How to create cyclic range of numbers C++

Question

I want a range of numbers (lets say 30-50) to be cyclic. So if you do 50 + 1 = 30, OR 49 + 3 = 31. How would I do this in C++? I believe I would do it with the % operator but I'm having trouble wrapping my head around it.

Answer 1

Before performing your addition or subtraction, you need to subtract 30, then perform your operation, after that divide modulo 20 (because 50-30=20) and finally add-up 30 to get your desired result.

Answer 2

You can simply use % operator. For instance, to calculate (49 + 3), you can rewrite it as: (30 + (22 % 20)). This will result to 32. What we are doing here is, simply take the whole value greater than 30 and then modulo it by 20, so that we get a number in the range 30 - 50 because when you use modulo 20 on a number, you will get a value of range 0 - 19.

Answer 3

You would be working in the ring Z/21Z. Just do the addition normally, then to map any number back into the "canonical" range, you would do something like:

// Maps `n` in ring Z/(stop-start+1)Z to the equivalent
// number between start and stop (inclusive)
template<typename T>
constexpr T to_ring(T n, T start, T stop) noexcept {
    T ring_size = stop - start + 1;

    n = n % ring_size;
    if (n < 0) n = (n + ring_size) % ring_size;
    // Now 0 <= n && n < ring_size

    // offset === 0 in this ring (offset % ring_size == 0),
    // so adding it will give an equivalent number
    T offset = start - (start % ring_size);
    n += offset;

    // ring_size === 0, so still equivalent, in case this number is outside the range
    // Only one of the following can be true, depending on the sign of `start`
    if (n < start) n += ring_size;
    if (n > stop) n -= ring_size;

    assert(start <= n && n <= stop);
    return n;
}

And then your addition would look like:

// 50 + 1 = 51 = 30
std::cout << "50 + 1 = " << to_ring(50 + 1, 30, 50) << '\n';
// 101 + 57 = 158 = 32
//          = 38 + 36 = 74 = 32
std::cout << "101 + 57 = " << to_ring(101 + 57, 30, 50) << '\n';
std::cout << to_ring(101, 30, 50) << " + " << to_ring(57, 30, 50) << " = "
          << to_ring(to_ring(101, 30, 50) + to_ring(57, 30, 50), 30, 50) << '\n';

Note it does not matter that you map the numbers before you add them, the result will be the same (since after mapping, they are equivalent numbers in the ring)

Answer 4

Here is my take on this. If you want a recursive function that does it for you, you can write it out in multiple steps like this:

#include <iostream>

int next_cyclical_number(int x, int min, int max){
    if( min >= max )
        return -99999;
    if( x < min )
        x = min;

    int mod_value = max - min;

    int offset = min;

    int temp = x - min;

    int remainder = (temp + 1)%mod_value;

    int ret_val = min + remainder;

    return ret_val;
}

int main(int argc, char *argv[])
{
    // show 100 numbers using the function

    int current_number = 0;
    for(int i = 0; i < 100; i++){
        current_number = next_cyclical_number(current_number, 30, 51);
        std::cout << "i: " << i << "\t" << "number: " << current_number << std::endl;
    }

    return 0;
}

Output:

i: 0    number: 31
i: 1    number: 32
i: 2    number: 33
i: 3    number: 34
i: 4    number: 35
i: 5    number: 36
i: 6    number: 37
i: 7    number: 38
i: 8    number: 39
i: 9    number: 40
i: 10   number: 41
i: 11   number: 42
i: 12   number: 43
i: 13   number: 44
i: 14   number: 45
i: 15   number: 46
i: 16   number: 47
i: 17   number: 48
i: 18   number: 49
i: 19   number: 50
i: 20   number: 30
i: 21   number: 31
i: 22   number: 32
i: 23   number: 33
i: 24   number: 34
i: 25   number: 35
i: 26   number: 36
i: 27   number: 37
i: 28   number: 38
i: 29   number: 39
i: 30   number: 40
i: 31   number: 41
i: 32   number: 42
i: 33   number: 43
i: 34   number: 44
i: 35   number: 45
i: 36   number: 46
i: 37   number: 47
i: 38   number: 48
i: 39   number: 49
i: 40   number: 50
i: 41   number: 30
i: 42   number: 31
i: 43   number: 32
i: 44   number: 33
i: 45   number: 34
i: 46   number: 35
i: 47   number: 36
i: 48   number: 37
i: 49   number: 38
i: 50   number: 39
i: 51   number: 40
i: 52   number: 41
i: 53   number: 42
i: 54   number: 43
i: 55   number: 44
i: 56   number: 45
i: 57   number: 46
i: 58   number: 47
i: 59   number: 48
i: 60   number: 49
i: 61   number: 50
i: 62   number: 30
i: 63   number: 31
i: 64   number: 32
i: 65   number: 33
i: 66   number: 34
i: 67   number: 35
i: 68   number: 36
i: 69   number: 37
i: 70   number: 38
i: 71   number: 39
i: 72   number: 40
i: 73   number: 41
i: 74   number: 42
i: 75   number: 43
i: 76   number: 44
i: 77   number: 45
i: 78   number: 46
i: 79   number: 47
i: 80   number: 48
i: 81   number: 49
i: 82   number: 50
i: 83   number: 30
i: 84   number: 31
i: 85   number: 32
i: 86   number: 33
i: 87   number: 34
i: 88   number: 35
i: 89   number: 36
i: 90   number: 37
i: 91   number: 38
i: 92   number: 39
i: 93   number: 40
i: 94   number: 41
i: 95   number: 42
i: 96   number: 43
i: 97   number: 44
i: 98   number: 45
i: 99   number: 46