Get the smallest string given a weight (all chars have a weight)

smallestString.cs

//Time: O(n) where n is weight
//Memory: O(1) weights helper with 26 key:value pairs

//In this solution, I am decreasing weights one by one
//and searching its value in the weigths helper.
//As bigger the weight is the longer will take to algorithm execute

//I wrote a better solution using an array instead of a hashmap as a helper
//https://gist.github.com/WennderSantos/2256be4706a4f3cd6121ab322116a918

public static string smallestString(long weight)
{
    var weigths = new Dictionary<long, char>();
    var prevWeight = 1;
    var asciiVal = 65;

    weigths.Add(1, 'A');

    for (int i = 2; i <= 26; i++)
    {
        var letter = Convert.ToChar(asciiVal + i -1);
        var letterWeight = i * prevWeight + prevWeight;

        weigths.Add(letterWeight, letter);
        prevWeight = letterWeight;
    }

    if (weigths.ContainsKey(weight))
        return weigths[weight].ToString();

    var sb = new StringBuilder();
    var j = weight - 1;
    var target = weight;

    while (j > 0)
    {
        if (weigths.ContainsKey(j))
        {
            var count = 1;
            while (j * count <= target)
            {
                sb.Insert(0, weigths[j]);
                count++;
            }
            target -= j * (count - 1);
        }

        j--;
    }
    return sb.ToString();
}