Rebin Rebin -4 years ago 101
C# Question

Generate all polynomials with coefficients 0 or 1 given degree n

I am trying to enumerate in 'C#' all the possible polynomials given the degree. Is there any algorithm to enumerate all possible polynomials given degree n? Maybe I dont know how to ask this question precisely but these are the examples

for example:

for n=1

x+1 return [1 1]
x return [1 0]


for n=2

x^2+x+1 return [1 1 1]
x^2+x return [1 1 0]
x^2 return [1 0 0]
x^2+1 return [1 0 1]


for x=3

x^3 return [1 0 0 0]
x^3+x^2 return [1 1 0 0]
x^3+x return [1 0 1 0]
x^3+x^2+x return [1 1 1 0]
x^3+1 return [1 0 0 1]
x^3+x^2+1 return [1 1 0 1]
x^3+x+1 return [1 0 1 1]
x^3+x^2+x+1 return [1 1 1 1]


Any pseudo code or algorithm would help.

Answer Source

Set the leftmost bit, then do a binary counter on the right n bits. You actually need n+1 bits to account for x^0, (in my first attempt I was off by 1).

You can generate an enumeration like so:

IEnumerable<int[]> GenPolys(int n)
{
    int[] a = new int[n + 1];
    a[0] = 1;
    bool ok = true;
    while (ok)
    {
        yield return a;
        ok = false;
        for (int i = 1; i < a.Length; i++)
        {
            a[i] = 1 - a[i]; // flip the ith bit
            if (a[i] == 1)
            {
                ok = true;
                break;
            }
        }
    }
}

Usage:

foreach (int[] poly in GenPolys(4))
{
    // your code here
}
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