<p>Given a string <code>s</code> containing only three types of characters: <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code> and <code>&#39;*&#39;</code>, return <code>true</code> <em>if</em> <code>s</code> <em>is <strong>valid</strong></em>.</p>

<p>The following rules define a <strong>valid</strong> string:</p>

<ul>
	<li>Any left parenthesis <code>&#39;(&#39;</code> must have a corresponding right parenthesis <code>&#39;)&#39;</code>.</li>
	<li>Any right parenthesis <code>&#39;)&#39;</code> must have a corresponding left parenthesis <code>&#39;(&#39;</code>.</li>
	<li>Left parenthesis <code>&#39;(&#39;</code> must go before the corresponding right parenthesis <code>&#39;)&#39;</code>.</li>
	<li><code>&#39;*&#39;</code> could be treated as a single right parenthesis <code>&#39;)&#39;</code> or a single left parenthesis <code>&#39;(&#39;</code> or an empty string <code>&quot;&quot;</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "()"
<strong>Output:</strong> true
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "(*)"
<strong>Output:</strong> true
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> s = "(*))"
<strong>Output:</strong> true
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 100</code></li>
	<li><code>s[i]</code> is <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code> or <code>&#39;*&#39;</code>.</li>
</ul>

class Solution {
public:
    bool generate(const string &s, int i, int left)
    {
        if (i == s.size())
        {
            return left == 0;
        }
        if (s[i] == '(')
        {
            ++left;
            if (unor[100*(i + 1) + left] == -1)
            {
                unor[100*(i + 1) + left] = generate(s, i + 1, left);
            }
            return unor[100*(i + 1) + left];
        }
        else if (s[i] == ')')
        {
            --left;
            if (left < 0)
            {
                unor[100*(i + 1) + left] = false;
                return false;
            } 
            //auto it = unor.find(100*(i + 1) + left);
            if (unor[100*(i + 1) + left] == -1)
            {
                unor[100*(i + 1) + left] = generate(s, i + 1, left);
            }
            return unor[100*(i + 1) + left];
        }
        else
        {
            //auto it = unor.find(100*(i + 1) + left + 1);
            if (unor[100*(i + 1) + left + 1] == -1)
            {
                unor[100*(i + 1) + left + 1] = generate(s, i + 1, left + 1);
            }
            bool first = unor[100*(i + 1) + left + 1];
            if ((left - 1) >= 0)
            {
                //auto it = unor.find(100*(i + 1) + left - 1);
                if (unor[100*(i + 1) + left - 1] == -1)
                {
                    unor[100*(i + 1) + left - 1] = generate(s, i + 1, left - 1);
                }
                //second = generate(s, i + 1, left - 1);
            }
            else
            {
                unor[100*(i + 1) + left - 1] = false;
            }
            bool second = unor[100*(i + 1) + left - 1];
            

            //bool third = generate(s, i + 1, left);
            
            //it = unor.find(100*(i + 1) + left);
            if (unor[100*(i + 1) + left] == -1)
            {
                unor[100*(i + 1) + left] = generate(s, i + 1, left);
            }
            bool third = unor[100*(i + 1) + left];
            return max(max(first, second), third);
        }
    }
    bool checkValidString(string s) {
        cout << s.size() << endl;
        unor.resize(10101, -1);
        return generate(s, 0, 0);
    }
private:
    vector<int> unor;
    //unordered_map<int, bool> unor;
};
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