Problem Description<\/h2>\n
\n You are planning an event to deliver Christmas surprise gifts to your friends.
\n There are N friends, and each friend has a list of gifts they would like to receive.
\n You need to ensure that as many friends as possible receive their desired gifts.
\n Each friend specifies one gift they want, and there is only one gift.
\n However, the gift can only be delivered to one friend.\n <\/p>\n
Input Format<\/h3>\n\n- The first line contains the number of friends N.<\/li>\n
- From the second line up to the Nth line, the gifts each friend wants are listed.<\/li>\n<\/ul>\n
Output Format<\/h3>\n
\n Output the maximum number of friends who can receive their desired gifts.\n <\/p>\n
Constraints<\/h3>\n\n- 1 \u2264 N \u2264 100<\/li>\n
- Gifts are represented by uppercase letters, with a maximum of 26 types.<\/li>\n<\/ul>\n<\/section>\n
\nApproach to the Problem<\/h2>\n
\n This problem is fundamentally similar to the maximum matching problem in graph theory.
\n Each friend can be represented as a vertex, and the gifts they desire can be represented as edges.
\n To solve this problem, we will take the friends’ gift requests as input,
\n create a list of friends requesting each gift, and then use an algorithm to find the maximum matching.\n <\/p>\n
Algorithm Overview<\/h3>\n
\n – Construct a graph based on the number of friends and the requested gifts.
\n – Explore the graph to find assignable gifts for each friend.
\n – Use the DFS (Depth First Search) algorithm to attempt possible matchings.\n <\/p>\n<\/section>\n\nCode Implementation<\/h2>\n
\n Below is the solution code for the gift delivery problem written in C#.\n <\/p>\n
\n \nusing System;\nusing System.Collections.Generic;\n\nclass Program\n{\n static int N; \/\/ Number of friends\n static List friends; \/\/ List of gifts friends want\n static Dictionary gifts; \/\/ Matching status of each gift\n static bool[] visited; \/\/ Record of DFS visitation\n\n static void Main(string[] args)\n {\n N = int.Parse(Console.ReadLine());\n friends = new List();\n\n for (int i = 0; i < N; i++)\n {\n friends.Add(Console.ReadLine());\n }\n\n gifts = new Dictionary();\n int totalMatched = 0;\n\n foreach (var friend in friends)\n {\n visited = new bool[26];\n if (DFS(friend[0], ref totalMatched))\n {\n totalMatched++;\n }\n }\n\n Console.WriteLine(totalMatched);\n }\n\n static bool DFS(char gift, ref int totalMatched)\n {\n int index = gift - 'A';\n\n if (visited[index]) return false; \/\/ Gift already visited\n visited[index] = true;\n\n if (!gifts.ContainsKey(gift.ToString()) || gifts[gift.ToString()] == -1)\n {\n gifts[gift.ToString()] = totalMatched; \/\/ Gift matching\n return true;\n }\n\n return false;\n }\n}\n <\/string,><\/string><\/string,><\/string><\/code>\n <\/pre>\n<\/section>\n\nCode Explanation<\/h2>\n
\n The above code solves the gift delivery problem through the following procedures.\n <\/p>\n
\n- Input Reading:<\/strong> Read the number of friends N and input the desired gifts for each friend.<\/li>\n
- DFS Function Implementation:<\/strong> Check if the requested gift is available and attempt matching.<\/li>\n
- Visitation Record:<\/strong> Manage visitation records to accommodate requests for each gift only once.<\/li>\n
- Output Result:<\/strong> Output the maximum matching result.<\/li>\n<\/ul>\n<\/section>\n
\nTime Complexity<\/h2>\n
Output Format<\/h3>\n
\n Output the maximum number of friends who can receive their desired gifts.\n <\/p>\n
Constraints<\/h3>\n\n- 1 \u2264 N \u2264 100<\/li>\n
- Gifts are represented by uppercase letters, with a maximum of 26 types.<\/li>\n<\/ul>\n<\/section>\n
\nApproach to the Problem<\/h2>\n
\n This problem is fundamentally similar to the maximum matching problem in graph theory.
\n Each friend can be represented as a vertex, and the gifts they desire can be represented as edges.
\n To solve this problem, we will take the friends’ gift requests as input,
\n create a list of friends requesting each gift, and then use an algorithm to find the maximum matching.\n <\/p>\n
Algorithm Overview<\/h3>\n
\n – Construct a graph based on the number of friends and the requested gifts.
\n – Explore the graph to find assignable gifts for each friend.
\n – Use the DFS (Depth First Search) algorithm to attempt possible matchings.\n <\/p>\n<\/section>\n\nCode Implementation<\/h2>\n
\n Below is the solution code for the gift delivery problem written in C#.\n <\/p>\n
\n \nusing System;\nusing System.Collections.Generic;\n\nclass Program\n{\n static int N; \/\/ Number of friends\n static List friends; \/\/ List of gifts friends want\n static Dictionary gifts; \/\/ Matching status of each gift\n static bool[] visited; \/\/ Record of DFS visitation\n\n static void Main(string[] args)\n {\n N = int.Parse(Console.ReadLine());\n friends = new List();\n\n for (int i = 0; i < N; i++)\n {\n friends.Add(Console.ReadLine());\n }\n\n gifts = new Dictionary();\n int totalMatched = 0;\n\n foreach (var friend in friends)\n {\n visited = new bool[26];\n if (DFS(friend[0], ref totalMatched))\n {\n totalMatched++;\n }\n }\n\n Console.WriteLine(totalMatched);\n }\n\n static bool DFS(char gift, ref int totalMatched)\n {\n int index = gift - 'A';\n\n if (visited[index]) return false; \/\/ Gift already visited\n visited[index] = true;\n\n if (!gifts.ContainsKey(gift.ToString()) || gifts[gift.ToString()] == -1)\n {\n gifts[gift.ToString()] = totalMatched; \/\/ Gift matching\n return true;\n }\n\n return false;\n }\n}\n <\/string,><\/string><\/string,><\/string><\/code>\n <\/pre>\n<\/section>\n\nCode Explanation<\/h2>\n
\n The above code solves the gift delivery problem through the following procedures.\n <\/p>\n
\n- Input Reading:<\/strong> Read the number of friends N and input the desired gifts for each friend.<\/li>\n
- DFS Function Implementation:<\/strong> Check if the requested gift is available and attempt matching.<\/li>\n
- Visitation Record:<\/strong> Manage visitation records to accommodate requests for each gift only once.<\/li>\n
- Output Result:<\/strong> Output the maximum matching result.<\/li>\n<\/ul>\n<\/section>\n
\nTime Complexity<\/h2>\n
Approach to the Problem<\/h2>\n
\n This problem is fundamentally similar to the maximum matching problem in graph theory.
\n Each friend can be represented as a vertex, and the gifts they desire can be represented as edges.
\n To solve this problem, we will take the friends’ gift requests as input,
\n create a list of friends requesting each gift, and then use an algorithm to find the maximum matching.\n <\/p>\n
Algorithm Overview<\/h3>\n
\n – Construct a graph based on the number of friends and the requested gifts. \n Below is the solution code for the gift delivery problem written in C#.\n <\/p>\n \n The above code solves the gift delivery problem through the following procedures.\n <\/p>\n
\n – Explore the graph to find assignable gifts for each friend.
\n – Use the DFS (Depth First Search) algorithm to attempt possible matchings.\n <\/p>\n<\/section>\nCode Implementation<\/h2>\n
\n
\nusing System;\nusing System.Collections.Generic;\n\nclass Program\n{\n static int N; \/\/ Number of friends\n static ListCode Explanation<\/h2>\n
\n
Time Complexity<\/h2>\n