sublist in matrix points to the same object and memory address.

If you ever need to initialize a list with a bunch of empty sublists, then use a list comprehension :

This time, when you populate the first sublist of matrix , your changes aren’t propagated to the other sublists. This is because all the sublists are different objects that live in different memory addresses.

Bitwise operators also have their augmented versions. The logic behind them is similar to that of the math operators. The following table summarizes the augmented bitwise operators that Python provides:

The augmented bitwise assignment operators perform the intended operation by taking the current value of the left operand as a starting point for the computation. Consider the following example, which uses the & and &= operators:

Programmers who work with high-level languages like Python rarely use bitwise operations in day-to-day coding. However, these types of operations can be useful in some situations.

For example, say that you’re implementing a Unix-style permission system for your users to access a given resource. In this case, you can use the characters "r" for reading, "w" for writing, and "x" for execution permissions, respectively. However, using bit-based permissions could be more memory efficient:

You can assign permissions to your users with the OR bitwise operator or the augmented OR bitwise operator. Finally, you can use the bitwise AND operator to check if a user has a certain permission, as you did in the final two examples.

You’ve learned a lot about augmented assignment operators and statements in this and the previous sections. These operators apply to math, concatenation, repetition, and bitwise operations. Now you’re ready to look at other assignment variants that you can use in your code or find in other developers’ code.

Other Assignment Variants

So far, you’ve learned that Python’s assignment statements and the assignment operator are present in many different scenarios and use cases. Those use cases include variable creation and initialization, parallel assignments, iterable unpacking, augmented assignments, and more.

In the following sections, you’ll learn about a few variants of assignment statements that can be useful in your future coding. You can also find these assignment variants in other developers’ code. So, you should be aware of them and know how they work in practice.

In short, you’ll learn about:

• Annotated assignment statements with type hints
• Assignment expressions with the walrus operator
• Managed attribute assignments with properties and descriptors
• Implicit assignments in Python

These topics will take you through several interesting and useful examples that showcase the power of Python’s assignment statements.

PEP 526 introduced a dedicated syntax for variable annotation back in Python 3.6 . The syntax consists of the variable name followed by a colon ( : ) and the variable type:

Even though these statements declare three variables with their corresponding data types, the variables aren’t actually created or initialized. So, for example, you can’t use any of these variables in an augmented assignment statement:

If you try to use one of the previously declared variables in an augmented assignment, then you get a NameError because the annotation syntax doesn’t define the variable. To actually define it, you need to use an assignment.

The good news is that you can use the variable annotation syntax in an assignment statement with the = operator:

The first statement in this example is what you can call an annotated assignment statement in Python. You may ask yourself why you should use type annotations in this type of assignment if everybody can see that counter holds an integer number. You’re right. In this example, the variable type is unambiguous.

However, imagine what would happen if you found a variable initialization like the following:

What would be the data type of each user in users ? If the initialization of users is far away from the definition of the User class, then there’s no quick way to answer this question. To clarify this ambiguity, you can provide the appropriate type hint for users :

Now you’re clearly communicating that users will hold a list of User instances. Using type hints in assignment statements that initialize variables to empty collection data types—such as lists, tuples, or dictionaries—allows you to provide more context about how your code works. This practice will make your code more explicit and less error-prone.

Up to this point, you’ve learned that regular assignment statements with the = operator don’t have a return value. They just create or update variables. Therefore, you can’t use a regular assignment to assign a value to a variable within the context of an expression.

Python 3.8 changed this by introducing a new type of assignment statement through PEP 572 . This new statement is known as an assignment expression or named expression .

Note: Expressions are a special type of statement in Python. Their distinguishing characteristic is that expressions always have a return value, which isn’t the case with all types of statements.

Unlike regular assignments, assignment expressions have a return value, which is why they’re called expressions in the first place. This return value is automatically assigned to a variable. To write an assignment expression, you must use the walrus operator ( := ), which was named for its resemblance to the eyes and tusks of a walrus lying on its side.

The general syntax of an assignment statement is as follows:

This expression looks like a regular assignment. However, instead of using the assignment operator ( = ), it uses the walrus operator ( := ). For the expression to work correctly, the enclosing parentheses are required in most use cases. However, there are certain situations in which these parentheses are superfluous. Either way, they won’t hurt you.

Assignment expressions come in handy when you want to reuse the result of an expression or part of an expression without using a dedicated assignment to grab this value beforehand.

Note: Assignment expressions with the walrus operator have several practical use cases. They also have a few restrictions. For example, they’re illegal in certain contexts, such as lambda functions, parallel assignments, and augmented assignments.

For a deep dive into this special type of assignment, check out The Walrus Operator: Python 3.8 Assignment Expressions .

A particularly handy use case for assignment expressions is when you need to grab the result of an expression used in the context of a conditional statement. For example, say that you need to write a function to compute the mean of a sample of numeric values. Without the walrus operator, you could do something like this:

In this example, the sample size ( n ) is a value that you need to reuse in two different computations. First, you need to check whether the sample has data points or not. Then you need to use the sample size to compute the mean. To be able to reuse n , you wrote a dedicated assignment statement at the beginning of your function to grab the sample size.

You can avoid this extra step by combining it with the first use of the target value, len(sample) , using an assignment expression like the following:

The assignment expression introduced in the conditional computes the sample size and assigns it to n . This way, you guarantee that you have a reference to the sample size to use in further computations.

Because the assignment expression returns the sample size anyway, the conditional can check whether that size equals 0 or not and then take a certain course of action depending on the result of this check. The return statement computes the sample’s mean and sends the result back to the function caller.

Python provides a few tools that allow you to fine-tune the operations behind the assignment of attributes. The attributes that run implicit operations on assignments are commonly referred to as managed attributes .

Properties are the most commonly used tool for providing managed attributes in your classes. However, you can also use descriptors and, in some cases, the .__setitem__() special method.

To understand what fine-tuning the operation behind an assignment means, say that you need a Point class that only allows numeric values for its coordinates, x and y . To write this class, you must set up a validation mechanism to reject non-numeric values. You can use properties to attach the validation functionality on top of x and y .

Here’s how you can write your class:

In Point , you use properties for the .x and .y coordinates. Each property has a getter and a setter method . The getter method returns the attribute at hand. The setter method runs the input validation using a try … except block and the built-in float() function. Then the method assigns the result to the actual attribute.

Here’s how your class works in practice:

When you use a property-based attribute as the left operand in an assignment statement, Python automatically calls the property’s setter method, running any computation from it.

Because both .x and .y are properties, the input validation runs whenever you assign a value to either attribute. In the first example, the input values are valid numbers and the validation passes. In the final example, "one" isn’t a valid numeric value, so the validation fails.

If you look at your Point class, you’ll note that it follows a repetitive pattern, with the getter and setter methods looking quite similar. To avoid this repetition, you can use a descriptor instead of a property.

A descriptor is a class that implements the descriptor protocol , which consists of four special methods :

• .__get__() runs when you access the attribute represented by the descriptor.
• .__set__() runs when you use the attribute in an assignment statement.
• .__delete__() runs when you use the attribute in a del statement.
• .__set_name__() sets the attribute’s name, creating a name-aware attribute.

Here’s how your code may look if you use a descriptor to represent the coordinates of your Point class:

You’ve removed repetitive code by defining Coordinate as a descriptor that manages the input validation in a single place. Go ahead and run the following code to try out the new implementation of Point :

Great! The class works as expected. Thanks to the Coordinate descriptor, you now have a more concise and non-repetitive version of your original code.

Another way to fine-tune the operations behind an assignment statement is to provide a custom implementation of .__setitem__() in your class. You’ll use this method in classes representing mutable data collections, such as custom list-like or dictionary-like classes.

As an example, say that you need to create a dictionary-like class that stores its keys in lowercase letters:

In this example, you create a dictionary-like class by subclassing UserDict from collections . Your class implements a .__setitem__() method, which takes key and value as arguments. The method uses str.lower() to convert key into lowercase letters before storing it in the underlying dictionary.

Python implicitly calls .__setitem__() every time you use a key as the left operand in an assignment statement. This behavior allows you to tweak how you process the assignment of keys in your custom dictionary.

Implicit Assignments in Python

Python implicitly runs assignments in many different contexts. In most cases, these implicit assignments are part of the language syntax. In other cases, they support specific behaviors.

Whenever you complete an action in the following list, Python runs an implicit assignment for you:

• Define or call a function
• Define or instantiate a class
• Use the current instance , self
• Import modules and objects
• Use a decorator
• Use the control variable in a for loop or a comprehension
• Use the as qualifier in with statements , imports, and try … except blocks
• Access the _ special variable in an interactive session

Behind the scenes, Python performs an assignment in every one of the above situations. In the following subsections, you’ll take a tour of all these situations.

When you define a function, the def keyword implicitly assigns a function object to your function’s name. Here’s an example:

From this point on, the name greet refers to a function object that lives at a given memory address in your computer. You can call the function using its name and a pair of parentheses with appropriate arguments. This way, you can reuse greet() wherever you need it.

If you call your greet() function with fellow as an argument, then Python implicitly assigns the input argument value to the name parameter on the function’s definition. The parameter will hold a reference to the input arguments.

When you define a class with the class keyword, you’re assigning a specific name to a class object . You can later use this name to create instances of that class. Consider the following example:

In this example, the name User holds a reference to a class object, which was defined in __main__.User . Like with a function, when you call the class’s constructor with the appropriate arguments to create an instance, Python assigns the arguments to the parameters defined in the class initializer .

Another example of implicit assignments is the current instance of a class, which in Python is called self by convention. This name implicitly gets a reference to the current object whenever you instantiate a class. Thanks to this implicit assignment, you can access .name and .job from within the class without getting a NameError in your code.

Import statements are another variant of implicit assignments in Python. Through an import statement, you assign a name to a module object, class, function, or any other imported object. This name is then created in your current namespace so that you can access it later in your code:

In this example, you import the sys module object from the standard library and assign it to the sys name, which is now available in your namespace, as you can conclude from the second call to the built-in dir() function.

You also run an implicit assignment when you use a decorator in your code. The decorator syntax is just a shortcut for a formal assignment like the following:

Here, you call decorator() with a function object as an argument. This call will typically add functionality on top of the existing function, func() , and return a function object, which is then reassigned to the func name.

The decorator syntax is syntactic sugar for replacing the previous assignment, which you can now write as follows:

Even though this new code looks pretty different from the above assignment, the code implicitly runs the same steps.

Another situation in which Python automatically runs an implicit assignment is when you use a for loop or a comprehension. In both cases, you can have one or more control variables that you then use in the loop or comprehension body:

The memory address of control_variable changes on each iteration of the loop. This is because Python internally reassigns a new value from the loop iterable to the loop control variable on each cycle.

The same behavior appears in comprehensions:

In the end, comprehensions work like for loops but use a more concise syntax. This comprehension creates a new list of strings that mimic the output from the previous example.

The as keyword in with statements, except clauses, and import statements is another example of an implicit assignment in Python. This time, the assignment isn’t completely implicit because the as keyword provides an explicit way to define the target variable.

In a with statement, the target variable that follows the as keyword will hold a reference to the context manager that you’re working with. As an example, say that you have a hello.txt file with the following content:

You want to open this file and print each of its lines on your screen. In this case, you can use the with statement to open the file using the built-in open() function.

In the example below, you accomplish this. You also add some calls to print() that display information about the target variable defined by the as keyword:

This with statement uses the open() function to open hello.txt . The open() function is a context manager that returns a text file object represented by an io.TextIOWrapper instance.

Since you’ve defined a hello target variable with the as keyword, now that variable holds a reference to the file object itself. You confirm this by printing the object and its memory address. Finally, the for loop iterates over the lines and prints this content to the screen.

When it comes to using the as keyword in the context of an except clause, the target variable will contain an exception object if any exception occurs:

In this example, you run a division that raises a ZeroDivisionError . The as keyword assigns the raised exception to error . Note that when you print the exception object, you get only the message because exceptions have a custom .__str__() method that supports this behavior.

There’s a final detail to remember when using the as specifier in a try … except block like the one in the above example. Once you leave the except block, the target variable goes out of scope , and you can’t use it anymore.

Finally, Python’s import statements also support the as keyword. In this context, you can use as to import objects with a different name:

In these examples, you use the as keyword to import the numpy package with the np name and pandas with the name pd . If you call dir() , then you’ll realize that np and pd are now in your namespace. However, the numpy and pandas names are not.

Using the as keyword in your imports comes in handy when you want to use shorter names for your objects or when you need to use different objects that originally had the same name in your code. It’s also useful when you want to make your imported names non-public using a leading underscore, like in import sys as _sys .

The final implicit assignment that you’ll learn about in this tutorial only occurs when you’re using Python in an interactive session. Every time you run a statement that returns a value, the interpreter stores the result in a special variable denoted by a single underscore character ( _ ).

You can access this special variable as you’d access any other variable:

These examples cover several situations in which Python internally uses the _ variable. The first two examples evaluate expressions. Expressions always have a return value, which is automatically assigned to the _ variable every time.

When it comes to function calls, note that if your function returns a fruitful value, then _ will hold it. In contrast, if your function returns None , then the _ variable will remain untouched.

The next example consists of a regular assignment statement. As you already know, regular assignments don’t return any value, so the _ variable isn’t updated after these statements run. Finally, note that accessing a variable in an interactive session returns the value stored in the target variable. This value is then assigned to the _ variable.

Note that since _ is a regular variable, you can use it in other expressions:

In this example, you first create a list of values. Then you call len() to get the number of values in the list. Python automatically stores this value in the _ variable. Finally, you use _ to compute the mean of your list of values.

Now that you’ve learned about some of the implicit assignments that Python runs under the hood, it’s time to dig into a final assignment-related topic. In the following few sections, you’ll learn about some illegal and dangerous assignments that you should be aware of and avoid in your code.

Illegal and Dangerous Assignments in Python

In Python, you’ll find a few situations in which using assignments is either forbidden or dangerous. You must be aware of these special situations and try to avoid them in your code.

In the following sections, you’ll learn when using assignment statements isn’t allowed in Python. You’ll also learn about some situations in which using assignments should be avoided if you want to keep your code consistent and robust.

You can’t use Python keywords as variable names in assignment statements. This kind of assignment is explicitly forbidden. If you try to use a keyword as a variable name in an assignment, then you get a SyntaxError :

Whenever you try to use a keyword as the left operand in an assignment statement, you get a SyntaxError . Keywords are an intrinsic part of the language and can’t be overridden.

If you ever feel the need to name one of your variables using a Python keyword, then you can append an underscore to the name of your variable:

In this example, you’re using the desired name for your variables. Because you added a final underscore to the names, Python doesn’t recognize them as keywords, so it doesn’t raise an error.

Note: Even though adding an underscore at the end of a name is an officially recommended practice , it can be confusing sometimes. Therefore, try to find an alternative name or use a synonym whenever you find yourself using this convention.

For example, you can write something like this:

In this example, using the name booking_class for your variable is way clearer and more descriptive than using class_ .

You’ll also find that you can use only a few keywords as part of the right operand in an assignment statement. Those keywords will generally define simple statements that return a value or object. These include lambda , and , or , not , True , False , None , in , and is . You can also use the for keyword when it’s part of a comprehension and the if keyword when it’s used as part of a ternary operator .

In an assignment, you can never use a compound statement as the right operand. Compound statements are those that require an indented block, such as for and while loops, conditionals, with statements, try … except blocks, and class or function definitions.

Sometimes, you need to name variables, but the desired or ideal name is already taken and used as a built-in name. If this is your case, think harder and find another name. Don’t shadow the built-in.

Shadowing built-in names can cause hard-to-identify problems in your code. A common example of this issue is using list or dict to name user-defined variables. In this case, you override the corresponding built-in names, which won’t work as expected if you use them later in your code.

Consider the following example:

The exception in this example may sound surprising. How come you can’t use list() to build a list from a call to map() that returns a generator of square numbers?

By using the name list to identify your list of numbers, you shadowed the built-in list name. Now that name points to a list object rather than the built-in class. List objects aren’t callable, so your code no longer works.

In Python, you’ll have nothing that warns against using built-in, standard-library, or even relevant third-party names to identify your own variables. Therefore, you should keep an eye out for this practice. It can be a source of hard-to-debug errors.

In programming, a constant refers to a name associated with a value that never changes during a program’s execution. Unlike other programming languages, Python doesn’t have a dedicated syntax for defining constants. This fact implies that Python doesn’t have constants in the strict sense of the word.

Python only has variables. If you need a constant in Python, then you’ll have to define a variable and guarantee that it won’t change during your code’s execution. To do that, you must avoid using that variable as the left operand in an assignment statement.

To tell other Python programmers that a given variable should be treated as a constant, you must write your variable’s name in capital letters with underscores separating the words. This naming convention has been adopted by the Python community and is a recommendation that you’ll find in the Constants section of PEP 8 .

In the following examples, you define some constants in Python:

The problem with these constants is that they’re actually variables. Nothing prevents you from changing their value during your code’s execution. So, at any time, you can do something like the following:

These assignments modify the value of two of your original constants. Python doesn’t complain about these changes, which can cause issues later in your code. As a Python developer, you must guarantee that named constants in your code remain constant.

The only way to do that is never to use named constants in an assignment statement other than the constant definition.

You’ve learned a lot about Python’s assignment operators and how to use them for writing assignment statements . With this type of statement, you can create, initialize, and update variables according to your needs. Now you have the required skills to fully manage the creation and mutation of variables in your Python code.

In this tutorial, you’ve learned how to:

• Write assignment statements using Python’s assignment operators
• Work with augmented assignments in Python
• Explore assignment variants, like assignment expression and managed attributes
• Identify illegal and dangerous assignments in Python

Learning about the Python assignment operator and how to use it in assignment statements is a fundamental skill in Python. It empowers you to write reliable and effective Python code.

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About Leodanis Pozo Ramos

Leodanis is an industrial engineer who loves Python and software development. He's a self-taught Python developer with 6+ years of experience. He's an avid technical writer with a growing number of articles published on Real Python and other sites.

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How to solve large scale generalized assignment problem

I am looking for a way to solve a large scale Generalized assignment problem (To be precise, it is a relaxation of the Generalized assignment problem, because the second constraint has $\le$ instead of $=$ ). Here, $m$ is the number of agents and $n$ is the number of tasks. $$ \begin{aligned} &\text{maximize} && \sum_{i}^{m} \sum_{j}^{n} p_{ij}x_{ij} \\\ &\text{subject to} && \sum_{j}^{n} w_{ij}x_{ij} \le t_{i} &&& \forall i \\\ & && \sum_{i}^{m} x_{ij} \le 1 &&& \forall j \\\ & && x_{ij} \in \{0, 1\} \end{aligned} $$

• $m \le 1,000$
• $n \le 10,000,000$
• $p_{ij} \le 1,000$
• $w_{ij} \le 1,000$
• $t_i \le 200,000$
• valid agent-task pair(i.e. number of non zero $p_{ij}$ ) $\le 200,000,000$
• time limit : 6 hours

Generalized assignment problem is NP-hard, so I'm not trying to find an exact solution. Are there any approximation algorithm or heuristic to solve this problem?

Also, are there any other approaches to solving large scale NP-hard problems? For example, I was wondering if it is possible to reduce the number of variables by clustering agents or tasks, but I did not find such a method.

• assignment-problem

• $\begingroup$ All else failing, there is the greedy heuristic: sort the $p_{ij}$ in descending order, then make assignments in that order, tracking the remaining capacity of each agent and skipping assignments that would exceed that capacity. I did not put this in as an answer because it is such a low hanging fruit. $\endgroup$ –  prubin ♦ Commented Jul 29, 2021 at 18:13
• $\begingroup$ The problem that you wrote is not exactly the Generalized Assignment Problem, because the second set of constraints has $\le$ instead of $=$. This makes the problem much easier since finding a feasible solution is not an issue anymore in this case. Is it what you meant to write? $\endgroup$ –  fontanf Commented Jul 29, 2021 at 20:22
• $\begingroup$ @prubin Thank you. If there is no other way, I will use greedy algorithm. $\endgroup$ –  user5966 Commented Jul 30, 2021 at 6:02
• $\begingroup$ @fontanf Yes, I'm trying to solve the relaxation of the Generalized assignment problem. I've added this to the post $\endgroup$ –  user5966 Commented Jul 30, 2021 at 6:11

2 Answers 2

The instances you plan to solve are orders of magnitude larger than the ones from the datasets used in the scientific literature on the Generalized Assignment Problem. The largest instances of the literature have $m = 80$ and $n = 1600$ . Most algorithms designed for these instances won't be suitable for you.

What seems the most relevant in your case are the polynomial algorithms described in "Knapsack problems: algorithms and computer implementations" (Martello et Toth, 1990):

• Greedy: sort all agent-task pairs according to a given criterion, and then assign greedily from best to worst the unassigned tasks. Complexity: $O(n m \log (n m))$
• Regret greedy: for all tasks, sort its assignments according to a given criterion. At each step, assign the task with the greatest difference between its best assignment and its second-best assignment, and update the structures. Complexity: $O(n m \log m + n^2)$

Various sorting criteria have been proposed: pij , pij/wij , -wij , -wij/ti ... -wij and -wij/ti are more suited for the case where all items have to be assigned. In your case pij and pij/wij might yield good results

Then, they propose to try to shift each task once to improve the solution. With at most one shift per task, the algorithms remain polynomial, but you can try more shifts if you have more time.

Note that these algorithms might be optimized if not all pairs are possible, as you indicate in your case.

I have some implementations here for the standard GAP (and a min objective). You can try to play with them to get an overview of what might work or not in your case

You could try using the greedy heuristic to get an initial solution and then try out one of the many neighborhood-search type metaheuristics. I mentioned sorting on $p_{ij}$ in a comment, but it might (or might not) be better to sort on $p_{ij}/w_{ij}$ (or, time permitting, try both and pick the better solution). For improving on the starting solution, GRASP and simulated annealing would be possibilities. Tabu search is popular with some people, but the memory requirements of maintaining a table of tabu solutions might be prohibitive. I'm fond of genetic algorithms, but I think we can rule out a GA (or other "evolutionary" metaheuristic) based on memory considerations. Personally, I'd be tempted to check out GRASP first.

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Assignment as a Minimum Cost Flow Problem

You can use the min cost flow solver to solve special cases of the assignment problem .

In fact, min cost flow can often return a solution faster than either the MIP or CP-SAT solver. However, MIP and CP-SAT can solve a larger class of problems than min cost flow, so in most cases MIP or CP-SAT are the best choices.

The following sections present Python programs that solve the following assignment problems using the min cost flow solver:

• A minimal linear assignment example .
• An assignment problem with teams of workers .

Linear assignment example

This section show how to solve the example, described in the section Linear Assignment Solver , as a min cost flow problem.

Import the libraries

The following code imports the required library.

Declare the solver

The following code creates the minimum cost flow solver.

Create the data

The flow diagram for the problem consists of the bipartite graph for the cost matrix (see the assignment overview for a slightly different example), with a source and sink added.

The data contains the following four arrays, corresponding to the start nodes, end nodes, capacities, and costs for the problem. The length of each array is the number of arcs in the graph.

To make clear how the data is set up, each array is divided into three sub-arrays:

• The first array corresponds to arcs leading out of the source.
• The second array corresponds to the arcs between workers and tasks. For the costs , this is just the cost matrix (used by the linear assignment solver), flattened into a vector.
• The third array corresponds to the arcs leading into the sink.

The data also includes the vector supplies , which gives the supply at each node.

How a min cost flow problem represents an assignment problem

How does the min cost flow problem above represent an assignment problem? First, since the capacity of every arc is 1, the supply of 4 at the source forces each of the four arcs leading into the workers to have a flow of 1.

Next, the flow-in-equals-flow-out condition forces the flow out of each worker to be 1. If possible, the solver would direct that flow across the minimum cost arc leading out of each worker. However, the solver cannot direct the flows from two different workers to a single task. If it did, there would be a combined flow of 2 at that task, which couldn't be sent across the single arc with capacity 1 from the task to the sink. This means that the solver can only assign a task to a single worker, as required by the assignment problem.

Finally, the flow-in-equals-flow-out condition forces each task to have an outflow of 1, so each task is performed by some worker.

Create the graph and constraints

The following code creates the graph and constraints.

Invoke the solver

The following code invokes the solver and displays the solution.

The solution consists of the arcs between workers and tasks that are assigned a flow of 1 by the solver. (Arcs connected to the source or sink are not part of the solution.)

The program checks each arc to see if it has flow 1, and if so, prints the Tail (start node) and the Head (end node) of the arc, which correspond to a worker and task in the assignment.

Output of the program

Here is the output of the program.

The result is the same as that for the linear assignment solver (except for the different numbering of workers and costs). The linear assignment solver is slightly faster than min cost flow — 0.000147 seconds versus 0.000458 seconds.

The entire program

The entire program is shown below.

Assignment with teams of workers

This section presents a more general assignment problem. In this problem, six workers are divided into two teams. The problem is to assign four tasks to the workers so that the workload is equally balanced between the teams — that is, so each team performs two of the tasks.

For a MIP solver solution to this problem see Assignment with Teams of Workers .

The following sections describe a program that solves the problem using the min cost flow solver.

The following code creates the data for the program.

The workers correspond to nodes 1 - 6. Team A consists of workers 1, 3, and 5, and team B consists of workers 2, 4, and 6. The tasks are numbered 7 - 10.

There are two new nodes, 11 and 12, between the source and workers. Node 11 is connected to the nodes for team A, and Node 12 is connected to the nodes for team B, with arcs of capacity 1. The graph below shows just the nodes and arcs from the source to the workers.

The key to balancing the workload is that the source 0 is connected to nodes 11 and 12 by arcs of capacity 2. This means that nodes 11 and 12 (and therefore teams A and B) can have a maximum flow of 2. As a result, each team can perform at most two of the tasks.

Create the constraints

The following shows the output of the program.

Team A is assigned tasks 9 and 10, while team B is assigned tasks 7 and 8.

Note that the min cost flow solver is faster for this problem than the MIP solver , which takes around 0.006 seconds.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-09-21 UTC.

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Python3 code for solving a generalized assignment problem.

stinodego/GeneralizedAssignment

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THIS CODE IS NOT BEING MAINTAINED.

Feel free to use this code for whatever purpose you'd like. I will not offer any support.

GeneralizedAssignment

This Python3 code may be used for solving an instance of the generalized assignment problem.

The generalized assignment problem

The generalized assignment problem is described quite well on Wikipedia .

This code actually allows for further generalization, multiple agents to perform a single task (regulated by a task budget).

The implementation

The implementation is a simple depth-first search algorithm. Therefore, it does not work well for very large problems.

The depth-first search expands most promising nodes first. True maximum assignment is guaranteed when algorithm is allowed to complete. Otherwise, the assignment printed last may be used as a best guess.

The code makes use of frozendict to keep track of the set of assignments. Simply install it using the following command: python -m pip install frozendict

Running the code

Solving your assignment problem is easy. Just specify your assignment problem at the bottom of the file, then run it. An example problem specification is given, to make clear what syntax is expected.

The code offers a few features:

• Optional 'hard assignment' initializes the assignment with certain agents assigned to certain tasks
• Optional 'fair' parameter maximizes the profits related to the least profitable task (and thus equalizes the profits among tasks).
• Optional 'complete' parameter requires agents and tasks to fully use their budgets.
• 'verbose' option prettily prints the assignment information after the code finishes. May be turned off.
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New to python assignments

Hi ! I’m new to python and all of this, if anyone could help me understand what to do i’d appreciate it Assignment: You will be developing a Python program to process an unknown number of exam scores, using a loop.

The exam scores are entered by the user at the keyboard, one score at a time

Exam scores need to be at least zero and at most 100

• if an exam score is at least 90, increment A_count by 1
• if it’s at least 80 and less than 90, increment B_count by 1
• if it is at least 70, and less than 80, increment C_count by 1
• if it’s at least 60 and less than 70, increment D_count by 1
• if it’s at least 0 and less than 60, increment F_count by 1

Once an exam score less than 0 or greater than 100 is entered, then report each of the above counts, one per line, and each along with an appropriate message

Stop the program

I don’t follow; what exactly is unclear about the assignment?

would I just be typing this into the program? Sorry there was more to the assignment but it wouldn’t let me upload it I just assumed that was the gist.

The program should ask you for the exam scores, which you type in one at a time. You indicate when you’ve finished all by typing in a score that is less than 0 or greater than 100.

here are some basic pointers:

You will be developing a Python program to process an unknown number of exam scores, using a loop.

• This implies a need for a while loop; i.e., you do not know the number of scores entered beforehand so we need to keep running until a condition is met. The condition being when you enter anything above 100 or below 0.

The exam scores are entered by the user at the keyboard, one score at a time.

This implies an input such as this: score_entered = int(input('Enter score: '))

Note that you have to append the prefix ‘int’ to the input statement as input outputs type strings. The int converts a string to a type integer which we need for comparison purposes.

if an exam score is at least 90, increment A_count by 1 if it’s at least 80 and less than 90, increment B_count by 1 if it is at least 70, and less than 80, increment C_count by 1 if it’s at least 60 and less than 70, increment D_count by 1 if it’s at least 0 and less than 60, increment F_count by 1

• This implies creating five different variables for each potential conditional statement. Be sure to initialize them to zero before the program starts to start a fresh count. Increment each variable by 1 each time that a conditional statement is met.

Once an exam score less than 0 or greater than 100 is entered, then report each of the above counts, one per line, and each along with an appropriate message.

This is the conditional statement by which your program will exit the program. This ties to the very first item described above. Thus, there should be a total of six conditional statements.

Once this conditional statement is satisfied, it will exit the program and print out the results. This is where the print statements come in as a summary to tabulate the results for the user.

Make sure to read the assignment requirements carefully and compare it with the topics that are currently being discussed in the course as well as with material that has been covered up to this point. You should be able to put two and two together as they say and quickly come up with a potential solution.

It’s hard to understand what you mean. First off, I can’t guess what you’re referring to by “this”. But more importantly: we aren’t in your class, so we don’t know what you’re expected to have learned by now; and we aren’t you, so we don’t know what you actually have learned so far.

So - thus far, have you been expected to write any Python programs, at all? What programs did you write, and what difficulties did you encounter with them? Before this assignment, what lessons were provided? Did you find anything specific confusing about the material?

If exit() the last statement, it’s not needed, because the program will stop at the end anyway.

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Solving the assignment problem with specific constraints

Imagine the following data (the code to reproduce all the outputs is at the end):

I'd like to swap the cars to get something like:

Now this is a typical assignment problem that was in the case above solved randomly, i.e. by cost matrix set to 0 in all cases.

What I'm interested in are the outcomes. In the above case, the solution yields the following stats:

That is to say, 1/4 of swaps had an equal horsepower, etc.

Here is my question: How to solve such assignments by setting constraints on what exactly should be the outcome statistics directly, without the trial-and-error approach with setting the costs?

For instance, what if I would like to have a solution where safety has more than 0.20 match, and year at least 0.10, like below?

Of course I could just set the cost matrix to a lower number in all cases where safety of cars is equal.

But is there a way to influence the result by directly setting the constraint on what should be the outcome statistics?

Perhaps there is a way to optimize the costs in order to arrive at the desired result?

I hope the examples above are sufficient, this is my first question so please let me know if I need to provide something more.

The code is in R , but I have also added the tag Python as I don't really mind the language of possible solutions.

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• mathematical-optimization

• Welcome to SO! Let me make sure I understand your question correctly. Are you saying: For each car type, choose a match, so that at least a % of the pairs have the same HP as each other, at least b % of the pairs have the same year as each other, and at least c % of the pairs have the same safety as each other? –  LarrySnyder610 Commented May 23, 2019 at 21:12
• Thank you! Exactly, that's a very good formulation. –  miscellaneous Commented May 23, 2019 at 21:13
• I would formulate this as an integer programming problem. How familiar are you with IP? –  LarrySnyder610 Commented May 23, 2019 at 21:14
• Not at all I must admit! Do you have some examples of similar types of problems and their solutions? –  miscellaneous Commented May 23, 2019 at 21:16
• Well in that case it would be a whole new field for you to learn. I will get you started on a formulation for this problem and you can decide whether you want to keep going with it or try another approach. –  LarrySnyder610 Commented May 23, 2019 at 21:18

Here is a partial formulation of this problem as an integer programming (IP) problem.

Let I be the set of car types. For car types i and j in I , let:

• h[i,j] = 1 if cars i and j have the same horsepower
• y[i,j] = 1 if cars i and j have the same year
• and similarly for s[i,j] (safety)

These are parameters , meaning inputs to your model. (You'll need to write code to calculate these binary quantities based on your data table.)

Now introduce the following decision variables , i.e., variables that your IP model will choose values of:

• x[i,j] = 1 if we assign car type j as type i 's match

Now, normally an IP has an objective function that we want to minimize or maximize. In this case, there is no objective function -- you just want to find a set of matches that satisfies your constraints. So your objective function can just be:

Here is the first constraint. It says: At least a of the matches must have the same horsepower. ( a is a fraction.) The left-hand side is the number of matches that have the same horsepower: For each pair of car types i and j , if j is assigned as i 's match and they have the same horsepower, count a 1; otherwise, count a 0. The right-hand side is the number of matches you want, i.e., a fraction of the whole set.

Now formulate similar constraints for the other categories.

Next, you need a constraint that says each car type i must be assigned to exactly one car type j :

Finally, you need constraints saying that the decision variables are binary:

Now, in terms of solving this thing, you will need to either use a mathematical modeling language like AMPL or GAMS, or a package like PuLP for Python.

I hope this helps. I might have bitten off more than you can chew here.

• Thanks a lot! This should get me started indeed. I will wait a bit to see if there are any other answers, otherwise I accept yours. –  miscellaneous Commented May 23, 2019 at 22:01
• No worries, that’s totally fine. –  LarrySnyder610 Commented May 23, 2019 at 22:08
• 1 Agreed this is a good fit for IP. Of note in this construction of the problem, when you are applying constraints to the outcome, you will likely get the first answer that satisfies your criteria, not the best/optimal answer because you don't have an objective function. Further, it isn't clear how you would set these constraints. How would you know beforehand that 20% horsepower match is achievable? This setup could fail to produce any results. I would make an objective function. However, if the problem is truly this small, just enumerate all the options (in this case 8!) and sort. –  AirSquid Commented May 24, 2019 at 1:49

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