clanker: veet-hard-problems (run)

problems/hard/shortest-path/solution.py

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+"""
+Shortest Path
+
+You're building a navigation system for a logistics company. Given a
+network of cities connected by weighted roads, implement a shortest-path
+finder that computes the minimum-cost route between two cities using
+Dijkstra's algorithm. The system must also detect when no route exists.
+
+Example 1:
+    Input: edges = [("A", "B", 4), ("A", "C", 2), ("C", "B", 1), ("B", "D", 5), ("C", "D", 8)], start = "A", end = "D"
+    Output: (7, ["A", "C", "B", "D"])
+    Explanation: A->C (2) + C->B (1) + B->D (5) = 7, cheaper than A->C->D (10) or A->B->D (9).
+
+Example 2:
+    Input: edges = [("X", "Y", 3)], start = "Y", end = "X"
+    Output: (-1, [])
+    Explanation: No path from Y to X because the edge is one-directional.
+
+Example 3:
+    Input: edges = [("A", "B", 1), ("B", "C", 2), ("A", "C", 10)], start = "A", end = "C"
+    Output: (3, ["A", "B", "C"])
+    Explanation: Going through B costs 3, which beats the direct edge of 10.
+
+Constraints:
+    - Edges are directed: (source, destination, weight)
+    - All weights are positive integers (>= 1)
+    - No duplicate edges (same source and destination)
+    - Node names are non-empty strings
+    - Return (-1, []) if no path exists
+    - Return (0, [start]) if start == end
+    - If multiple shortest paths exist, return any one of them
+    - The path list includes both start and end nodes
+"""
+
+
+def shortest_path(
+    edges: list[tuple[str, str, int]], start: str, end: str
+) -> tuple[int, list[str]]:
+    """Return (cost, path) for shortest path, or (-1, []) if unreachable."""
+    pass  # Your implementation here

problems/hard/shortest-path/tests.py

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+"""Tests for shortest-path."""
+import pytest
+from solution import shortest_path
+
+
+class TestBasicCases:
+    """Test basic functionality with typical inputs."""
+
+    def test_example_one(self):
+        """Test first example from problem description."""
+        edges = [("A", "B", 4), ("A", "C", 2), ("C", "B", 1), ("B", "D", 5), ("C", "D", 8)]
+        assert shortest_path(edges, "A", "D") == (7, ["A", "C", "B", "D"])
+
+    def test_example_two(self):
+        """Test second example with no reverse path."""
+        edges = [("X", "Y", 3)]
+        assert shortest_path(edges, "Y", "X") == (-1, [])
+
+    def test_example_three(self):
+        """Test indirect path cheaper than direct edge."""
+        edges = [("A", "B", 1), ("B", "C", 2), ("A", "C", 10)]
+        assert shortest_path(edges, "A", "C") == (3, ["A", "B", "C"])
+
+    def test_direct_edge_is_shortest(self):
+        """Test when the direct edge is the cheapest route."""
+        edges = [("A", "B", 1), ("A", "C", 5), ("C", "B", 5)]
+        assert shortest_path(edges, "A", "B") == (1, ["A", "B"])
+
+
+class TestEdgeCases:
+    """Test edge cases and boundary conditions."""
+
+    def test_start_equals_end(self):
+        """Test when start and end are the same node."""
+        edges = [("A", "B", 1)]
+        assert shortest_path(edges, "A", "A") == (0, ["A"])
+
+    def test_no_edges(self):
+        """Test with empty edge list and different start/end."""
+        assert shortest_path([], "A", "B") == (-1, [])
+
+    def test_single_edge_path(self):
+        """Test path that is a single edge."""
+        edges = [("A", "B", 7)]
+        assert shortest_path(edges, "A", "B") == (7, ["A", "B"])
+
+    def test_long_chain(self):
+        """Test shortest path through a long chain of nodes."""
+        edges = [("A", "B", 1), ("B", "C", 1), ("C", "D", 1), ("D", "E", 1)]
+        assert shortest_path(edges, "A", "E") == (4, ["A", "B", "C", "D", "E"])
+
+    def test_disconnected_graph(self):
+        """Test with disconnected components."""
+        edges = [("A", "B", 1), ("C", "D", 1)]
+        assert shortest_path(edges, "A", "D") == (-1, [])
+
+    def test_multiple_paths_picks_cheapest(self):
+        """Test graph with many paths to verify optimal is chosen."""
+        edges = [
+            ("S", "A", 10), ("S", "B", 3), ("B", "A", 1),
+            ("A", "T", 2), ("B", "T", 20),
+        ]
+        cost, path = shortest_path(edges, "S", "T")
+        assert cost == 6
+        assert path[0] == "S" and path[-1] == "T"
+
+    def test_large_weights(self):
+        """Test with large edge weights."""
+        edges = [("A", "B", 1000000), ("B", "C", 1000000)]
+        assert shortest_path(edges, "A", "C") == (2000000, ["A", "B", "C"])
+
+    def test_end_node_not_in_graph(self):
+        """Test when end node has no edges at all."""
+        edges = [("A", "B", 1), ("B", "C", 2)]
+        assert shortest_path(edges, "A", "Z") == (-1, [])