From 743f9660a88df89c091ccaad5a1a05a8e4597575 Mon Sep 17 00:00:00 2001 From: Deniz Altunkapan <93663085+DenizAltunkapan@users.noreply.github.com> Date: Tue, 1 Apr 2025 00:18:19 +0200 Subject: [PATCH] Add Traveling Salesman Problem (#6205) --- .../graph/TravelingSalesman.java | 155 ++++++++++++++++++ .../graph/TravelingSalesmanTest.java | 127 ++++++++++++++ 2 files changed, 282 insertions(+) create mode 100644 src/main/java/com/thealgorithms/graph/TravelingSalesman.java create mode 100644 src/test/java/com/thealgorithms/graph/TravelingSalesmanTest.java diff --git a/src/main/java/com/thealgorithms/graph/TravelingSalesman.java b/src/main/java/com/thealgorithms/graph/TravelingSalesman.java new file mode 100644 index 000000000..14bf89f57 --- /dev/null +++ b/src/main/java/com/thealgorithms/graph/TravelingSalesman.java @@ -0,0 +1,155 @@ +package com.thealgorithms.graph; + +import java.util.ArrayList; +import java.util.Arrays; +import java.util.Collections; +import java.util.List; + +/** + * This class provides solutions to the Traveling Salesman Problem (TSP) using both brute-force and dynamic programming approaches. + * For more information, see Wikipedia. + * @author Deniz Altunkapan + */ + +public final class TravelingSalesman { + + // Private constructor to prevent instantiation + private TravelingSalesman() { + } + + /** + * Solves the Traveling Salesman Problem (TSP) using brute-force approach. + * This method generates all possible permutations of cities, calculates the total distance for each route, and returns the shortest distance found. + * + * @param distanceMatrix A square matrix where element [i][j] represents the distance from city i to city j. + * @return The shortest possible route distance visiting all cities exactly once and returning to the starting city. + */ + public static int bruteForce(int[][] distanceMatrix) { + if (distanceMatrix.length <= 1) { + return 0; + } + + List cities = new ArrayList<>(); + for (int i = 1; i < distanceMatrix.length; i++) { + cities.add(i); + } + + List> permutations = generatePermutations(cities); + int minDistance = Integer.MAX_VALUE; + + for (List permutation : permutations) { + List route = new ArrayList<>(); + route.add(0); + route.addAll(permutation); + int currentDistance = calculateDistance(distanceMatrix, route); + if (currentDistance < minDistance) { + minDistance = currentDistance; + } + } + + return minDistance; + } + + /** + * Computes the total distance of a given route. + * + * @param distanceMatrix A square matrix where element [i][j] represents the + * distance from city i to city j. + * @param route A list representing the order in which the cities are visited. + * @return The total distance of the route, or Integer.MAX_VALUE if the route is invalid. + */ + public static int calculateDistance(int[][] distanceMatrix, List route) { + int distance = 0; + for (int i = 0; i < route.size() - 1; i++) { + int d = distanceMatrix[route.get(i)][route.get(i + 1)]; + if (d == Integer.MAX_VALUE) { + return Integer.MAX_VALUE; + } + distance += d; + } + int returnDist = distanceMatrix[route.get(route.size() - 1)][route.get(0)]; + return (returnDist == Integer.MAX_VALUE) ? Integer.MAX_VALUE : distance + returnDist; + } + + /** + * Generates all permutations of a given list of cities. + * + * @param cities A list of cities to permute. + * @return A list of all possible permutations. + */ + private static List> generatePermutations(List cities) { + List> permutations = new ArrayList<>(); + permute(cities, 0, permutations); + return permutations; + } + + /** + * Recursively generates permutations using backtracking. + * + * @param arr The list of cities. + * @param k The current index in the permutation process. + * @param output The list to store generated permutations. + */ + private static void permute(List arr, int k, List> output) { + if (k == arr.size()) { + output.add(new ArrayList<>(arr)); + return; + } + for (int i = k; i < arr.size(); i++) { + Collections.swap(arr, i, k); + permute(arr, k + 1, output); + Collections.swap(arr, i, k); + } + } + + /** + * Solves the Traveling Salesman Problem (TSP) using dynamic programming with the Held-Karp algorithm. + * + * @param distanceMatrix A square matrix where element [i][j] represents the distance from city i to city j. + * @return The shortest possible route distance visiting all cities exactly once and returning to the starting city. + * @throws IllegalArgumentException if the input matrix is not square. + */ + public static int dynamicProgramming(int[][] distanceMatrix) { + if (distanceMatrix.length == 0) { + return 0; + } + int n = distanceMatrix.length; + + for (int[] row : distanceMatrix) { + if (row.length != n) { + throw new IllegalArgumentException("Matrix must be square"); + } + } + + int[][] dp = new int[n][1 << n]; + for (int[] row : dp) { + Arrays.fill(row, Integer.MAX_VALUE); + } + dp[0][1] = 0; + + for (int mask = 1; mask < (1 << n); mask++) { + for (int u = 0; u < n; u++) { + if ((mask & (1 << u)) == 0 || dp[u][mask] == Integer.MAX_VALUE) { + continue; + } + for (int v = 0; v < n; v++) { + if ((mask & (1 << v)) != 0 || distanceMatrix[u][v] == Integer.MAX_VALUE) { + continue; + } + int newMask = mask | (1 << v); + dp[v][newMask] = Math.min(dp[v][newMask], dp[u][mask] + distanceMatrix[u][v]); + } + } + } + + int minDistance = Integer.MAX_VALUE; + int fullMask = (1 << n) - 1; + for (int i = 1; i < n; i++) { + if (dp[i][fullMask] != Integer.MAX_VALUE && distanceMatrix[i][0] != Integer.MAX_VALUE) { + minDistance = Math.min(minDistance, dp[i][fullMask] + distanceMatrix[i][0]); + } + } + + return minDistance == Integer.MAX_VALUE ? 0 : minDistance; + } +} diff --git a/src/test/java/com/thealgorithms/graph/TravelingSalesmanTest.java b/src/test/java/com/thealgorithms/graph/TravelingSalesmanTest.java new file mode 100644 index 000000000..b93c9f89c --- /dev/null +++ b/src/test/java/com/thealgorithms/graph/TravelingSalesmanTest.java @@ -0,0 +1,127 @@ +package com.thealgorithms.graph; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import org.junit.jupiter.api.Test; + +public class TravelingSalesmanTest { + + // Test Case 1: A simple distance matrix with 4 cities + @Test + public void testBruteForceSimple() { + int[][] distanceMatrix = {{0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0}}; + int expectedMinDistance = 80; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingSimple() { + int[][] distanceMatrix = {{0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0}}; + int expectedMinDistance = 80; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 2: A distance matrix with 3 cities + @Test + public void testBruteForceThreeCities() { + int[][] distanceMatrix = {{0, 10, 15}, {10, 0, 35}, {15, 35, 0}}; + int expectedMinDistance = 60; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingThreeCities() { + int[][] distanceMatrix = {{0, 10, 15}, {10, 0, 35}, {15, 35, 0}}; + int expectedMinDistance = 60; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 3: A distance matrix with 5 cities (larger input) + @Test + public void testBruteForceFiveCities() { + int[][] distanceMatrix = {{0, 2, 9, 10, 1}, {2, 0, 6, 5, 8}, {9, 6, 0, 4, 3}, {10, 5, 4, 0, 7}, {1, 8, 3, 7, 0}}; + int expectedMinDistance = 15; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingFiveCities() { + int[][] distanceMatrix = {{0, 2, 9, 10, 1}, {2, 0, 6, 5, 8}, {9, 6, 0, 4, 3}, {10, 5, 4, 0, 7}, {1, 8, 3, 7, 0}}; + int expectedMinDistance = 15; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 4: A distance matrix with 2 cities (simple case) + @Test + public void testBruteForceTwoCities() { + int[][] distanceMatrix = {{0, 1}, {1, 0}}; + int expectedMinDistance = 2; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingTwoCities() { + int[][] distanceMatrix = {{0, 1}, {1, 0}}; + int expectedMinDistance = 2; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 5: A distance matrix with identical distances + @Test + public void testBruteForceEqualDistances() { + int[][] distanceMatrix = {{0, 10, 10, 10}, {10, 0, 10, 10}, {10, 10, 0, 10}, {10, 10, 10, 0}}; + int expectedMinDistance = 40; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingEqualDistances() { + int[][] distanceMatrix = {{0, 10, 10, 10}, {10, 0, 10, 10}, {10, 10, 0, 10}, {10, 10, 10, 0}}; + int expectedMinDistance = 40; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 6: A distance matrix with only one city + @Test + public void testBruteForceOneCity() { + int[][] distanceMatrix = {{0}}; + int expectedMinDistance = 0; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingOneCity() { + int[][] distanceMatrix = {{0}}; + int expectedMinDistance = 0; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + // Test Case 7: Distance matrix with large numbers + @Test + public void testBruteForceLargeNumbers() { + int[][] distanceMatrix = {{0, 1000000, 2000000}, {1000000, 0, 1500000}, {2000000, 1500000, 0}}; + int expectedMinDistance = 4500000; + int result = TravelingSalesman.bruteForce(distanceMatrix); + assertEquals(expectedMinDistance, result); + } + + @Test + public void testDynamicProgrammingLargeNumbers() { + int[][] distanceMatrix = {{0, 1000000, 2000000}, {1000000, 0, 1500000}, {2000000, 1500000, 0}}; + int expectedMinDistance = 4500000; + int result = TravelingSalesman.dynamicProgramming(distanceMatrix); + assertEquals(expectedMinDistance, result); + } +}