Hello!<\/strong> In this tutorial, we will cover the “Travelling Salesman Problem,” a common algorithm problem encountered in coding tests, using the Swift language. This problem requires an understanding of graph theory, combinatorial optimization, and overall algorithm problem-solving.<\/p>\n<\/header>\n The Travelling Salesman Problem (TSP) involves finding the shortest route for a salesman to visit n cities exactly once and return to the starting city, given the distances between each pair of cities. The inputs consist of the number of cities n and the distance matrix between those cities.<\/p>\n Output the length of the shortest route that visits all cities and returns to the starting city.<\/p>\n<\/section>\n This problem belongs to the NP-Hard category, so it can be solved using dynamic programming techniques combined with pruning. This method allows us to only choose the least costly paths while constructing routes, rather than exploring all possible paths.<\/p>\n First, declare a 2D array to store distance information between cities. Additionally, declare an array to check which cities have been visited and a variable to store the total distance so far.<\/p>\n Use bitmasking to represent whether each city has been visited. Every time we move to the next city via a recursive function, check off the visited cities and calculate the distance of the path taken once all cities have been visited and the route returns to the starting city. Since visited cities can be easily represented with a bitmask, they can be processed efficiently.<\/p>\n Instead of exploring all possible paths, proceed by calculating the minimum distance among the currently selected paths. If the given path has visited all cities, compare it with the previous distance to update the minimum value.<\/p>\n<\/section>\n Below is the code for finding the travelling salesman route using Swift.<\/p>\n This code uses bitmasking to check visit completion and recursively explores possible routes to calculate the minimum route. Every time a city is visited, the total distance is updated, and it finally returns the distance of the route that goes back to the starting city after visiting all cities.<\/p>\n The dp array stores the minimum route distances based on each city and visit status. Initially, all elements are set to -1 to indicate an unvisited state.<\/p>\n The recursive function tsp() takes the current position (pos) and the visited city bitmask (visited) as parameters to compute the optimal route. If all cities have been visited, it compares the cost of returning to the starting city and returns the minimum value.<\/p>\nProblem Definition<\/h2>\n
Input Format<\/h3>\n
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Output Format<\/h3>\n
Problem-Solving Approach<\/h2>\n
Step 1: Data Structure Design<\/h3>\n
Step 2: Using Bitmask and Recursive Functions<\/h3>\n
Step 3: Finding the Optimal Route<\/h3>\n
Swift Code Implementation<\/h2>\n
\nlet INF = Int.max\nvar dist: [[Int]] = []\nvar n = 0\nvar dp: [[Int]] = []\nvar visited: Int = 0\nvar ans: Int = INF\n\nfunc tsp(pos: Int, visited: Int) -> Int {\n if visited == (1 << n) - 1 {\n return dist[pos][0] != 0 ? dist[pos][0] : INF\n }\n \n if dp[pos][visited] != -1 {\n return dp[pos][visited]\n }\n \n var minimum = INF\n for city in 0..Code Analysis and Functionality<\/h2>\n
1. Initializing the dp Array<\/h3>\n
2. Recursive Function tsp()<\/h3>\n
3. Route Calculation<\/h3>\n