Hello! In this post, we will take some time to solve algorithm problems using Java. The topic is “Planning a Trip<\/strong>“. We will solve the problem through an algorithmic approach by selecting various places, just like planning a trip, and finding the optimal route.<\/p>\n The trip planning problem is given in the following form. A total of n<\/strong> travel destinations are provided, and the travel costs between each destination are specified. Our goal is to select some of the given destinations and find the minimum cost route to visit those destinations.<\/p>\n This problem can be viewed as one of the representative shortest path problems. The destinations can be represented as vertices, and the travel costs can be expressed as edge weights. This structure is typically solved using graph algorithms. In particular, since all vertices need to be visited, it can be solved similarly to the Traveling Salesman Problem (TSP)<\/strong>.<\/p>\n There are various methods to solve the trip planning problem, but the basic idea is as follows:<\/p>\n To achieve this, the recursive backtracking<\/strong> method is effective and can guarantee an optimal solution. Additionally, using a memoization technique can reduce duplicate calculations.<\/p>\n Below is the Java code to solve the problem:<\/p>\n The above code is written based on an example with 5 destinations. The findMinCost<\/strong> method takes the current city, current cost, and the number of visited cities as parameters and records the minimum cost when all cities have been visited.<\/p>\n When the above code is executed, it will output the minimum cost for the given example. This algorithm exhaustively explores all cities, so the time complexity is O(n!)<\/strong>. As the number of cities increases, the execution time increases, so practical improvements are necessary:<\/p>\nProblem Description<\/h2>\n
Problem Definition<\/h3>\n
\nInput:\n- Number of destinations n<\/strong> (1 \u2264 n \u2264 100)\n- A n x n<\/strong> matrix cost<\/strong> representing the travel costs between each destination (cost[i][j]: cost of traveling from i to j)\n\nOutput:\n- The minimum cost to visit the selected destinations\n<\/pre>\n
Problem Analysis<\/h2>\n
Algorithm Design<\/h3>\n
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Java Implementation<\/h3>\n
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\nimport java.util.Arrays;\n\npublic class TravelPlan {\n\n private static int n; \/\/ Number of destinations\n private static int[][] cost; \/\/ Travel costs\n private static boolean[] visited; \/\/ Visit status\n private static int minCost = Integer.MAX_VALUE; \/\/ Minimum cost\n\n public static void main(String[] args) {\n n = 5; \/\/ Example number of destinations\n cost = new int[][] {\n {0, 10, 15, 20, 25},\n {10, 0, 35, 25, 30},\n {15, 35, 0, 30, 20},\n {20, 25, 30, 0, 15},\n {25, 30, 20, 15, 0}\n };\n visited = new boolean[n];\n visited[0] = true; \/\/ Mark starting point as visited\n findMinCost(0, 0, 1);\n System.out.println(\"Minimum cost: \" + minCost);\n }\n\n private static void findMinCost(int currentCity, int currentCost, int count) {\n if (count == n) {\n \/\/ If all cities have been visited\n minCost = Math.min(minCost, currentCost + cost[currentCity][0]); \/\/ Add the cost to return to the starting point\n return;\n }\n\n for (int nextCity = 0; nextCity < n; nextCity++) {\n if (!visited[nextCity]) {\n visited[nextCity] = true; \/\/ Mark as visited\n findMinCost(nextCity, currentCost + cost[currentCity][nextCity], count + 1);\n visited[nextCity] = false; \/\/ Backtrack\n }\n }\n }\n}\n<\/code>\n<\/pre>\nCode Explanation<\/h2>\n
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Result Analysis<\/h2>\n