Add Constrained Shortest Path Problem (CSPP) / Shortest Path Problem with Resource Constraints (SPPRC) (#6155)

Author: DenizAltunkapan

src/main/java/com/thealgorithms/graph/ConstrainedShortestPath.java

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+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+/**
+ * This class implements a solution for the Constrained Shortest Path Problem (CSPP).
+ * also known as Shortest Path Problem with Resource Constraints (SPPRC).
+ * The goal is to find the shortest path between two nodes while ensuring that
+ * the resource constraint is not exceeded.
+ *
+ * @author  <a href="https://github.com/DenizAltunkapan">Deniz Altunkapan</a>
+ */
+public class ConstrainedShortestPath {
+
+    /**
+     * Represents a graph using an adjacency list.
+     * This graph is designed for the Constrained Shortest Path Problem (CSPP).
+     */
+    public static class Graph {
+
+        private List<List<Edge>> adjacencyList;
+
+        public Graph(int numNodes) {
+            adjacencyList = new ArrayList<>();
+            for (int i = 0; i < numNodes; i++) {
+                adjacencyList.add(new ArrayList<>());
+            }
+        }
+
+        /**
+         * Adds an edge to the graph.
+         * @param from the starting node
+         * @param to the ending node
+         * @param cost the cost of the edge
+         * @param resource the resource required to traverse the edge
+         */
+        public void addEdge(int from, int to, int cost, int resource) {
+            adjacencyList.get(from).add(new Edge(from, to, cost, resource));
+        }
+
+        /**
+         * Gets the edges that are adjacent to a given node.
+         * @param node the node to get the edges for
+         * @return the list of edges adjacent to the node
+         */
+        public List<Edge> getEdges(int node) {
+            return adjacencyList.get(node);
+        }
+
+        /**
+         * Gets the number of nodes in the graph.
+         * @return the number of nodes
+         */
+        public int getNumNodes() {
+            return adjacencyList.size();
+        }
+
+        public record Edge(int from, int to, int cost, int resource) {
+        }
+    }
+
+    private Graph graph;
+    private int maxResource;
+
+    /**
+     * Constructs a CSPSolver with the given graph and maximum resource constraint.
+     *
+     * @param graph       the graph representing the problem
+     * @param maxResource the maximum allowable resource
+     */
+    public ConstrainedShortestPath(Graph graph, int maxResource) {
+        this.graph = graph;
+        this.maxResource = maxResource;
+    }
+
+    /**
+     * Solves the CSP to find the shortest path from the start node to the target node
+     * without exceeding the resource constraint.
+     *
+     * @param start  the starting node
+     * @param target the target node
+     * @return the minimum cost to reach the target node within the resource constraint,
+     *         or -1 if no valid path exists
+     */
+    public int solve(int start, int target) {
+        int numNodes = graph.getNumNodes();
+        int[][] dp = new int[maxResource + 1][numNodes];
+
+        // Initialize dp table with maximum values
+        for (int i = 0; i <= maxResource; i++) {
+            Arrays.fill(dp[i], Integer.MAX_VALUE);
+        }
+        dp[0][start] = 0;
+
+        // Dynamic Programming: Iterate over resources and nodes
+        for (int r = 0; r <= maxResource; r++) {
+            for (int u = 0; u < numNodes; u++) {
+                if (dp[r][u] == Integer.MAX_VALUE) {
+                    continue;
+                }
+                for (Graph.Edge edge : graph.getEdges(u)) {
+                    int v = edge.to();
+                    int cost = edge.cost();
+                    int resource = edge.resource();
+
+                    if (r + resource <= maxResource) {
+                        dp[r + resource][v] = Math.min(dp[r + resource][v], dp[r][u] + cost);
+                    }
+                }
+            }
+        }
+
+        // Find the minimum cost to reach the target node
+        int minCost = Integer.MAX_VALUE;
+        for (int r = 0; r <= maxResource; r++) {
+            minCost = Math.min(minCost, dp[r][target]);
+        }
+
+        return minCost == Integer.MAX_VALUE ? -1 : minCost;
+    }
+}

src/test/java/com/thealgorithms/graph/ConstrainedShortestPathTest.java

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+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import com.thealgorithms.graph.ConstrainedShortestPath.Graph;
+import org.junit.jupiter.api.Test;
+
+public class ConstrainedShortestPathTest {
+
+    /**
+     * Tests a simple linear graph to verify if the solver calculates the shortest path correctly.
+     * Expected: The minimal path cost from node 0 to node 2 should be 5 while not exceeding the resource limit.
+     */
+    @Test
+    public void testSimpleGraph() {
+        Graph graph = new Graph(3);
+        graph.addEdge(0, 1, 2, 3);
+        graph.addEdge(1, 2, 3, 2);
+
+        int maxResource = 5;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(5, solver.solve(0, 2));
+    }
+
+    /**
+     * Tests a graph where no valid path exists due to resource constraints.
+     * Expected: The solver should return -1, indicating no path is feasible.
+     */
+    @Test
+    public void testNoPath() {
+        Graph graph = new Graph(3);
+        graph.addEdge(0, 1, 2, 6);
+        graph.addEdge(1, 2, 3, 6);
+
+        int maxResource = 5;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(-1, solver.solve(0, 2));
+    }
+
+    /**
+     * Tests a graph with multiple paths between source and destination.
+     * Expected: The solver should choose the path with the minimal cost of 5, considering the resource limit.
+     */
+    @Test
+    public void testMultiplePaths() {
+        Graph graph = new Graph(4);
+        graph.addEdge(0, 1, 1, 1);
+        graph.addEdge(1, 3, 5, 2);
+        graph.addEdge(0, 2, 2, 1);
+        graph.addEdge(2, 3, 3, 2);
+
+        int maxResource = 3;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(5, solver.solve(0, 3));
+    }
+
+    /**
+     * Verifies that the solver allows a path exactly matching the resource limit.
+     * Expected: The path is valid with a total cost of 5.
+     */
+    @Test
+    public void testExactResourceLimit() {
+        Graph graph = new Graph(3);
+        graph.addEdge(0, 1, 2, 3);
+        graph.addEdge(1, 2, 3, 2);
+
+        int maxResource = 5;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(5, solver.solve(0, 2));
+    }
+
+    /**
+     * Tests a disconnected graph where the destination node cannot be reached.
+     * Expected: The solver should return -1, as the destination is unreachable.
+     */
+    @Test
+    public void testDisconnectedGraph() {
+        Graph graph = new Graph(4);
+        graph.addEdge(0, 1, 2, 2);
+        graph.addEdge(2, 3, 3, 2);
+
+        int maxResource = 5;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(-1, solver.solve(0, 3));
+    }
+
+    /**
+     * Tests a graph with cycles to ensure the solver does not fall into infinite loops and correctly calculates costs.
+     * Expected: The solver should compute the minimal path cost of 6.
+     */
+    @Test
+    public void testGraphWithCycles() {
+        Graph graph = new Graph(4);
+        graph.addEdge(0, 1, 2, 1);
+        graph.addEdge(1, 2, 3, 1);
+        graph.addEdge(2, 0, 1, 1);
+        graph.addEdge(1, 3, 4, 2);
+
+        int maxResource = 3;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(6, solver.solve(0, 3));
+    }
+
+    /**
+     * Tests the solver's performance and correctness on a large linear graph with 1000 nodes.
+     * Expected: The solver should efficiently calculate the shortest path with a cost of 999.
+     */
+    @Test
+    public void testLargeGraphPerformance() {
+        int nodeCount = 1000;
+        Graph graph = new Graph(nodeCount);
+        for (int i = 0; i < nodeCount - 1; i++) {
+            graph.addEdge(i, i + 1, 1, 1);
+        }
+
+        int maxResource = 1000;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(999, solver.solve(0, nodeCount - 1));
+    }
+
+    /**
+     * Tests a graph with isolated nodes to ensure the solver recognizes unreachable destinations.
+     * Expected: The solver should return -1 for unreachable nodes.
+     */
+    @Test
+    public void testIsolatedNodes() {
+        Graph graph = new Graph(5);
+        graph.addEdge(0, 1, 2, 1);
+        graph.addEdge(1, 2, 3, 1);
+
+        int maxResource = 5;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(-1, solver.solve(0, 3));
+    }
+
+    /**
+     * Tests a cyclic large graph with multiple overlapping paths.
+     * Expected: The solver should calculate the shortest path cost of 5.
+     */
+    @Test
+    public void testCyclicLargeGraph() {
+        Graph graph = new Graph(10);
+        for (int i = 0; i < 9; i++) {
+            graph.addEdge(i, (i + 1) % 10, 1, 1);
+        }
+        graph.addEdge(0, 5, 5, 3);
+
+        int maxResource = 10;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(5, solver.solve(0, 5));
+    }
+
+    /**
+     * Tests a large complex graph with multiple paths and varying resource constraints.
+     * Expected: The solver should identify the optimal path with a cost of 19 within the resource limit.
+     */
+    @Test
+    public void testLargeComplexGraph() {
+        Graph graph = new Graph(10);
+        graph.addEdge(0, 1, 4, 2);
+        graph.addEdge(0, 2, 3, 3);
+        graph.addEdge(1, 3, 2, 1);
+        graph.addEdge(2, 3, 5, 2);
+        graph.addEdge(2, 4, 8, 4);
+        graph.addEdge(3, 5, 7, 3);
+        graph.addEdge(3, 6, 6, 2);
+        graph.addEdge(4, 6, 3, 2);
+        graph.addEdge(5, 7, 1, 1);
+        graph.addEdge(6, 7, 2, 2);
+        graph.addEdge(7, 8, 3, 1);
+        graph.addEdge(8, 9, 2, 1);
+
+        int maxResource = 10;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(19, solver.solve(0, 9));
+    }
+
+    /**
+     * Edge case test where the graph has only one node and no edges.
+     * Expected: The minimal path cost is 0, as the start and destination are the same.
+     */
+    @Test
+    public void testSingleNodeGraph() {
+        Graph graph = new Graph(1);
+
+        int maxResource = 0;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(0, solver.solve(0, 0));
+    }
+
+    /**
+     * Tests a graph with multiple paths but a tight resource constraint.
+     * Expected: The solver should return -1 if no path can be found within the resource limit.
+     */
+    @Test
+    public void testTightResourceConstraint() {
+        Graph graph = new Graph(4);
+        graph.addEdge(0, 1, 3, 4);
+        graph.addEdge(1, 2, 1, 2);
+        graph.addEdge(0, 2, 2, 2);
+
+        int maxResource = 3;
+        ConstrainedShortestPath solver = new ConstrainedShortestPath(graph, maxResource);
+
+        assertEquals(2, solver.solve(0, 2));
+    }
+}