Java Coding Test Course, Travel Planning

Hello! In this post, we will take some time to solve algorithm problems using Java. The topic is “Planning a Trip“. We will solve the problem through an algorithmic approach by selecting various places, just like planning a trip, and finding the optimal route.

Problem Description

The trip planning problem is given in the following form. A total of n 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.

Problem Definition

Input:
- Number of destinations n (1 ≤ n ≤ 100)
- A n x n matrix cost representing the travel costs between each destination (cost[i][j]: cost of traveling from i to j)

Output:
- The minimum cost to visit the selected destinations

Problem Analysis

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).

Algorithm Design

There are various methods to solve the trip planning problem, but the basic idea is as follows:

• We need to consider all possible routes to visit the destinations.
• Calculate the costs for each possible route.
• Find the route with the lowest total cost.

To achieve this, the recursive backtracking method is effective and can guarantee an optimal solution. Additionally, using a memoization technique can reduce duplicate calculations.

Java Implementation

Below is the Java code to solve the problem:

import java.util.Arrays;

public class TravelPlan {

    private static int n; // Number of destinations
    private static int[][] cost; // Travel costs
    private static boolean[] visited; // Visit status
    private static int minCost = Integer.MAX_VALUE; // Minimum cost

    public static void main(String[] args) {
        n = 5; // Example number of destinations
        cost = new int[][] {
            {0, 10, 15, 20, 25},
            {10, 0, 35, 25, 30},
            {15, 35, 0, 30, 20},
            {20, 25, 30, 0, 15},
            {25, 30, 20, 15, 0}
        };
        visited = new boolean[n];
        visited[0] = true; // Mark starting point as visited
        findMinCost(0, 0, 1);
        System.out.println("Minimum cost: " + minCost);
    }

    private static void findMinCost(int currentCity, int currentCost, int count) {
        if (count == n) {
            // If all cities have been visited
            minCost = Math.min(minCost, currentCost + cost[currentCity][0]); // Add the cost to return to the starting point
            return;
        }

        for (int nextCity = 0; nextCity < n; nextCity++) {
            if (!visited[nextCity]) {
                visited[nextCity] = true; // Mark as visited
                findMinCost(nextCity, currentCost + cost[currentCity][nextCity], count + 1);
                visited[nextCity] = false; // Backtrack
            }
        }
    }
}

Code Explanation

The above code is written based on an example with 5 destinations. The findMinCost 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.

• It recursively moves to the next city while accumulating the costs.
• It adds the cost of returning to the starting point after visiting all cities.

Result Analysis

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!). As the number of cities increases, the execution time increases, so practical improvements are necessary:

• Using dynamic programming (DP) techniques to reduce duplicate calculations.
• Employing heuristic methods like the nearest neighbor algorithm to find approximate solutions.

Conclusion

Today, we learned about recursive backtracking and graph search techniques through the algorithm problem of planning a trip. This problem is frequently encountered in coding tests, so ample practice and understanding are necessary. If you desire a deeper understanding of algorithms, solving various modified problems is also a good approach.

I hope this article helps you prepare for your coding tests! In the next post, we will discuss methods using dynamic programming.