Add the solution file for exercise 1

notes-and-examples/2026.08.11/exercise1_solution.py

@@ -0,0 +1,60 @@
+# see the overview from 2026.07.31
+
+sample_graph = {
+    'Alice': set(['Bob', 'Carol']),
+    'Bob': set(['Alice', 'Dave']),
+    'Carol': set(['Alice', 'Eve', 'Mallory']),
+    'Dave': set(['Frank', 'Eve', 'Bob']),
+    'Eve': set(['Carol', 'Grace', 'Dave']),
+    'Frank': set(['Dave', 'Heidi']),
+    'Grace': set(['Eve', 'Ivan', 'Mallory']),
+    'Heidi': set(['Frank', 'Ivan']),
+    'Ivan': set(['Heidi', 'Grace']),
+    'Mallory': set(['Carol', 'Grace'])
+}
+
+
+# SOLUTION
+
+def nth_degree_connections(
+        graph: dict[str, set[str]],
+        starting_vertex: str,
+        max_n: int
+):
+    # what traversal algorithm is this?
+
+    # since we "visit" when looping through neighbors,
+    # mark the starting vertex as visited already
+    visited = {starting_vertex}
+    queue = [(starting_vertex, 0)]  # (vertex, n)
+
+    to_return: list[list[str]] = []
+
+    # check for both conditions at once
+    # queue is not empty, and we have not exceeded the max_n
+    while queue and queue[0][1] <= max_n:
+        element = queue.pop(0)
+        vertex = element[0]
+        current_n = element[1]
+
+        if current_n == len(to_return):
+            to_return.append([])
+        to_return[current_n].append(element[0])
+
+        for neighbor in graph[vertex]:
+            if neighbor not in visited:
+                queue.append((neighbor, current_n + 1))
+                visited.add(neighbor)
+
+                # we can also
+
+    # match the example: don't include the 0th-degree connection
+    to_return.pop(0)
+    return to_return
+
+
+print(nth_degree_connections(sample_graph, 'Mallory', 2))
+print(nth_degree_connections(sample_graph, 'Alice', 4))
+print(nth_degree_connections(sample_graph, 'Ivan', 1))
+print(nth_degree_connections(sample_graph, 'Grace', 0))
+print(nth_degree_connections(sample_graph, 'Carol', 100))