diff --git a/src/main/java/com/thealgorithms/graph/ConstrainedShortestPath.java b/src/main/java/com/thealgorithms/graph/ConstrainedShortestPath.java new file mode 100644 index 000000000000..f397989911d9 --- /dev/null +++ b/src/main/java/com/thealgorithms/graph/ConstrainedShortestPath.java @@ -0,0 +1,123 @@ +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 Deniz Altunkapan + */ +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> 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 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; + } +} diff --git a/src/test/java/com/thealgorithms/graph/ConstrainedShortestPathTest.java b/src/test/java/com/thealgorithms/graph/ConstrainedShortestPathTest.java new file mode 100644 index 000000000000..eccd359f2634 --- /dev/null +++ b/src/test/java/com/thealgorithms/graph/ConstrainedShortestPathTest.java @@ -0,0 +1,218 @@ +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)); + } +}