<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:

    int ans[101][101];


    bool solve(string s, int ind, int count){
        if(count<0) return false;
        if(ind == s.length()){
            return count == 0;
        }

        if(ans[ind][count] !=-1){
            return ans[ind][count];
        }

        bool res;

        if(s[ind] == '('){
            res = solve(s, ind+1, count+1);
        }
        else if(s[ind] == ')') {
            res = solve(s, ind+1, count-1);
        }
        else if(s[ind] == '*'){
            res = solve(s, ind+1, count+1) || solve(s, ind+1, count-1) || solve(s, ind+1, count);
        }

        ans[ind][count] = res;
        return res;
    }

    bool checkValidString(string s) {
        for(int i=0;i<=100;i++){
            for(int j=0;j<=100;j++){
                ans[i][j] = -1;
            }
        }
        return solve(s, 0, 0);
    }
};
26100