csp assignment operator definition

AP CSP: Unit 1: Operators

... are symbols which you can use to modify or combine values. In addition to having operators that perform basic mathematical operations like addition, subtraction, multiplication, and division, C also has operators that perform other functions: like finding the remainder when dividing, or updating the value of a variable.

... is called an assignment operator. It looks like a mathematic equal sign, but it has a different function. The assignment operator makes a value, equal to whatever's on the right side of the equals sign:. Ex. e = f + 1; (if f was the value 1 then this would return the value 2) provide a variety of ways to update the value of a variable.

...is called the modulus operator, which gives us the remainder when the number on the left of the operator is divided by the number on the right. Ex. int f = 13 % 3; would return the value 1.

will set a variable to its existing value divided by some other number.

will set a variable to its existing value minus some other number.

will set a variable to its existing value multiplied by some other number.

will set a variable to its existing value plus some other number.

The arithmetic operator which adds two numbers, (-), (*) , (/) .

The arithmetic operator which divides one number by another (Ints can only store whole numbers, so if you divide 10/3 you will receive the int 3. If you want to receive the value with decimal points you can use the data type float).

The arithmetic operator which multiplies two numbers

The arithmetic operator which subtracts one number from another

arithmetic operators

C's ... perform mathematical functions on numbers.

assignment operators

C's ... provide a variety of ways to update the value of a variable

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Assignment Operators in Programming

Assignment operators in programming are symbols used to assign values to variables. They offer shorthand notations for performing arithmetic operations and updating variable values in a single step. These operators are fundamental in most programming languages and help streamline code while improving readability.

Table of Content

What are Assignment Operators?

• Types of Assignment Operators
• Assignment Operators in C
• Assignment Operators in C++
• Assignment Operators in Java
• Assignment Operators in Python
• Assignment Operators in C#
• Assignment Operators in JavaScript
• Application of Assignment Operators

Assignment operators are used in programming to  assign values  to variables. We use an assignment operator to store and update data within a program. They enable programmers to store data in variables and manipulate that data. The most common assignment operator is the equals sign ( = ), which assigns the value on the right side of the operator to the variable on the left side.

Types of Assignment Operators:

• Simple Assignment Operator ( = )
• Addition Assignment Operator ( += )
• Subtraction Assignment Operator ( -= )
• Multiplication Assignment Operator ( *= )
• Division Assignment Operator ( /= )
• Modulus Assignment Operator ( %= )

Below is a table summarizing common assignment operators along with their symbols, description, and examples:

Assignment Operators in C:

Here are the implementation of Assignment Operator in C language:

Assignment Operators in C++:

Here are the implementation of Assignment Operator in C++ language:

Assignment Operators in Java:

Here are the implementation of Assignment Operator in java language:

Assignment Operators in Python:

Here are the implementation of Assignment Operator in python language:

Assignment Operators in C#:

Here are the implementation of Assignment Operator in C# language:

Assignment Operators in Javascript:

Here are the implementation of Assignment Operator in javascript language:

Application of Assignment Operators:

• Variable Initialization : Setting initial values to variables during declaration.
• Mathematical Operations : Combining arithmetic operations with assignment to update variable values.
• Loop Control : Updating loop variables to control loop iterations.
• Conditional Statements : Assigning different values based on conditions in conditional statements.
• Function Return Values : Storing the return values of functions in variables.
• Data Manipulation : Assigning values received from user input or retrieved from databases to variables.

Conclusion:

In conclusion, assignment operators in programming are essential tools for assigning values to variables and performing operations in a concise and efficient manner. They allow programmers to manipulate data and control the flow of their programs effectively. Understanding and using assignment operators correctly is fundamental to writing clear, efficient, and maintainable code in various programming languages.

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Constraint Satisfaction Problems

Learning objectives.

Describe definition of CSP problems and its connection with general search problems

Formulate a real-world problem as a CSP

Describe and implement backtracking algorithm

Define arc consistency

Describe and implement forward checking and AC-3

Explain the differences between MRV and LCV heuristics

Understand the complexity of general binary CSP and tree-structured binary CSP

Discuss how ethical problems can be approached using CSP concepts/formulation

Search and CSPs

Search serves two main purposes:

planning: sequence of actions

the path to the goal is most important

paths and costs have various depths

heuristics give problem-specific guidance

identification: assignments to variables

the goal is the most important (not the path)

all paths are are at the same depths (for some formulations)

Previously, when we learned about search algorithms, we were primarily concerned with finding a path from our start state to our goal state. Now, we will look into constraint satisfaction problems (CSPs) , which are primarily identification problems.

Standard Search Problems have

State: arbitrary data structure

Goal Test: any function over states

Successor Function: anything

Specifications for CSPs

State: variables \(X_i\) with values from domain \(D_i\)

Goal Test: set of constraints specifying allowable combinations of values for subsets of variables

CSP Formulation

Whenever we formulate a CSP, we need to identify the following: set of variables \(X\) , set of domains \(D\) , and set of constraints \(C\) .

Variable \(X_i\) : Factored representation of each state.

Domain \(D_i\) : Set of allowable values for variable \(X_i\) .

Constraint \(C_i\) : Consists of tuple of variables that participate in the constraint, and relation that defines the values that those variables can take on.

There are a variety of types of constraints:

Unary Constraints : Involve a single variable. It is equivalent to reducing domains. For map coloring it would be \(A \neq Green\)

Binary Constraints : Involve pairs of variables. For map coloring, an example would be \(A \neq B\)

Higher Order Constraints : Involve three or more variables

Variables: WA, NT, Q, NSW, V, SA, T

Domain: \(\{\) red, green, blue \(\}\)

Constraints: adjacent regions must have different colors

Explicit Constraint Example: (WA, NT) \(\in \{\) (red, green), (red, blue), (blue, green), (blue, red), (green, red), (green, blue) \(\}\)

Implicit Constraint Example: WA \(\neq\) NT

Solution: assignments satisfying all constraints

Example: \(\{\) WA=red, NT=green, Q=red, NSW=greeen, V=red, SA=blue, T=green \(\}\)

Constraint Graph

In a binary CSP problem, each constraint relates (at most) two variables. We can represent this problem as a binary constraint graph , where

Each node corresponds to a variable

An edge between any two nodes indicates a constraint between them

General purpose CSP algorithms take advantage of the graph's structure to speed up search.

Consider our CSP problem formulation for the map coloring example from earlier. The corresponding constraint graph is below:

Note that node T (corresponding to Tasmania) has no edges connecting it to other nodes in the CSP graph. This indicates that coloring Tasmania is an independent subproblem.

Algorithms for Solving CSPs

Naive algorithm.

Our first attempt at formulating a CSP into a search problem might be as follows:

States are partial assignments of the variables. Full assignments are goal states.

Actions involve adding an assignment var = value , where var is an unassigned variable, to a partial assignment. An action is legal if it does not result in a assignment that violates constraints.

We could then run any one of our standard search algorithms to find a satisfying assignment.

Let's conduct a cost analysis. Let \(n\) be the number of variables, and \(d\) be the size of the domain. At depth 0, there is a branching factor of \(nd\) , as we choose among \(n\) variables to assign, then choose 1 of \(d\) values. At depth 1 there is a branching factor of \((n - 1)d\) , as there is one less variable to assign. At depth i we then have a branching factor of \((n - i)d\) . To choose among the leaves of the search tree, we have the following multi-step process:

Then the number of leaves is \(\prod_{i=0}^{n-1}\big((n - i)d\big) = d^n\prod_{i=0}^{n-1}(n - i) = n!d^n\) . But wait - the number of solutions to this CSP should be bounded by \(d^n\) , the number of ways to assign \(n\) variables with each having \(d\) options. Many of these goal states are equivalent because the order of assignment of variables doesn't matter - actions in this domain are commutative. With this observation we can restrict the search to choosing between \(d\) options to assign to a single variable at each level, giving us the expected number of leaves \(d^n\) .

Backtracking Search

The following algorithm formalizes running depth-first search with the more restrictive formulation we arrived at in the last section. We repeatedly choose an unassigned variable and cycle through possible assignments of that variable. If no consistent assignments can be found of the remaining variables for any assignment of the considered variable, we indicate failure, backtracking to the previous assignment.

Since backtracking is an uninformed algorithm for solving CSPs, it can be slow. We can solve CSPs faster by considering the following:

Filtering: By filtering out inconsistent values from domains, can we detect inevitable failure early?

Ordering: Which variables should be assigned next ( select_unassigned_variable )? In what order should its values be tried ( order_domain_values )?

Structure: Can we exploit the problem structure?

Filtering Algorithms

The main idea behind filtering algorithms for CSPs are to

keep track of domains for unassigned variables

eliminate bad domain values (i.e., values that violate constraints) along the way

Most filtering algorithms try to achieve arc consistency .

Note that filtering algorithms are added within the backtracking search algorithm above.

Let \(A\) and \(B\) be unassigned variables in our CSP with a binary constraint between them.

An arc \(A \rightarrow B\) is consistent if and only if for all values \(a\) remaining in \(A\) 's domain, there's some corresponding value \(b\) remaining in \(B\) 's domain such that \(a\) and \(b\) satisfy all constraints between \(A\) and \(B\) . We refer to \(A\) as the tail, and \(B\) as the head. If arc consistency is not satisfied at some point in our process of solving the CSP, we enforce it by removing values from the current domain of \(A\) until the arc is consistent.

Complexity : Enforcing arc consistency for a single arc \(A \rightarrow B\) is \(O(d^2)\) . Recall from the pseudocode that in the context of backtracking search, we would run a filtering algorithm on our current CSP after assigning a value to a variable. We'll now delve into two specific filtering algorithms.

Forward Checking

Forward checking enforces consistency of the arcs corresponding to a single variable , i.e., the arcs between that variable and its immediate neighbors.

Note: Since this forward checking pseudocode take as input a single variable, in the context of the backtracking search algorithm, we would likely call

These are minor implementation details that aren't super important. The main shortcoming of forward checking is it does not provide early detection for all failures which may be induced by a domain change/assignment.

Complexity : A single run of forward checking (i.e., for a single variable/a single call to the above function) is \(O(nd^2)\) .

Forward checking only checks arcs pointing to newly assigned variables. AC-3 checks even more. AC-3 enforces consistency of arcs corresponding to a particular variable, and then enforces arc consistency for any variables whose domains were affected in the process. This effectively propagates any domain changes outward from the original variable (for which consistency was enforced) to its neighbors, neighbors' neighbors, etc.

Note that we could alternatively also pass in a single variable \(X\) to AC-3 (like in the provided forward checking implementation), and initialize the queue with just the incoming arcs to \(X\) instead of all arcs in the CSP.

Complexity : A single run of AC-3 is \(O(n^2d^3)\) .

We start with all \(O(n^2)\) arcs on the queue.

The number of arcs added to the queue while running AC-3 is bounded by \(O(n^2d)\) . This is because at most we can remove \(O(nd)\) values from domains ( \(n\) total variables, each with domain of size \(d\) ), and would add \(O(n)\) arcs after each removal.

Enforcing arc consistency of each arc is \(O(d^2)\) .

Total: \(O(n^2d^3)\)

When it comes to picking which variables to assign and which values to assign to them, we have two main heuristics for prioritizing the options. Recall that variables refer to the factored representation of each state, and values refer to the set of allowable values for each variable. Minimum Remaining Values: pick the variable with the smallest number of remaining assignable values.

Motivation: fail-fast approach. We need to assign all variables a value at some point, so we might as well do the harder variables first. This heuristic allows us to prune the search tree faster and detect whether we need to backtrack earlier.

Least Constraining Value: pick the value that constrains the smallest number of the chosen variable's neighbors.

Motivation: we want just one solution. We don't need to try all combinations of values, just ones that are more likely to be part of a valid solution.

Tree-Structured CSPs

While heuristics and filtering generally help us increase the efficiency of solving a CSP, the worst-case time complexity of solving a CSP is still \(O(d^n)\) . However, if the binary constraint graph of the CSP is tree-structured (i.e., doesn’t have any cycles), we can solve it in \(O(nd^2)\) time as follows.

Complexity : \(O(nd^2)\)

remove backward: \(O(nd^2)\) ( \(O(d^2)\) per arc for \(O(n)\) arcs)

assign forward: \(O(nd)\) ( \(O(d)\) per node and \(O(n)\) nodes)

Properties :

After backward pass, all root-to-leaf arcs are consistent

During backward pass, every node except the root was visited once

When \(X_i\) was visited, we enforced arc-consistency of \(Parent(X_i) \rightarrow X_i\) by reducing the domain of \(Parent(X_i)\) .

By definition, for every value in the reduced domain of \(Parent(X_i)\) , there was some \(x\) in the domain of \(X_i\) which could be assigned without violating the constraint involving \(Parent(X_i)\) and \(X_i\) .

After that, \(Parent(X_i) \rightarrow X_i\) kept consistent until the end of the backward pass.

The domain of \(X_i\) would not have been reduced after \(X_i\) is visited because \(X_i\) ’s children were visited before \(X_i\) .

The domain of \(Parent(X_i)\) could have been reduced further. Arc consistency would still hold by definition.

If root-to-leaf arcs are consistent, forward assignment will not backtrack.

Suppose we have successfully reached node \(X_i\)

In the current step, the potential failure can only be caused by the constraint between \(X_i\) and \(Parent(X_i)\) , since all other variables that are in a same constraint of \(X_i\) have not assigned a value yet

Due to the arc consistency of \(Parent(X_i) \rightarrow X_i\) , \(\exists x\) in the domain of \(X_i\) that does not violate the constraint

We can successfully assign a value to \(X_i\) and go to the next node

By induction, we can successfully assign a value to a variable in each step of the algorithm

A solution is found in the end

This algorithm does not work with cycles in the constraint graph

We can still apply the algorithm (choose an arbitrary order and draw "forward" arcs)

Remove backward: We can enforce all arcs pointing to \(X_i\) when \(X_i\) is visited. The complexity is \(O(n^2d^2)\)

After backward pass, the reduced domains do not exclude any solution and all the forward arcs are consistent

Assign forward: In a step of assigning values, we may encounter failure because we need to make sure the constraints involving the current node and any parent node is satisfied, which could be impossible. Therefore, we may need to backtrack.

cppreference.com

Copy assignment operator.

A copy assignment operator is a non-template non-static member function with the name operator = that can be called with an argument of the same class type and copies the content of the argument without mutating the argument.

[ edit ] Syntax

For the formal copy assignment operator syntax, see function declaration . The syntax list below only demonstrates a subset of all valid copy assignment operator syntaxes.

[ edit ] Explanation

The copy assignment operator is called whenever selected by overload resolution , e.g. when an object appears on the left side of an assignment expression.

[ edit ] Implicitly-declared copy assignment operator

If no user-defined copy assignment operators are provided for a class type, the compiler will always declare one as an inline public member of the class. This implicitly-declared copy assignment operator has the form T & T :: operator = ( const T & ) if all of the following is true:

• each direct base B of T has a copy assignment operator whose parameters are B or const B & or const volatile B & ;
• each non-static data member M of T of class type or array of class type has a copy assignment operator whose parameters are M or const M & or const volatile M & .

Otherwise the implicitly-declared copy assignment operator is declared as T & T :: operator = ( T & ) .

Due to these rules, the implicitly-declared copy assignment operator cannot bind to a volatile lvalue argument.

A class can have multiple copy assignment operators, e.g. both T & T :: operator = ( T & ) and T & T :: operator = ( T ) . If some user-defined copy assignment operators are present, the user may still force the generation of the implicitly declared copy assignment operator with the keyword default . (since C++11)

The implicitly-declared (or defaulted on its first declaration) copy assignment operator has an exception specification as described in dynamic exception specification (until C++17) noexcept specification (since C++17)

Because the copy assignment operator is always declared for any class, the base class assignment operator is always hidden. If a using-declaration is used to bring in the assignment operator from the base class, and its argument type could be the same as the argument type of the implicit assignment operator of the derived class, the using-declaration is also hidden by the implicit declaration.

[ edit ] Implicitly-defined copy assignment operator

If the implicitly-declared copy assignment operator is neither deleted nor trivial, it is defined (that is, a function body is generated and compiled) by the compiler if odr-used or needed for constant evaluation (since C++14) . For union types, the implicitly-defined copy assignment copies the object representation (as by std::memmove ). For non-union class types, the operator performs member-wise copy assignment of the object's direct bases and non-static data members, in their initialization order, using built-in assignment for the scalars, memberwise copy-assignment for arrays, and copy assignment operator for class types (called non-virtually).

[ edit ] Deleted copy assignment operator

An implicitly-declared or explicitly-defaulted (since C++11) copy assignment operator for class T is undefined (until C++11) defined as deleted (since C++11) if any of the following conditions is satisfied:

• T has a non-static data member of a const-qualified non-class type (or possibly multi-dimensional array thereof).
• T has a non-static data member of a reference type.
• T has a potentially constructed subobject of class type M (or possibly multi-dimensional array thereof) such that the overload resolution as applied to find M 's copy assignment operator
• does not result in a usable candidate, or
• in the case of the subobject being a variant member , selects a non-trivial function.

[ edit ] Trivial copy assignment operator

The copy assignment operator for class T is trivial if all of the following is true:

• it is not user-provided (meaning, it is implicitly-defined or defaulted);
• T has no virtual member functions;
• T has no virtual base classes;
• the copy assignment operator selected for every direct base of T is trivial;
• the copy assignment operator selected for every non-static class type (or array of class type) member of T is trivial.

A trivial copy assignment operator makes a copy of the object representation as if by std::memmove . All data types compatible with the C language (POD types) are trivially copy-assignable.

[ edit ] Eligible copy assignment operator

Triviality of eligible copy assignment operators determines whether the class is a trivially copyable type .

[ edit ] Notes

If both copy and move assignment operators are provided, overload resolution selects the move assignment if the argument is an rvalue (either a prvalue such as a nameless temporary or an xvalue such as the result of std::move ), and selects the copy assignment if the argument is an lvalue (named object or a function/operator returning lvalue reference). If only the copy assignment is provided, all argument categories select it (as long as it takes its argument by value or as reference to const, since rvalues can bind to const references), which makes copy assignment the fallback for move assignment, when move is unavailable.

It is unspecified whether virtual base class subobjects that are accessible through more than one path in the inheritance lattice, are assigned more than once by the implicitly-defined copy assignment operator (same applies to move assignment ).

See assignment operator overloading for additional detail on the expected behavior of a user-defined copy-assignment operator.

[ edit ] Example

[ edit ] defect reports.

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

[ edit ] See also

• converting constructor
• copy constructor
• copy elision
• default constructor
• aggregate initialization
• constant initialization
• copy initialization
• default initialization
• direct initialization
• initializer list
• list initialization
• reference initialization
• value initialization
• zero initialization
• move assignment
• move constructor
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CSP Unit 4: Variables, Conditionals, and Functions

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