Code Snippit - Determining whether brackets are balanced

We usually have coding challenges at work quite often. This one was quite useful. The aims were to do something that regular expressions struggle doing; that is, determine whether brackets are balanced.

Example of a legal expression: “([as](<{}>))”.

Example of an illegal expression: “({<)>}”.

Here's what I came up with...

private bool IsValid(string str)
{
    if (!string.IsNullOrEmpty(str))
    {
        List<char> LeftParenthesis = new List<char>() { '(', '{', '[', '<' };
        List<char> RightParenthesis = new List<char>() { ')', '}', ']', '>' };
        List<char> items = new List<char>(str.Length);

        // Loop through each character
        for (int i = 0; i < str.Length; i++)
        {
            char c = str[i];

            if (LeftParenthesis.Contains(c))
            {
                items.Add(c); // Add each opening bracket
            }
            else if (RightParenthesis.Contains(c))
            {
                int rpIndex = RightParenthesis.IndexOf(c);

                // Invalid if there are no open brackets and we find a closing one
                int lastPairIndex = items.LastIndexOf(LeftParenthesis[rpIndex]);

                if (lastPairIndex >= 0)
                {
                    if (items[items.Count - 1] != items[lastPairIndex]) // Last item must be matching bracket
                        return false;
                    else
                        items.RemoveAt(lastPairIndex); // Remove last pair
                }
                else
                    return false;
            }
        }

        // Look for any other brackets left over
        if (items.Count > 0)
            return false;
    }

    return true;
}