## Outline

We'll continue to go over breadth-first search and depth-first search.

To start, please implement the breadth-first search algorithm from last week.
Then, if time permits, I'd like you to work through these exercises.

## Exercise 1

Consider a graph that is used to represent people connections.

```
                 Bob --------- Dave ---- Frank ------- Heidi
                /               |                        |
               /                |                        |
   Alice -----+       +------- Eve ---+                  |
       \             /                 \                 |
        \           /                   \                |
         +------ Carol                   Grace ------- Ivan
                      \                  /
                       \                /
                        +-- Mallory ---+
```

We say that person A has an "Nth-degree connection" to another person B, if
person B is reachable from person A by traversing at minimum N edges.

Write an algorithm to return that person's Nth-degree connections, in a list of
lists sorted by N. 1st-degree connections should appear in the first inner list,
with 2nd-degree connections in the second inner list, and so forth.

Your algorithm should take a starting person and a *maximum N*, such that your
algorithm does not return connections past the maximum Nth connection.

Example: `nth_degree_connections(Mallory, 2)` would return the following lists
in a list:

- `[Carol, Grace]`: 1st-degree connections
- `[Eve, Ivan, Alice]`: 2nd-degree connections

It would not return anything else because of the maximum N specified.

Consider the following:

- Which algorithm does this use?
- How do we know when to stop at the maximum N?

## Exercise 2

In a *weighted* road network, return all possible paths that a car can take to
reach point A to point B. For each path, also sum up the total weight that
taking that path requires.

Your algorithm should take the starting and ending points, and return a list
of tuples. Each tuple should contain the traversal from point A to point B,
followed by the total weight.

In this fictitious graph, calling `possible_paths("Santa Ana", "San Francisco")`
should yield the return below.

```python
graph = {
    'Santa Ana': {
        'Los Angeles': 5,
        'Palm Springs': 50
    },
    'Los Angeles': {
        'San Francisco': 25,
        'Santa Ana': 5
    },
    'Palm Springs': {
        'San Francisco': 30,
        'Santa Ana': 50
    },
    'San Francisco': {
        'Los Angeles': 25,
        'Palm Springs': 30
    } 
}
```

```
[
    (
        ["Santa Ana", "Los Angeles", "San Francisco"],
        30
    ),
    (
        ["Santa Ana", "Palm Springs", "San Francisco"],
        80
    )
]
```