Add 2026.07.28 session outline

notes-and-examples/2026.07.29/overview.md

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+## Outline
+
+We'll continue to go over breadth-first search and depth-first search.
+
+## 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?
+
+```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
+    )
+]
+```