Hello! Today, I will address an algorithm problem on the topic of ‘Taking Pebbles’ for those preparing for a C# coding test. This article is carefully designed with various components. It will help provide a deep understanding through an overview of the problem, approach, implementation, examples, and explanations.
Problem Description
Imagine a game where pebbles are randomly placed in different sections. The pebbles have a chaotic distribution. Users must take pebbles to create a box, but there are restrictions on the number of pebbles that can be placed in the box. When taking pebbles, the user must always take a fixed number from each section, and the function must calculate and output the number of possible ways to select pebbles that satisfy this condition.
Problem Definition
We have an integer array stones representing the number of pebbles in each section and an integer array pick defining the number of pebbles to take from each section. The lengths of both arrays are equal, and you need to write a function countWays(stones, pick) that calculates and returns the number of ways to take pebbles from each section.
Input
stones: An integer array representing the number of pebbles in each section.pick: An integer array representing the number of pebbles to take from each section.
Output
- Returns the number of ways to take pebbles from all sections as an integer.
Constraints
- 1 ≤
stones.Length,pick.Length≤ 50 - 0 ≤
stones[i]≤ 100 - 0 ≤
pick[i]≤stones[i]
Approach
To solve this problem, we will use the combination formula to calculate the number of ways to take pebbles from each section. If there are multiple sections, we can find the total number of cases by multiplying the combinations for each section. This is based on mathematical concepts and helps us efficiently calculate the number of combinations.
The number of combinations C(n, k) is defined by the following formula:
C(n, k) = n! / (k! * (n - k)!)
Here, n represents the number of pebbles, and k represents the number of pebbles to be taken. By calculating the combinations for each section and multiplying them, we derive the final number of cases.
Implementation
Now, let’s actually write the code. We will implement a function that meets the requirements using the C# language.
using System;
public class Solution {
public int countWays(int[] stones, int[] pick) {
int totalWays = 1; // Initial value to multiply all cases
for (int i = 0; i < stones.Length; i++) {
totalWays *= Combinations(stones[i], pick[i]);
}
return totalWays;
}
// Helper method to calculate combinations
private int Combinations(int n, int k) {
if (k > n) return 0;
if (k == 0 || k == n) return 1;
int numerator = Factorial(n);
int denominator = Factorial(k) * Factorial(n - k);
return numerator / denominator;
}
// Method to calculate factorial
private int Factorial(int num) {
if (num == 0) return 1;
int result = 1;
for (int i = 1; i <= num; i++) {
result *= i;
}
return result;
}
}
Examples
We will look at a few test cases to verify that the code we wrote works correctly.
Example 1
Input:
stones = [5, 3, 8]
pick = [2, 1, 3]
Output: 840
Explanation: The number of ways to take 2 from section 0: C(5, 2) = 10, the number of ways to take 1 from section 1: C(3, 1) = 3, the number of ways to take 3 from section 2: C(8, 3) = 56. Total number of ways = 10 * 3 * 56 = 1680.
Example 2
Input:
stones = [2, 2, 2]
pick = [1, 1, 1]
Output: 8
Explanation: The number of ways to take 1 from each: C(2, 1) = 2. Multiplying the number of ways in all three sections: 2 * 2 * 2 = 8.
Conclusion
Today, we solved the ‘Taking Pebbles’ problem for those preparing for a C# coding test. When solving algorithm problems, it’s important to understand the essence of each problem and adopt an appropriate approach accordingly. I hope you continue to solve a variety of problems to enhance your skills.
Coding tests require practice, and the more varied types of problems you encounter, the more experience you can gain. Wishing you happy coding!