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.
Problem Description
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 ≤ M ≤ 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.
Input Format
- The first line contains two integers N (number of ingredients) and M (number of ingredients to select).
- The second line contains N integers representing the alcohol amounts of each ingredient.
- The third line contains the target alcohol amount K.
Output Format
Print the number of possible cocktail combinations modulo 1,000,000,007.
Example Input
5 3 1 2 3 4 5 5
Example Output
5
Problem Solving Process
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.
Step 1: Input Parsing
First, parse the input data and store N, M, the alcohol amounts, and K in variables.
using System;
using System.Collections.Generic;
class Program
{
static void Main(string[] args)
{
var input = Console.ReadLine().Split();
int N = int.Parse(input[0]);
int M = int.Parse(input[1]);
var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
int K = int.Parse(Console.ReadLine());
// We will find combinations through recursive calls later.
}
}
Step 2: Implementing the Function to Find Combinations
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.
static int CountCombinations(int[] alcohols, int N, int M, int K, int index, int count, int currentSum)
{
if(count == M)
{
return currentSum == K ? 1 : 0;
}
if(index >= N)
{
return 0;
}
// Selecting the current ingredient and making a recursive call
int includeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count + 1, currentSum + alcohols[index]);
// Not selecting the current ingredient and making a recursive call
int excludeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count, currentSum);
return includeCurrent + excludeCurrent;
}
Step 3: Main Function and Calling Combinations
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.
static void Main(string[] args)
{
var input = Console.ReadLine().Split();
int N = int.Parse(input[0]);
int M = int.Parse(input[1]);
var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
int K = int.Parse(Console.ReadLine());
long result = CountCombinations(alcohols, N, M, K, 0, 0, 0);
const int MOD = 1000000007;
Console.WriteLine(result % MOD);
}
Complete Source Code
using System;
using System.Collections.Generic;
class Program
{
static void Main(string[] args)
{
var input = Console.ReadLine().Split();
int N = int.Parse(input[0]);
int M = int.Parse(input[1]);
var alcohols = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
int K = int.Parse(Console.ReadLine());
long result = CountCombinations(alcohols, N, M, K, 0, 0, 0);
const int MOD = 1000000007;
Console.WriteLine(result % MOD);
}
static int CountCombinations(int[] alcohols, int N, int M, int K, int index, int count, int currentSum)
{
if(count == M)
{
return currentSum == K ? 1 : 0;
}
if(index >= N)
{
return 0;
}
// Selecting the current ingredient and making a recursive call
int includeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count + 1, currentSum + alcohols[index]);
// Not selecting the current ingredient and making a recursive call
int excludeCurrent = CountCombinations(alcohols, N, M, K, index + 1, count, currentSum);
return includeCurrent + excludeCurrent;
}
}
Conclusion
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.
We will continue to cover various algorithms and problem-solving methods, so we appreciate your interest!