<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 {
private:
    short int solve(string& a, string& b, vector<vector<short int>>&dp, int i, int j) {
        // if(i == 0 && j == 0) return 1;
        // if(j == 0 && i > 0) return 0;

        if(j == 0) return i == 0;

        if(i == 0 && j > 0) { // true if all remaining b[0...j] are '*'
            for(int k = 0; k < j; k++) {
                if(b[k] != '*')
                    return 0;
            }
            return 1;
        }

        if(dp[i][j] != -1)
            return dp[i][j];

        if (b[j - 1] == '*') {
            return dp[i][j] = solve(a, b, dp, i - 1, j) | solve(a, b, dp, i, j - 1);
        }
        if (a[i - 1] == b[j - 1] or b[j - 1] == '?') {
            return dp[i][j] = solve(a, b, dp, i - 1, j - 1);
        }
        return dp[i][j] = 0;
    }

public:
    bool isMatch(string s, string p) { 
        int n = s.size(), m = p.size();

        vector<vector<short int>>dp(n + 1, vector<short int>(m + 1, -1));

        int res = solve(s, p, dp, n, m); 
        return res == 1;
    }
};
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