<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 {
    bool ismatch(int i, int j, string& s1, string& s2,
                 vector<vector<int>>& dp) {
        // base case;
        if (i < 0 and j < 0)
            return true;
        if (i < 0 and j >= 0)
            return false;
        if (j < 0 and i >= 0) {
            for (int x = i; x >= 0; x--) {
                if (s1[x] != '*')
                    return false;
            }
            return true;
        }
        if (dp[i][j] != -1)
            return dp[i][j];
        if (s1[i] == s2[j] or s1[i] == '?')
            return dp[i][j] = ismatch(i - 1, j - 1, s1, s2, dp);
        else if (s1[i] == '*') {
            return dp[i][j] = ismatch(i - 1, j, s1, s2, dp) ||
                              ismatch(i, j - 1, s1, s2,
                                      dp); // i-1 when * is considered empty, i
                                           // when star is considered to match
                                           // any number of characters

        } else
            return dp[i][j] = false;
    }

public:
    bool isMatch(string s, string p) {
        int n = s.size();
        int m = p.size();
        string s1=p,s2=s;
        vector<vector<bool>> dp(m + 1, vector<bool>(n + 1, 0));
        dp[0][0] = 1;
        int star = 0;
       for (int i = 1; i <= m; i++) {
        if (s1[i - 1] == '*') {
            dp[i][0] = dp[i - 1][0];  // '*' can match empty sequence
        }
    }
          
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (s1[i - 1] == s2[j - 1] or s1[i - 1] == '?')
                    dp[i][j] = dp[i - 1][j - 1];
                else if (s1[i - 1] == '*') {
                    dp[i][j] = dp[i - 1][j] || dp[i][j - 1];
                    // i-1 when * is considered empty, i when star is
                    // considered to match any number of characters

                } else
                    dp[i][j] = false;
            }
        }
        
    
    return  dp[m][n];
}

};

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