feat: Enhanced Functionality Introducing Graph Algorithms

pydatastructs/graphs/algorithms.py

@@ -2,6 +2,7 @@
 Contains algorithms associated with graph
 data structure.
 """
+import pytest
 from collections import deque
 from concurrent.futures import ThreadPoolExecutor
 from pydatastructs.utils.misc_util import (
@@ -700,6 +701,8 @@ 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' -> A* algorithm as given in [3].
     source: str
         The name of the source the node.
     target: str
@@ -736,12 +739,24 @@ 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'})
+        >>> start = AdjacencyListGraphNode("0,0")
+    >>> middle = AdjacencyListGraphNode("1,1")
+    >>> goal = AdjacencyListGraphNode("2,2")
+    >>> G2 = Graph(start, middle, goal)
+    >>> G2.add_edge('0,0', '1,1', 2)
+    >>> G2.add_edge('1,1', '2,2', 2)
+    >>> dist, pred = shortest_paths(G2, 'a_star', '0,0', '2,2')
+    >>> dist
+    4
+    >>> pred == {'0,0': None, '1,1': '0,0', '2,2': '1,1'}
+    True
 
     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))
@@ -811,6 +826,86 @@ def _dijkstra_adjacency_list(graph: Graph, start: str, target: str):
 
 _dijkstra_adjacency_matrix = _dijkstra_adjacency_list
 
+def _a_star_adjacency_list(graph: Graph, source: str, target: str) -> tuple:
+    """
+    A* pathfinding algorithm implementation similar to Dijkstra's structure.
+
+    Parameters
+    ==========
+    graph: Graph
+        The graph to search through.
+    source: str
+        Starting node name.
+    target: str
+        Target node name.
+
+    Returns
+    =======
+    (distance, predecessors): tuple
+        Distance to target and dictionary of predecessors.
+    """
+
+    def heuristic(node: str, goal: str) -> float:
+        """Manhattan distance heuristic for A*"""
+        try:
+            x1, y1 = map(int, node.split(','))
+            x2, y2 = map(int, goal.split(','))
+            return abs(x1 - x2) + abs(y1 - y2)
+        except ValueError:
+            raise ValueError(f"Invalid node format: {node}. Expected 'x,y'.")
+
+    if source not in graph.vertices or target not in graph.vertices:
+        raise KeyError(f"Either source '{source}' or target '{target}' is not in the graph.")
+
+    visited = {v: False for v in graph.vertices}
+    dist = {v: float('inf') for v in graph.vertices}
+    pred = {v: None for v in graph.vertices}
+    dist[source] = 0
+
+    from pydatastructs.miscellaneous_data_structures.queue import PriorityQueue, BinomialHeapPriorityQueue
+    pq = PriorityQueue(implementation='binomial_heap')
+
+    f_score = heuristic(source, target)
+    pq.push(source, f_score)
+
+    while not pq.is_empty:
+        current = pq.pop()
+
+        if current == target:
+            return dist[target], dict(sorted(pred.items()))
+
+        if visited[current]:
+            continue
+
+        visited[current] = True
+        neighbors = graph.neighbors(current)
+
+        if not neighbors:
+            continue
+
+        for neighbor in neighbors:
+            if visited[neighbor.name]:
+                continue
+
+            edge = graph.get_edge(current, neighbor.name)
+            if not edge:
+                continue
+
+            new_dist = dist[current] + edge.value
+            if new_dist < dist[neighbor.name]:
+                dist[neighbor.name] = new_dist
+                pred[neighbor.name] = current
+                f_score = new_dist + heuristic(neighbor.name, target)
+                pq.push(neighbor.name, f_score)
+
+    if dist[target] == float('inf'):
+        raise ValueError(f"Either source '{source}' and target '{target}' have no path between them.")
+
+    return float('inf'), dict(sorted(pred.items()))
+
+
+_a_star_adjacency_matrix = _a_star_adjacency_list
+
 def all_pair_shortest_paths(graph: Graph, algorithm: str,
                             **kwargs) -> tuple:
     """

pydatastructs/graphs/tests/test_algorithms.py

@@ -314,13 +314,71 @@ def _test_shortest_paths_negative_edges(ds, algorithm):
         dist, pred = shortest_paths(graph, algorithm, 's', 'd')
         assert dist == 2
         assert pred == {'s': None, 'a': 'b', 'b': 's', 'c': 'a', 'd': 'c'}
+    def _test_a_star_manhattan(ds):
+        """
+        Test suite for the A* algorithm using the Manhattan distance heuristic.
+        """
 
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+
+        # Case 1: Simple Path Test
+        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", 2)
+
+        distance, pred = shortest_paths(graph, 'a_star', "0,0", "2,2")
+        assert distance == 4
+        assert pred == {'0,0': None, '1,1': '0,0', '2,2': '1,1'}
+
+        # Case 2: No Path Between Nodes
+        no_path_graph = Graph(
+            GraphNode("0,0"),
+            GraphNode("1,1"),
+            GraphNode("2,2")
+        )
+        with pytest.raises(ValueError, match="Either source '0,0' and target '2,2' have no path between them."):
+            shortest_paths(no_path_graph, 'a_star', "0,0", "2,2")
+
+        # Case 3: Same Source and Target Node
+        same_node_graph = Graph(GraphNode("1,1"))
+        distance, pred = shortest_paths(same_node_graph, 'a_star', "1,1", "1,1")
+        assert distance == 0
+        assert pred == {'1,1': None}
+
+        # Case 4: Invalid Node Format
+        invalid_graph = Graph(GraphNode("invalid"))
+        with pytest.raises(ValueError, match="Invalid node format: invalid. Expected 'x,y'."):
+            shortest_paths(invalid_graph, 'a_star', "invalid", "invalid")
+
+        # Case 5: Complex Graph with Multiple Paths
+        complex_vertices = [
+            GraphNode("0,0"),
+            GraphNode("0,1"),
+            GraphNode("1,0"),
+            GraphNode("1,1")
+        ]
+        complex_graph = Graph(*complex_vertices)
+        complex_graph.add_edge("0,0", "0,1", 1)
+        complex_graph.add_edge("0,1", "1,1", 1)
+        complex_graph.add_edge("0,0", "1,0", 2)
+        complex_graph.add_edge("1,0", "1,1", 1)
+
+        distance, pred = shortest_paths(complex_graph, 'a_star', "0,0", "1,1")
+        assert distance == 2
+        assert pred == {'0,0': None, '0,1': '0,0', '1,1': '0,1', '1,0': '0,0'}
     _test_shortest_paths_positive_edges("List", 'bellman_ford')
     _test_shortest_paths_positive_edges("Matrix", 'bellman_ford')
     _test_shortest_paths_negative_edges("List", 'bellman_ford')
     _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():