<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 f(int ind, string &s, int count, vector<vector<int>>&dp)
{
    if(ind==s.size())
    {
        // cout<<count<<endl;
        if(count==0) return 1;
        else return 0;
    }
    if(dp[ind][count]!=-1) return dp[ind][count];
    bool pushs=0, pops=0, noops=0;
    if(s[ind]=='(')
    {
        return dp[ind][count] = f(ind+1,s,count+1,dp);
    }
    else if(s[ind]==')')
    {
        if(count==0) return dp[ind][count] = 0;
        return dp[ind][count] = f(ind+1,s,count-1,dp);
    }
    else
    {
    pushs=f(ind+1,s,count+1,dp);
    if(count>0)
    {
        pops=f(ind+1,s,count-1,dp);
    }
    noops=f(ind+1,s,count,dp);
    }
    cout<<pushs<<" "<<pops<<" "<<noops<<endl;
    return  dp[ind][count] = pushs | pops | noops;
}
    bool checkValidString(string s) {
       stack<char>st;
       vector<vector<int>>dp(s.size()+1,vector<int>(s.size()+1,-1));
       return f(0,s,0,dp);
    }
};

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