# `Yog.Layout.Random`
[🔗](https://github.com/code-shoily/yog_ex/blob/v1.0.0/lib/yog/layout/random.ex#L1)

Random layout algorithm for positioning graph nodes in Elixir.

Positions nodes uniformly at random within a 2D bounding box. This layout serves
as a baseline layout, an initialization method for iterative layout algorithms (such
as the Spring layout), or a test benchmark.

## Mathematical Model

Given a bounding box with width $W$, height $H$, and center $(c_x, c_y)$, the coordinates
for each node $i$ are generated as:

$$x_i \sim U\left(c_x - \frac{W}{2}, c_x + \frac{W}{2}\right)$$
$$y_i \sim U\left(c_y - \frac{H}{2}, c_y + \frac{H}{2}\right)$$

where $U(a, b)$ is the uniform distribution.

## Complexities

* **Time Complexity:** $O(V)$ where $V$ is the number of nodes.
* **Space Complexity:** $O(V)$ auxiliary space to allocate the coordinates map.

# `layout`

```elixir
@spec layout(
  Yog.Graph.t() | Yog.DAG.t(),
  keyword()
) :: %{required(Yog.Graph.node_id()) => {float(), float()}}
```

Positions nodes randomly within a specified bounding box.

## Options

  * `:width` - The width of the bounding box (default: `1.0`).
  * `:height` - The height of the bounding box (default: `1.0`).
  * `:center` - The `{x, y}` coordinates of the center of the bounding box (default: `{0.0, 0.0}`).
  * `:seed` - Optional integer seed or term for reproducible random positioning.

## Examples

    iex> graph = Yog.undirected() |> Yog.add_nodes_from([1, 2, 3])
    iex> pos = Yog.Layout.Random.layout(graph)
    iex> Map.keys(pos) |> Enum.sort()
    [1, 2, 3]

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*Consult [api-reference.md](api-reference.md) for complete listing*