JavaScript Coding Test Course, Ax + By = C

Coding tests are an important step in assessing your capabilities as a software developer. In particular, algorithm problems are a great way to test problem-solving skills and creativity. In this course, we will solve the problem of finding the most basic solution to a linear equation using JavaScript. We will find the solution to the given equation Ax + By = C.

Problem Definition

The problem is as follows:

Given integers A, B, and C, find all pairs of integers (x, y) that satisfy Ax + By = C. Note that x and y must be at least 0 and can be at most 10000.

Problem Analysis

This problem is about finding the solution to a simple linear equation, which must satisfy the following conditions for the two variables x and y:

  • Ax + By = C
  • 0 ≤ x, y ≤ 10000

To solve this problem, we can use a loop to substitute all possible x values, calculate the corresponding y values, and check whether the conditions are satisfied.

Solution Strategy

1. Iterate x from 0 to 10000.

2. For each x, calculate y:

y = (C - Ax) / B

3. Check if y is a non-negative integer.

4. Store all pairs (x, y) that satisfy the conditions.

JavaScript Code Implementation

Now, based on the above strategy, let’s implement the code using JavaScript. Below is an example of the code:

function findSolutions(A, B, C) {
    const solutions = [];
    
    for (let x = 0; x <= 10000; x++) {
        // Handle the case when B is 0
        if (B === 0) {
            if (A * x === C) {
                solutions.push([x, 0]);
            }
            continue;
        }
        
        const y = (C - A * x) / B;

        // Check if y is an integer and non-negative
        if (y >= 0 && Number.isInteger(y)) {
            solutions.push([x, y]);
        }
    }
    
    return solutions;
}

// Example execution
const A = 1, B = 2, C = 3;
const result = findSolutions(A, B, C);
console.log(result); // [ [ 0, 1 ], [ 1, 1 ], [ 3, 0 ] ]

Code Explanation

The above JavaScript function findSolutions works as follows:

  1. Create an array solutions to store the results.
  2. Iterate x from 0 to 10000.
  3. For each x, calculate y. Check if B is 0, and handle the case where B is 0 as an exception.
  4. After confirming that y is non-negative and an integer, add the (x, y) pair to the solutions array if the conditions are satisfied.
  5. Return the solutions array after all iterations are complete.

Test Cases

Now let’s verify that the function works correctly with several test cases.

console.log(findSolutions(1, 2, 3)); // [ [ 0, 1 ], [ 1, 1 ], [ 3, 0 ] ]
console.log(findSolutions(2, 3, 6)); // [ [ 0, 2 ], [ 3, 0 ] ]
console.log(findSolutions(0, 1, 5)); // [ [ 0, 5 ] ]
console.log(findSolutions(1, 0, 5)); // [ [ 5, 0 ] ]
console.log(findSolutions(0, 0, 0)); // [ [ 0, 0 ] ]

Conclusion

In this article, we implemented an algorithm to find the solutions to the given linear equation Ax + By = C using JavaScript. We detailed the logic step by step to approach the problem and confirmed that the function works correctly through various test cases. Such problems are often presented in coding tests, and developing an algorithmic mindset through them will be greatly beneficial. We hope to elevate your coding skills further through a variety of algorithmic challenges.