Add A* Search Algorithm for Weighted Graph Pathfinding

Author: surajdm123

src/main/java/com/thealgorithms/others/AStarSearch.java

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+package com.thealgorithms.others;
+
+import java.util.*;
+
+/**
+ * A* (A-Star) Search Algorithm implementation for finding the shortest path
+ * between two nodes in a graph.
+ *
+ * <p>This algorithm uses a heuristic to guide its search, making it more efficient
+ * than Dijkstra’s algorithm in many cases.
+ *
+ * <p>f(n) = g(n) + h(n)
+ * where:
+ * - g(n): cost from start node to current node
+ * - h(n): estimated cost from current node to goal (heuristic)
+ *
+ * <p>Time Complexity:
+ * - Worst case: O(E log V)
+ *
+ * <p>Space Complexity:
+ * - O(V)
+ *
+ * <p>Use Cases:
+ * - Pathfinding (maps, games)
+ * - AI planning
+ *
+ * @author Suraj Devatha
+ */
+public class AStarSearch {
+
+    /**
+     * Finds shortest path using A*.
+     *
+     * @param graph     adjacency list
+     * @param start     start node
+     * @param goal      goal node
+     * @param heuristic heuristic function
+     * @return list of nodes representing shortest path
+     */
+    public static List<Node> findPath(
+            Map<Node, List<Edge>> graph,
+            Node start,
+            Node goal,
+            Heuristic heuristic
+    ) {
+
+        Map<Node, Double> gScore = new HashMap<>();
+        Map<Node, Double> fScore = new HashMap<>();
+        Map<Node, Node> cameFrom = new HashMap<>();
+
+        PriorityQueue<Node> openSet = new PriorityQueue<>(
+                Comparator.comparingDouble(fScore::get)
+        );
+
+        gScore.put(start, 0.0);
+        fScore.put(start, heuristic.estimate(start, goal));
+
+        openSet.add(start);
+
+        while (!openSet.isEmpty()) {
+            Node current = openSet.poll();
+
+            if (current.equals(goal)) {
+                return reconstructPath(cameFrom, current);
+            }
+
+            for (Edge edge : graph.getOrDefault(current, Collections.emptyList())) {
+                Node neighbor = edge.target;
+                double tentativeG = gScore.get(current) + edge.cost;
+
+                if (tentativeG < gScore.getOrDefault(neighbor, Double.POSITIVE_INFINITY)) {
+                    cameFrom.put(neighbor, current);
+                    gScore.put(neighbor, tentativeG);
+                    fScore.put(neighbor, tentativeG + heuristic.estimate(neighbor, goal));
+
+                    if (!openSet.contains(neighbor)) {
+                        openSet.add(neighbor);
+                    }
+                }
+            }
+        }
+
+        return Collections.emptyList(); // No path found
+    }
+
+    /**
+     * Reconstructs path from goal to start.
+     */
+    private static List<Node> reconstructPath(Map<Node, Node> cameFrom, Node current) {
+        List<Node> path = new ArrayList<>();
+        path.add(current);
+
+        while (cameFrom.containsKey(current)) {
+            current = cameFrom.get(current);
+            path.add(current);
+        }
+
+        Collections.reverse(path);
+        return path;
+    }
+
+    /**
+     * Heuristic interface (can plug different heuristics).
+     */
+    public interface Heuristic {
+        double estimate(Node current, Node goal);
+    }
+
+    /**
+     * Node class representing a vertex in the graph.
+     */
+    static class Node {
+        String id;
+
+        Node(String id) {
+            this.id = id;
+        }
+
+        @Override
+        public boolean equals(Object o) {
+            if (this == o) return true;
+            if (!(o instanceof Node)) return false;
+            Node node = (Node) o;
+            return Objects.equals(id, node.id);
+        }
+
+        @Override
+        public int hashCode() {
+            return Objects.hash(id);
+        }
+    }
+
+    /**
+     * Edge class representing weighted connections.
+     */
+    static class Edge {
+        Node target;
+        double cost;
+
+        Edge(Node target, double cost) {
+            this.target = target;
+            this.cost = cost;
+        }
+    }
+}

src/test/java/com/thealgorithms/others/AStarSearchTest.java

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+package com.thealgorithms.others;
+
+import org.junit.jupiter.api.BeforeAll;
+import org.junit.jupiter.api.Test;
+
+import java.util.*;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+/**
+ * Test cases for AStarSearch algorithm.
+ */
+class AStarSearchTest {
+
+    /**
+     * Simple heuristic that returns 0 (reduces A* to Dijkstra).
+     */
+    private static final AStarSearch.Heuristic ZERO_HEURISTIC = (node, goal) -> 0;
+    private static Map<AStarSearch.Node, List<AStarSearch.Edge>> graph;
+    private static AStarSearch.Node A;
+    private static AStarSearch.Node B;
+    private static AStarSearch.Node C;
+    private static AStarSearch.Node D;
+
+    @BeforeAll
+    static void setUp() {
+        graph = new HashMap<>();
+
+        A = new AStarSearch.Node("A");
+        B = new AStarSearch.Node("B");
+        C = new AStarSearch.Node("C");
+        D = new AStarSearch.Node("D");
+
+        graph.put(A, Arrays.asList(
+                new AStarSearch.Edge(B, 1),
+                new AStarSearch.Edge(C, 4)
+        ));
+
+        graph.put(B, Arrays.asList(
+                new AStarSearch.Edge(C, 2),
+                new AStarSearch.Edge(D, 5)
+        ));
+
+        graph.put(C, Arrays.asList(
+                new AStarSearch.Edge(D, 1)
+        ));
+
+        graph.put(D, Collections.emptyList());
+    }
+
+    @Test
+    void testPathExists() {
+        List<AStarSearch.Node> path =
+                AStarSearch.findPath(graph, A, D, ZERO_HEURISTIC);
+
+        // Expected shortest path: A -> B -> C -> D
+        List<AStarSearch.Node> expected = Arrays.asList(A, B, C, D);
+
+        assertEquals(expected, path);
+    }
+
+    @Test
+    void testDirectPath() {
+        List<AStarSearch.Node> path =
+                AStarSearch.findPath(graph, A, B, ZERO_HEURISTIC);
+
+        List<AStarSearch.Node> expected = Arrays.asList(A, B);
+
+        assertEquals(expected, path);
+    }
+
+    @Test
+    void testStartEqualsGoal() {
+        List<AStarSearch.Node> path =
+                AStarSearch.findPath(graph, A, A, ZERO_HEURISTIC);
+
+        List<AStarSearch.Node> expected = Collections.singletonList(A);
+
+        assertEquals(expected, path);
+    }
+
+    @Test
+    void testNoPathExists() {
+        AStarSearch.Node E = new AStarSearch.Node("E");
+
+        List<AStarSearch.Node> path =
+                AStarSearch.findPath(graph, E, A, ZERO_HEURISTIC);
+
+        assertTrue(path.isEmpty());
+    }
+
+    @Test
+    void testPathCostOptimality() {
+        List<AStarSearch.Node> path =
+                AStarSearch.findPath(graph, A, D, ZERO_HEURISTIC);
+
+        // Calculate total cost
+        double cost = calculatePathCost(path);
+
+        // Expected shortest cost = 1 (A->B) + 2 (B->C) + 1 (C->D) = 4
+        assertEquals(4.0, cost);
+    }
+
+    /**
+     * Utility method to calculate path cost.
+     */
+    private double calculatePathCost(List<AStarSearch.Node> path) {
+        double total = 0;
+
+        for (int i = 0; i < path.size() - 1; i++) {
+            AStarSearch.Node current = path.get(i);
+            AStarSearch.Node next = path.get(i + 1);
+
+            for (AStarSearch.Edge edge : graph.getOrDefault(current, Collections.emptyList())) {
+                if (edge.target.equals(next)) {
+                    total += edge.cost;
+                    break;
+                }
+            }
+        }
+
+        return total;
+    }
+}