2.7 KiB
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: nthDegreeConnections(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 possiblePaths("Santa Ana", "San Francisco")
should yield the return below. Which path is better?
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
)
]