<p>Given an input string (<code>s</code>) and a pattern (<code>p</code>), implement wildcard pattern matching with support for <code>&#39;?&#39;</code> and <code>&#39;*&#39;</code> where:</p>

<ul>
	<li><code>&#39;?&#39;</code> Matches any single character.</li>
	<li><code>&#39;*&#39;</code> Matches any sequence of characters (including the empty sequence).</li>
</ul>

<p>The matching should cover the <strong>entire</strong> input string (not partial).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> &quot;a&quot; does not match the entire string &quot;aa&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong>&nbsp;&#39;*&#39; matches any sequence.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cb&quot;, p = &quot;?a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong>&nbsp;&#39;?&#39; matches &#39;c&#39;, but the second letter is &#39;a&#39;, which does not match &#39;b&#39;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= s.length, p.length &lt;= 2000</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
	<li><code>p</code> contains only lowercase English letters, <code>&#39;?&#39;</code> or <code>&#39;*&#39;</code>.</li>
</ul>

class Solution {
public:
    bool solve(vector<vector<optional<bool>>> &memo, const string& s, const string& p, int i , int j) {
        int n = s.size();
        int m = p.size();
    
        if (i == n && j == m) {
            return true;
        }
        if (i > n || j == m) {
            return false;
        }
        if (memo[i][j].has_value()) {
            return memo[i][j].value();
        }
        bool ans = false;
        if (p[j] == '*') {
            ans = solve(memo, s, p , i + 1, j) | solve(memo, s, p, i + 1 , j + 1) | solve(memo, s, p , i , j + 1);
        } else if (s[i] == p[j] || p[j] == '?') {
            ans = solve(memo, s, p, i + 1 , j + 1);
        }
        memo[i][j] = ans;
        return ans;

    }
    bool isMatch(string s, string p) {
        int n = s.size();
        int m = p.size();
        vector<vector<optional<bool>>> memo(n + 1, vector<optional<bool>>(m));
        return solve(memo, s, p, 0, 0);
    }
};
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