<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(string& s, string& p, int i, int j, vector<vector<int>>& dp) {
        // Base Cases
        if (i < 0 && j < 0) return true;  // Both strings are fully matched
        if (i >= 0 && j < 0) return false;  // Pattern exhausted but string still has characters
        if (i < 0 && j >= 0) {
            // Check if the remaining characters in the pattern are all '*'
            for (int k = 0; k <= j; k++) {
                if (p[k] != '*') return false;
            }
            return true;
        }

        // Check if the current state has already been computed
        if (dp[i][j] != -1) return dp[i][j];

        // If characters match or pattern has '?', recurse for the next pair
        if (s[i] == p[j] || p[j] == '?') {
            return dp[i][j] = solve(s, p, i - 1, j - 1, dp);
        }
        
        // If pattern has '*', it can match zero or more characters
        if (p[j] == '*') {
            return dp[i][j] = (solve(s, p, i, j - 1, dp) || solve(s, p, i - 1, j, dp));
        }

        // If characters don't match and no wildcard, return false
        return dp[i][j] = false;
    }

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

        // Memoization table initialized with -1 (uncomputed states)
        vector<vector<int>> dp(n, vector<int>(m, -1));

        // Start the recursion from the end of the strings
        return solve(s, p, n - 1, m - 1, dp);
    }
};
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