Matching parentheses

I have a string that contains a random order of parenthesis {[()]}. I want to check if for any given parenthesis is there a matching closing one.

Example:

}}}{{{ //true
 {[]    //false
 {[()]} //true

private static bool checkIfWellFormatted(string inputString)
{

    if (string.IsNullOrEmpty(inputString))
        throw new ArgumentException("String is empty");
    if ((inputString.Length % 2) != 0)
        return false;

    Dictionary _inputDictionary = new Dictionary();

    foreach (Char c in inputString)
    {
        if (!_inputDictionary.ContainsKey(c))
            _inputDictionary.Add(c, 0);
        else
            _inputDictionary[c] += 1;

    }

    foreach (var item in _inputDictionary)
    {
        char oppKey = '\0';
        if (item.Key == '{')
            oppKey = '}';
        if (item.Key == '}')
            oppKey = '{';

        if (item.Key == '(')
            oppKey = ')';
        if (item.Key == ')')
            oppKey = '(';

        if (item.Key == '[')
            oppKey = ']';
        if (item.Key == ']')
            oppKey = '[';

        if (_inputDictionary.ContainsKey(oppKey))
        {
            var value = _inputDictionary[oppKey];
            if (value != item.Value)
                return false;

        }
        else
            return false;

    }

    return true;
}

Here, the second iteration over the dictionary has \$O(n)\$ complexity. Can I improve its time complexity?

You could evict the count dictionary altogether and use three counters. Next, you scan each character and increment/decrement the corresponding counter. The answer is true if after scanning all the characters all three counters are zero. For example, if we scan [, we increment the counter for [ and ]; if we scan ], we decrement that very same counter. (Before the scan all counters are set to zero.)

All in all, I had this in mind:

private static bool WellFormatted(string inputString)
{
    int braceCount = 0;         // Counts '{' and '}'.
    int parenthesisCount = 0;   // Counts '(' and ')'.
    int squareBracketCount = 0; // Counts '[' and ']'.

    foreach (char c in inputString)
    {
        switch (c)
        {
            case '{':
                braceCount++;
                break;

            case '}':
                braceCount--;
                break;

            case '(':
                parenthesisCount++;
                break;

            case ')':
                parenthesisCount--;
                break;

            case '[':
                squareBracketCount++;
                break;

            case ']':
                squareBracketCount--;
                break;
        }
    }

    return braceCount == 0
        && parenthesisCount == 0
        && squareBracketCount == 0;
}

Also, from mathematical perspective, I would accept the empty string as a valid "parenthezation."

StackExchange Code Review Q#155034, answer score: 11