public BinomialData ParseBinomial(string btxt)
{
BinomialData res = new BinomialData();
//(ax+b)^n
string[] arr = btxt.Replace("(", string.Empty).Replace(")", string.Empty).Split('^');
res.n = Int64.Parse(arr[1]);
//ax+b
res.b = 1;
string[] arr2 = arr[0].Split('+');
if (arr2.Length == 1)
{
res.b = -1;
arr2 = arr[0].Split('-');
}
res.b *= Int64.Parse(arr2[arr2.Length - 1]);
//ax
string s = arr[0].Remove(arr[0].Length - arr2[arr2.Length - 1].Length - 1);
res.x = s[s.Length - 1];
s = s.Remove(s.Length - 1);
if (!Int64.TryParse(s, out res.a))
{
res.a = (s == "-") ? -1 : 1;
}
return(res);
}
public string GetSolution(BinomialData data, Func <BinomialData, Int64, int, string> singleElementGenerator)
{
StringBuilder res = new StringBuilder();
Int64 currcoef = 1;
res.Append(singleElementGenerator(data, currcoef, 0));
for (int x = 0; x < data.n; x++)
{
currcoef = currcoef * (data.n - x) / (x + 1);
res.Append(singleElementGenerator(data, currcoef, x + 1));
}
return(res.ToString().Trim());
}
public string Expand(string expr)
{
BinomialData data = ParseBinomial(expr);
if (data.n == 0)
{
return("1");
}
//Int64[] coefs = GenerateCoefs(data.n);
//StringBuilder res = new StringBuilder();
//for (int i = 0; i < coefs.Length; i++)
// res.Append(GetSingleElement(data, coefs[i], i));
//return res.ToString().Trim();
return(GetSolution(data, GetSingleElement));
}
public string GetSingleElement(BinomialData data, Int64 coef, int index)
{
if (index == data.n)
{
Int64 lastc = (Int64)Math.Pow(data.b, data.n);
if (lastc == 0)
{
return("");
}
return((lastc > 0 ? "+" : "") + lastc.ToString());
}
Int64 c = coef * (Int64)(Math.Pow(data.a, data.n - index) * Math.Pow(data.b, index));
if (c == 0)
{
return("");
}
string spow = "";
if (data.n - index > 0)
{
spow = data.x.ToString() + ((data.n - index > 1) ? "^" + (data.n - index).ToString() : "");
}
if (c == 1)
{
return(spow);
}
if (c == -1)
{
return("-" + spow);
}
return((((c > 0) && (index > 0)) ? "+" : "") + c.ToString() + spow);
}