# Constraints definition and system solving

A system within Kiwi is defined by a set of constraints, which may be either equalities or inequalities (limited to >= and <=, as strict inequalities are not supported). Each constraint can be assigned a specific ‘strength’, indicating its relative importance in the problem-solving process. The subsequent sections will delve into the methods of defining these constraints and extracting results from the solver.

## Defining variables and constraints

The initial step involves defining variables, which represent
the values that the solver aims to determine. These variables are
encapsulated by `Variable`

objects. The creation of these objects
can be accomplished as follows:

```
from kiwisolver import Variable
x1 = Variable('x1')
x2 = Variable('x2')
xm = Variable('xm')
```

```
#include <kiwi/kiwi.h>
using namespace kiwi
Variable x1("x1");
Variable x2("x2");
Variable xm("xm");
```

Note

Naming your variables is not mandatory but it is recommended since it will help the solver in providing more meaningful error messages.

Now that we have some variables we can define our constraints.

```
constraints = [x1 >= 0, x2 <= 100, x2 >= x1 + 10, xm == (x1 + x2) / 2]
```

```
Constraint constraints[] = { Constraint {x1 >= 0},
Constraint {x2 <= 100},
Constraint {x2 >= x1 + 20},
Constraint {xm == (x1 + x2) / 2}
};
```

Next, add these variables to the solver, an instance of `Solver`

:

```
from kiwisolver import Solver
solver = Solver()
for cn in constraints:
solver.addConstraint(cn)
```

```
Solver solver;
for(auto& constraint : constraints)
{
solver.addConstraint(constraint);
}
```

Note

- You can start adding constraints to the solver without creating all your
variables first.

So far, we have defined a system representing three points on the segment [0, 100], with one of them being the middle of the others, which cannot get closer than 10. All those constraints have to be satisfied; in the context of Cassowary, they are required constraints.

Note

Cassowary (and Kiwi) allows for redundant constraints, which means even with two constraints (x == 10, x + y == 30) being equivalent to a third one (y == 20), all three can be added to the solver without issues.

However, it is advisable not to add the same constraint multiple times in the same form to the solver.

## Managing constraints strength

Cassowary also supports constraints that are not required. Those are only
respected on a best effort basis. To express that a constraint is not required
we need to assign it a *strength*. Kiwi specifies three standard strengths
besides the “required” strength: strong, medium, weak. A strong constraint
will always win over a medium constraint, which in turn will always override
a weak constraint [1] .

In our example, let’s assume x1 would like to be at 40, without this being a requirement. This is translated as follows:

```
solver.addConstraint((x1 == 40) | "weak")
```

```
solver.addConstraint(x1 == 40 | strength::weak);
```

## Adding edit variables

So far our system is pretty static; we have no way of trying to find solutions for a particular value of xm, let’s say. This is a problem. In a real application (e.g. a GUI layout), we would like to find the size of the widgets based on the top window but also react to the window resizing, so actually adding and removing constraints all the time wouldn’t be optimal. And there is a better way: edit variables.

Edit variables are variables for which you can suggest values. Edit variables have a strength which can be at most strong (the value of a edit variable can never be required).

For the sake of our example, we will make “xm” editable:

```
solver.addEditVariable(xm, 'strong')
```

```
solver.addEditVariable(xm, strength::strong);
```

Once a variable has been added as an edit variable, you can suggest a value for it and the solver will try to solve the system with it.

```
solver.suggestValue(xm, 60)
```

```
solver.suggestValue(xm, 60);
```

This would give the following solution: `xm == 60, x1 == 40, x2 == 80`

.

## Solving and updating variables

Kiwi solves the system each time a constraint is added or removed, or a new value is suggested for an edit variable. Solving the system each time makes for faster updates and allows to keep the solver in a consinstent state. However, the variable values are not updated automatically, and you need to ask the solver to perform this operation before reading the values, as illustrated below:

```
solver.suggestValue(xm, 90)
solver.updateVariables()
print(xm.value(), x1.value(), x2.value())
```

```
solver.suggestValue(xm, 90);
solver.updateVariables();
std::cout << xm.value() << ", " << x1.value() << ", " << x2.value();
```

This last update creates an infeasible situation by pushing x2 further than
100, if we keep x1 where it would like to be. As a consequence, we get the
following solution: `xm == 90, x1 == 80, x2 == 100`

Note

To determine if a non-required constraint was violated when solving the system,
you can use the constraint’s `violated`

method.

Added in version 1.4.