Layout isn't a simple thing for a computer to solve and

many people have attempted to solve the problem in different ways.

Back in 2001, two computer scientists at the University of Washington,

Greg Badros and Alan Borning, along with Peter Stuckey

of the University of Melbourne, wrote a paper detailing their approach and

called it The Cassowary Linear Arithmetic Constraint Solving Algorithm.

Cassowary, according to the authors, is an incremental constraint solving toolkit

that efficiently solves systems of linear equalities and equalities.

Auto Layout is actually built on top of this algorithm, and

is pretty good at solving the layout issues in an efficient and rapid manner.

Auto Layout was introduced in 2012 on iOS, and

is a constraint-based, descriptive layout system.

Much of this system is still based on the original premise of

the Cassowary Algorithm,

in that relationships between views can be expressed as linear equations.

Using Auto Layout, rather than specifying coordinate values, we can describe

the position of a view in relation to its superview or neighboring views.

We can say that we want a view or label to be centered horizontally in its superview.

And we want that label to be some distance away from the bottom of its superview.

In Cassaway, and as an extension, Auto Layout,

these relationships can be expressed as a series of linear equations.

For the first description, where we want the label to always be in the horizontal

center of the superview, we can write an equation that looks something like this.

label.centerX = superview.centerX.

And similarly for

the second description, we can define a linear equation that looks like this.

We can say label.bottom = superview.bottom- {padding}.

In Auto Layout, these descriptive linear equations are what we call constraints.

A constraint provides a fluent layout language that allows

us to define relationships between views in terms of linear equations.

While it might seem like there are many different ways to express these

relationships, they all boil down to a simple equation.

The As in this equation refer to view attributes.

What are attributes?

Don't worry, we'll get to that.

If we generically call a view an item, our equation looks like this.

Constraints are relationships described either between attributes on a view,

or between attributes on two different views.

So A1 can be an attribute on view 1, and A2 an attribute on view 2.

A2 can also be an attribute on view 1.

The M in this equation refers to a multiplier.

This allows us to modify the relationship by a certain amount.

The C refers to a constant value, and

is used to offset the equation by a certain amount.

Now, people often joke about the fact that the only thing you can change once

a constraint is created is this value that's called constant.

So this is essentially the basic premise or

building block underlying Auto Layout, a constraint equation.