{"id":34510,"date":"2024-11-01T09:28:48","date_gmt":"2024-11-01T09:28:48","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=34510"},"modified":"2024-11-01T11:40:58","modified_gmt":"2024-11-01T11:40:58","slug":"javascript-coding-test-course-solving-the-traveling-salesman-problem","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/34510\/","title":{"rendered":"JavaScript Coding Test Course, Solving the Traveling Salesman Problem"},"content":{"rendered":"

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Hello! In this tutorial, we will cover one of the frequently asked problems in coding tests, the Traveling Salesman Problem (TSP)<\/strong>. This problem helps to understand important concepts in graphs and dynamic programming.<\/p>\n

1. Problem Description<\/h2>\n

The Traveling Salesman Problem is the problem of finding the minimum cost path that visits all given cities once and returns to the starting city. This problem is typically represented by a distance matrix that provides the cost of moving between cities, and the salesman must visit all cities exactly once.<\/p>\n

2. Mathematical Representation of the Problem<\/h2>\n

Let the number of cities be represented as N<\/strong>. The distance matrix between cities is defined in the form of cost[i][j]<\/code>. Here, cost[i][j]<\/code> represents the cost of moving from city i<\/code> to city j<\/code>. The path that the salesman must take can be expressed as follows:<\/p>\n

\nmin(cost[0][1] + cost[1][2] + ... + cost[N-1][0])\n<\/pre>\n
3. Approach to Solve the Problem<\/h2>\n
Since the Traveling Salesman Problem is NP-hard, the time complexity is very high for solving it using brute force. Therefore, we can solve the problem more efficiently using dynamic programming<\/strong>.<\/p>\n
To solve this problem using a dynamic programming approach, we will use bit masking. Bit masking helps to easily check the visiting status by representing each city as a bit. Let’s approach the problem using the following algorithmic steps.<\/p>\n
3.1 State Representation through Bit Masking<\/h3>\n
We represent the state of visited cities as a bitmask. For example, if there are 4 cities:<\/p>\n