Add in-progress notes for 2026.07.21

notes-and-examples/2026.07.01/red_black_tree.py

@@ -1,3 +1,5 @@
+import traceback
+
 class Node:
     def __init__(self, value, left=None, right=None, parent=None, is_red=False):
         self.value = value
@@ -451,8 +453,10 @@ def run_tests():
             print("    Your rebalance likely created a cycle or otherwise broke the")
             print("    tree structure (a child pointing back up at an ancestor).\n")
             continue
-        except Exception as e:
+        except Exception:
-            print(f"  RESULT: ERROR - {type(e).__name__}: {e}\n")
+            print(f"  RESULT: ERROR - see stack trace below\n")
+            print(traceback.format_exc())
+            print("")
             continue
 
         # Guard the author (you) against a typo when adding a new case: the

notes-and-examples/2026.07.21/breadth-first-search.md

@@ -0,0 +1,13 @@
+## Breadth-first search (BFS)
+
+In the notes on [depth-first search](./depth-first-search.md), we mention that the difference between DFS and BFS is the order in which nodes are traversed.
+
+Using the same example, what would a breadth-first traversal look like if we start at vertex 0 in this graph?
+
+```
+    0 --- 1
+    |     |
+    3 --- 2
+```
+
+Can we also formalize an algorithm for breadth-first search?

notes-and-examples/2026.07.21/depth-first-search.md

@@ -0,0 +1,46 @@
+## Traversal introduction
+
+Many algorithms that involve graphs must involve some way to traverse the elements of a graph. The two simplest ways of traversal are depth-first search (DFS) and [breadth-first search (BFS)](https://en.wikipedia.org/wiki/Breadth-first_search). The major difference here is the *order* in which nodes are traversed.
+
+If we start from vertex 0 in the tree, in what order would you expect depth-first search to traverse the nodes? (There are multiple correct answers!)
+
+```
+        0
+       / \
+      1   2
+     / \
+    3   4
+```
+
+Note that a single traversal step checks for already-visited nodes. So, if the path is `0 -> 1 -> 3`, the path cannot become `0 -> 1 -> 3 -> 1`.
+
+What about starting from vertex 0 in this graph?
+
+```
+    0 --- 1
+    |     |
+    3 --- 2
+```
+
+What about this one?
+
+```
+        0
+       / \
+      1   5
+     / \   \
+    2   3   6
+     \ /   /
+      4   7
+       \ /
+        8
+```
+
+## Formalizing the algorithm
+
+Based on these examples, can we create a formal algorithm that takes a starting node, producing a valid traversal path for all three graphs?
+
+Some starter questions:
+
+- Could recursion help us here?
+- What are some ways we can track already-visited nodes? What's the most *time-efficient* way to do so?

notes-and-examples/2026.07.21/main.py

@@ -0,0 +1,25 @@
+# Adjacency list
+first_graph = {
+    1: [3, 20],
+    2: [20],
+    3: [1, 20],
+    20: [2, 3]
+}
+
+# First exercise: go from 1, to 20, to 2
+first_graph[first_graph[1][1]][0]
+
+# pass visited by reference
+def depth_first_search(graph: dict, start, visited=set()):
+    print(start)
+    if len(visited)==len(graph):
+        return visited
+
+    for x in graph[start]:
+        if x not in visited:
+            visited.add(x)
+            return depth_first_search(graph, x, visited)
+    pass
+    
+
+depth_first_search(first_graph, 1)

notes-and-examples/2026.07.21/overview.md

@@ -0,0 +1,11 @@
+## Outline
+
+To make our knowledge of graphs useful, we'll go over our first traversal method today: [depth-first search](./depth-first-search.md). We will also go over [breadth-first search](./breadth-first-search.md), and how both algorithms can be useful.
+
+Assignment: write functions for depth-first search and breadth-first search. Because there is no starter file, the constraints are listed below:
+
+- You may use either an adjacency list or adjacency matrix to represent your graph
+- You should demonstrate that your algorithm works by running it through some test cases
+    - For each test case, specify the graph, starting point, and expected output(s)
+
+Bonus: can you output *all* the valid paths for both DFS and BFS in a particular case?