Implemented A* algorithm and updated test cases

pydatastructs/graphs/algorithms.py

@@ -11,6 +11,7 @@
 from pydatastructs.graphs.graph import Graph
 from pydatastructs.linear_data_structures.algorithms import merge_sort_parallel
 from pydatastructs import PriorityQueue
+from pydatastructs.graphs.graph import AdjacencyListGraphNode
 
 __all__ = [
     'breadth_first_search',
@@ -24,6 +25,7 @@
     'topological_sort',
     'topological_sort_parallel',
     'max_flow'
+    'a_star_with_manhattan'
 ]
 
 Stack = Queue = deque
@@ -700,6 +702,7 @@ def shortest_paths(graph: Graph, algorithm: str,
         'bellman_ford' -> Bellman-Ford algorithm as given in [1].
 
         'dijkstra' -> Dijkstra algorithm as given in [2].
+        'a_star_with_manhattan' -> A* algorithm with Manhattan distance
     source: str
         The name of the source the node.
     target: str
@@ -736,16 +739,27 @@ def shortest_paths(graph: Graph, algorithm: str,
     ({'V1': 0, 'V2': 11, 'V3': 21}, {'V1': None, 'V2': 'V1', 'V3': 'V2'})
     >>> shortest_paths(G, 'dijkstra', 'V1')
     ({'V2': 11, 'V3': 21, 'V1': 0}, {'V1': None, 'V2': 'V1', 'V3': 'V2'})
-
+    >>> grid_graph = Graph(AdjacencyListGraphNode("0,0"), AdjacencyListGraphNode("1,1"))
+    >>> grid_graph.add_edge('0,0', '1,1', 2)
+    >>> shortest_paths(grid_graph, 'a_star_with_manhattan', '0,0', '1,1')
+    (2, {'1,1': '0,0'})
     References
     ==========
 
     .. [1] https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
     .. [2] https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
+    .. [3] https://en.wikipedia.org/wiki/A*_search_algorithm
     """
     raise_if_backend_is_not_python(
         shortest_paths, kwargs.get('backend', Backend.PYTHON))
     import pydatastructs.graphs.algorithms as algorithms
+    if algorithm == 'a_star_with_manhattan':
+        # A* with this implementation requires both source and target
+        if not target:
+            raise ValueError("Target must be specified for A* algorithm")
+
+        func = "_a_star_with_manhattan_" + graph._impl
+        return getattr(algorithms, func)(graph, source, target)
     func = "_" + algorithm + "_" + graph._impl
     if not hasattr(algorithms, func):
         raise NotImplementedError(
@@ -811,6 +825,57 @@ def _dijkstra_adjacency_list(graph: Graph, start: str, target: str):
 
 _dijkstra_adjacency_matrix = _dijkstra_adjacency_list
 
+def _a_star_with_manhattan_adjacency_list(graph: Graph, start: str, target: str, **kwargs):
+    """
+    A* algorithm with Manhattan distance as the heuristic function for grid-based graphs.
+    """
+    def manhattan_distance(node1: str, node2: str) -> float:
+        try:
+            x1, y1 = map(int, node1.split(","))
+            x2, y2 = map(int, node2.split(","))
+            return abs(x1 - x2) + abs(y1 - y2)
+        except (ValueError, TypeError):
+            raise ValueError(f"Invalid node format. Expected 'x,y', got {node1} or {node2}")
+    # Validate inputs
+    if start == target:
+        return 0, {start: None}
+    if start not in graph.vertices or target not in graph.vertices:
+        raise ValueError(f"Start or target node not in graph. Start: {start}, Target: {target}")
+    g_score = {v: float('inf') for v in graph.vertices}
+    f_score = {v: float('inf') for v in graph.vertices}
+    pred = {v: None for v in graph.vertices}
+    visited = {v: False for v in graph.vertices}
+    g_score[start] = 0
+    f_score[start] = manhattan_distance(start, target)
+    pq = PriorityQueue(implementation='binomial_heap')
+    pq.push(start, f_score[start])
+    while not pq.is_empty:
+        current = pq.pop()
+        if current == target:
+            path_pred = {}
+            node = target
+            while node is not None:
+                path_pred[node] = pred[node]
+                node = pred[node]
+            return g_score[target], path_pred
+        visited[current] = True
+        for neighbor in graph.neighbors(current):
+            if visited[neighbor.name]:
+                continue
+            edge = graph.get_edge(current, neighbor.name)
+            if not edge:
+                continue
+            tentative_g_score = g_score[current] + edge.value
+            if tentative_g_score < g_score[neighbor.name]:
+                pred[neighbor.name] = current
+                g_score[neighbor.name] = tentative_g_score
+                f_score[neighbor.name] = (
+                    tentative_g_score + 
+                    manhattan_distance(neighbor.name, target)
+                )
+                pq.push(neighbor.name, f_score[neighbor.name])
+    raise ValueError(f"No path exists between {start} and {target}")
+_a_star_with_manhattan_adjacency_matrix = _a_star_with_manhattan_adjacency_list
 def all_pair_shortest_paths(graph: Graph, algorithm: str,
                             **kwargs) -> tuple:
     """

pydatastructs/graphs/tests/test_algorithms.py

@@ -4,7 +4,6 @@
 depth_first_search, shortest_paths, topological_sort,
 topological_sort_parallel, max_flow)
 from pydatastructs.utils.raises_util import raises
-
 def test_breadth_first_search():
 
     def _test_breadth_first_search(ds):
@@ -293,7 +292,34 @@ def _test_shortest_paths_positive_edges(ds, algorithm):
         graph.remove_edge('SLC', 'D')
         graph.add_edge('D', 'SLC', -10)
         assert raises(ValueError, lambda: shortest_paths(graph, 'bellman_ford', 'SLC'))
-
+    def _test_a_star_manhattan(ds):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+        vertices = [
+            GraphNode("0,0"),
+            GraphNode("1,1"),
+            GraphNode("2,2")
+        ]
+        graph = Graph(*vertices)
+        graph.add_edge("0,0", "1,1", 2)
+        graph.add_edge("1,1", "2,2", 3)
+        distance, pred = shortest_paths(graph, 'a_star_with_manhattan', "0,0", "2,2")
+        assert distance == 5  # 2 + 3
+        assert pred['2,2'] == '1,1'
+        assert pred['1,1'] == '0,0'
+        # No path scenario
+        no_path_graph = Graph(
+            GraphNode("0,0"),
+            GraphNode("1,1"),
+            GraphNode("2,2")
+        )
+        with raises(ValueError, match="No path exists"):
+            shortest_paths(no_path_graph, 'a_star_with_manhattan', "0,0", "2,2")
+        # Same node scenario
+        same_node_graph = Graph(GraphNode("1,1"))
+        distance, pred = shortest_paths(same_node_graph, 'a_star_with_manhattan', "1,1", "1,1")
+        assert distance == 0
+        assert pred == {'1,1': None}
     def _test_shortest_paths_negative_edges(ds, algorithm):
         import pydatastructs.utils.misc_util as utils
         GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
@@ -321,6 +347,8 @@ def _test_shortest_paths_negative_edges(ds, algorithm):
     _test_shortest_paths_negative_edges("Matrix", 'bellman_ford')
     _test_shortest_paths_positive_edges("List", 'dijkstra')
     _test_shortest_paths_positive_edges("Matrix", 'dijkstra')
+    _test_a_star_manhattan("List")
+    _test_a_star_manhattan("Matrix")
 
 def test_all_pair_shortest_paths():