How to find position of two endpoints given a distance to travel?

Question

Let's say I walking on the number line starting from 0 to 5. When I reach 5, If there still distance I need to travel, I go the reverse direction, walking from 5 to 0. Examples:

• Given 3 units of distance, I reach 3.
• Given 5 units of distance, I reach 5.
• Given 6 units of distance, I reach 4.
• Given 8 units of distance, I reach 2.
• Given 10 units of distance, I reach 0.

In general, given two points, a and b, and a < b, on the number line and distance D to travel, how do I find the position of the person when D == 0.

The expression I came up with is final_pos = start_pos + distance mod (end_pos - start_pos). which fails when it does the returning.

Answer 1

The end position depends on the evenness of the quotient when distance is divided by b-a. If it is even then the end position is a+r where r is the remainder when distance divided by b-a. Otherwise, the end position is b-r.

using static System.Console;


class Program
{
    static void Main(string[] args)
    {
        int a = 1;
        int b = 3;
        int distance = 7;

        int quotient = distance / (b - a);
        int remainder = distance % (b - a);
        if (quotient % 2 == 0)
            WriteLine($"end position: {a + remainder }");
        else
            WriteLine($"end position: {b - remainder }");

    }
}

Edit

Or you can represent as follows:

$$ \text{end position} = \frac{(a+r)\left(1+(-1)^q\right)+(b-r)\left(1-(-1)^q\right)}{2} $$

where $r$ is the remainder and $q$ is the quotient.