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| 1 | +// TSP.java |
| 2 | +// From Classic Computer Science Problems in Java Chapter 9 |
| 3 | +// Copyright 2020 David Kopec |
| 4 | +// |
| 5 | +// Licensed under the Apache License, Version 2.0 (the "License"); |
| 6 | +// you may not use this file except in compliance with the License. |
| 7 | +// You may obtain a copy of the License at |
| 8 | +// |
| 9 | +// http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | +// |
| 11 | +// Unless required by applicable law or agreed to in writing, software |
| 12 | +// distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | +// See the License for the specific language governing permissions and |
| 15 | +// limitations under the License. |
| 16 | + |
| 17 | +package chapter9; |
| 18 | + |
| 19 | +import java.util.ArrayList; |
| 20 | +import java.util.Arrays; |
| 21 | +import java.util.List; |
| 22 | +import java.util.Map; |
| 23 | + |
| 24 | +public class TSP { |
| 25 | + private final Map<String, Map<String, Integer>> distances; |
| 26 | + |
| 27 | + public TSP(Map<String, Map<String, Integer>> distances) { |
| 28 | + this.distances = distances; |
| 29 | + } |
| 30 | + |
| 31 | + public static <T> void swap(T[] array, int first, int second) { |
| 32 | + T temp = array[first]; |
| 33 | + array[first] = array[second]; |
| 34 | + array[second] = temp; |
| 35 | + } |
| 36 | + |
| 37 | + private static <T> void allPermutationsHelper(T[] permutation, List<T[]> permutations, int n) { |
| 38 | + // Base case - we found a new permutation, add it and return |
| 39 | + if (n <= 0) { |
| 40 | + permutations.add(permutation); |
| 41 | + return; |
| 42 | + } |
| 43 | + // Recursive case - find more permutations by doing swaps |
| 44 | + T[] tempPermutation = Arrays.copyOf(permutation, permutation.length); |
| 45 | + for (int i = 0; i < n; i++) { |
| 46 | + swap(tempPermutation, i, n - 1); // move element at i to the end |
| 47 | + // move everything else around, holding the end constant |
| 48 | + allPermutationsHelper(tempPermutation, permutations, n - 1); |
| 49 | + swap(tempPermutation, i, n - 1); // backtrack |
| 50 | + } |
| 51 | + } |
| 52 | + |
| 53 | + private static <T> List<T[]> permutations(T[] original) { |
| 54 | + List<T[]> permutations = new ArrayList<>(); |
| 55 | + allPermutationsHelper(original, permutations, original.length); |
| 56 | + return permutations; |
| 57 | + } |
| 58 | + |
| 59 | + public int pathDistance(String[] path) { |
| 60 | + String last = path[0]; |
| 61 | + int distance = 0; |
| 62 | + for (String next : Arrays.copyOfRange(path, 1, path.length)) { |
| 63 | + distance += distances.get(last).get(next); |
| 64 | + // distance to get back from last city to first city |
| 65 | + last = next; |
| 66 | + } |
| 67 | + return distance; |
| 68 | + } |
| 69 | + |
| 70 | + public String[] findShortestPath() { |
| 71 | + String[] cities = distances.keySet().toArray(String[]::new); |
| 72 | + List<String[]> paths = permutations(cities); |
| 73 | + String[] shortestPath = null; |
| 74 | + int minDistance = Integer.MAX_VALUE; // arbitrarily high |
| 75 | + for (String[] path : paths) { |
| 76 | + int distance = pathDistance(path); |
| 77 | + // distance from last to first must be added |
| 78 | + distance += distances.get(path[path.length - 1]).get(path[0]); |
| 79 | + if (distance < minDistance) { |
| 80 | + minDistance = distance; |
| 81 | + shortestPath = path; |
| 82 | + } |
| 83 | + } |
| 84 | + // add first city on to end and return |
| 85 | + shortestPath = Arrays.copyOf(shortestPath, shortestPath.length + 1); |
| 86 | + shortestPath[shortestPath.length - 1] = shortestPath[0]; |
| 87 | + return shortestPath; |
| 88 | + } |
| 89 | + |
| 90 | + public static void main(String[] args) { |
| 91 | + Map<String, Map<String, Integer>> vtDistances = Map.of( |
| 92 | + "Rutland", Map.of( |
| 93 | + "Burlington", 67, |
| 94 | + "White River Junction", 46, |
| 95 | + "Bennington", 55, |
| 96 | + "Brattleboro", 75), |
| 97 | + "Burlington", Map.of( |
| 98 | + "Rutland", 67, |
| 99 | + "White River Junction", 91, |
| 100 | + "Bennington", 122, |
| 101 | + "Brattleboro", 153), |
| 102 | + "White River Junction", Map.of( |
| 103 | + "Rutland", 46, |
| 104 | + "Burlington", 91, |
| 105 | + "Bennington", 98, |
| 106 | + "Brattleboro", 65), |
| 107 | + "Bennington", Map.of( |
| 108 | + "Rutland", 55, |
| 109 | + "Burlington", 122, |
| 110 | + "White River Junction", 98, |
| 111 | + "Brattleboro", 40), |
| 112 | + "Brattleboro", Map.of( |
| 113 | + "Rutland", 75, |
| 114 | + "Burlington", 153, |
| 115 | + "White River Junction", 65, |
| 116 | + "Bennington", 40)); |
| 117 | + TSP tsp = new TSP(vtDistances); |
| 118 | + String[] shortestPath = tsp.findShortestPath(); |
| 119 | + int distance = tsp.pathDistance(shortestPath); |
| 120 | + System.out.println("The shortest path is " + Arrays.toString(shortestPath) + " in " + |
| 121 | + distance + " miles."); |
| 122 | + } |
| 123 | +} |
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