kotlin coding test course, Ax + By = C

One of the mathematical problems that frequently appears in recent coding tests is related to equations of the form Ax + By = C. In this tutorial, we will analyze this problem and explain in detail how to solve it using Kotlin.

Problem Description

We are given integers with the following conditions:

  • A, B, and C are integers, and 1 <= |A|, |B|, |C| <= 1000.
  • x and y are non-negative integers.

Find all pairs (x, y) that satisfy Ax + By = C for the given A, B, and C.

Input Format

The first line contains A, B, and C separated by spaces.

Output Format

Output all pairs (x, y) that satisfy Ax + By = C. The pairs should be sorted in ascending order, and in case of equal x values, they should be sorted based on the y value.

Example Input

2 3 6

Example Output

0 2
1 1
2 0

Approach to the Problem

To solve this problem, let’s first discuss the method of finding integer x and y that satisfy the condition Ax + By = C. To find the pairs (x, y) that satisfy this condition, we follow these steps:

  1. Set up a loop: Change the value of x from 0 to C/A (be cautious if C is not divisible by A) and check. The value of y can be calculated from C – Ax.
  2. Check integer conditions: The calculated y must be non-negative and an integer. Verify this condition.
  3. Store and print results: Store the (x, y) pairs that satisfy the condition in a list and finally sort and print them.

Kotlin Implementation

fun findSolutions(A: Int, B: Int, C: Int) {
    val solutions = mutableListOf>()
    
    for(x in 0..C / A) {
        val yValue = (C - (A * x)) / B
        
        // Add (x, y) pair if conditions are met
        if (yValue >= 0 && (C - A * x) % B == 0) {
            solutions.add(Pair(x, yValue))
        }
    }

    // Sort
    solutions.sortWith(compareBy({ it.first }, { it.second }))
    
    // Print
    for (solution in solutions) {
        println("${solution.first} ${solution.second}")
    }
}

Complete Code

fun main() {
    val input = readLine()!!.split(" ")
    val A = input[0].toInt()
    val B = input[1].toInt()
    val C = input[2].toInt()
    
    findSolutions(A, B, C)
}

Conclusion

In this tutorial, we explored the algorithm and its implementation for solving the Ax + By = C problem. Problems of this type frequently appear in coding tests, and it is essential to understand the structure of the problem and clarify the approach. By practicing problems like this, you can develop your algorithmic thinking and strengthen your ability to solve various problems using Kotlin.

Additional Learning Resources