In this course, we will address a problem frequently found in actual coding tests with the theme of ‘Making Cocktails’. This problem requires various algorithmic thinking and will be solved using the C# programming language. Problems related to making cocktails may include combinations, divide and conquer, optimization problems, etc., and in this course, we will select a specific problem to solve step by step.<\/p>\n
You have N ingredients. Each ingredient contains a specific amount of alcohol. Additionally, each ingredient is assigned an index from 1 to N. You wish to select M (1 \u2264 M \u2264 N) ingredients to make a cocktail. The sum of the alcohol amounts from the selected ingredients must equal K (K is a given integer). Your goal is to find various combinations to calculate the number of possible cocktails you can make.<\/p>\n
Print the number of possible cocktail combinations modulo 1,000,000,007.<\/p>\n
\n5 3\n1 2 3 4 5\n5\n<\/pre>\nExample Output<\/h2>\n
\n5\n<\/pre>\nProblem Solving Process<\/h2>\n
To solve this problem, you need to make various combinations of ingredients and check the sum of their alcohol amounts. In C#, you can use recursive calls to find combinations. Below is a basic algorithm design to solve this problem.<\/p>\n
Step 1: Input Parsing<\/h3>\n
First, parse the input data and store N, M, the alcohol amounts, and K in variables.<\/p>\n
\nusing System;\nusing System.Collections.Generic;\n\nclass Program\n{\n static void Main(string[] args)\n {\n var input = Console.ReadLine().Split();\n int N = int.Parse(input[0]);\n int M = int.Parse(input[1]);\n\n var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);\n int K = int.Parse(Console.ReadLine());\n \n \/\/ We will find combinations through recursive calls later.\n }\n}\n<\/pre>\nStep 2: Implementing the Function to Find Combinations<\/h3>\n
We will implement a recursive function to find combinations. This function will take the current index, the number of selected ingredients, and the current alcohol amount as parameters.<\/p>\n
\nstatic int CountCombinations(int[] alcohols, int N, int M, int K, int index, int count, int currentSum)\n{\n if(count == M)\n {\n return currentSum == K ? 1 : 0;\n }\n \n if(index >= N)\n {\n return 0;\n }\n\n \/\/ Selecting the current ingredient and making a recursive call\n int includeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count + 1, currentSum + alcohols[index]);\n \/\/ Not selecting the current ingredient and making a recursive call\n int excludeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count, currentSum);\n\n return includeCurrent + excludeCurrent;\n}\n<\/pre>\nStep 3: Main Function and Calling Combinations<\/h3>\n
Now, we will call the combination function defined above in the main function to output the result. Additionally, we will output the result modulo 1,000,000,007.<\/p>\n
\nstatic void Main(string[] args)\n{\n var input = Console.ReadLine().Split();\n int N = int.Parse(input[0]);\n int M = int.Parse(input[1]);\n\n var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);\n int K = int.Parse(Console.ReadLine());\n\n long result = CountCombinations(alcohols, N, M, K, 0, 0, 0);\n const int MOD = 1000000007;\n\n Console.WriteLine(result % MOD);\n}\n<\/pre>\nComplete Source Code<\/h2>\n
\nusing System;\nusing System.Collections.Generic;\n\nclass Program\n{\n static void Main(string[] args)\n {\n var input = Console.ReadLine().Split();\n int N = int.Parse(input[0]);\n int M = int.Parse(input[1]);\n\n var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);\n int K = int.Parse(Console.ReadLine());\n\n long result = CountCombinations(alcohols, N, M, K, 0, 0, 0);\n const int MOD = 1000000007;\n\n Console.WriteLine(result % MOD);\n }\n\n static int CountCombinations(int[] alcohols, int N, int M, int K, int index, int count, int currentSum)\n {\n if(count == M)\n {\n return currentSum == K ? 1 : 0;\n }\n \n if(index >= N)\n {\n return 0;\n }\n\n \/\/ Selecting the current ingredient and making a recursive call\n int includeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count + 1, currentSum + alcohols[index]);\n \/\/ Not selecting the current ingredient and making a recursive call\n int excludeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count, currentSum);\n\n return includeCurrent + excludeCurrent;\n }\n}\n<\/pre>\nConclusion<\/h2>\n
This algorithm problem can be solved with a simple approach utilizing combinations and recursion. It is a useful way to create specific values by combining multiple ingredients. Since it frequently appears in coding tests, it is highly recommended to practice this problem.<\/p>\n
We will continue to cover various algorithms and problem-solving methods, so we appreciate your interest!<\/p>\n
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