<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 isMatch(string s, string p) 
    {
        int m = s.size(), n = p.size();
        std::memset(dp_, 0, sizeof(dp_));

        s = "#" + s;
        p = "#" + p;

        dp_[0][0] = 1;
        for (int j = 1; j <= n; ++j)
        {
            if (p[j] != '*')
                break;
            dp_[0][j] = 1;
        }

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                if (p[j] == '?' || s[i] == p[j])
                    dp_[i][j] = dp_[i - 1][j - 1];
                else if (p[j] == '*')
                {
                    // original method
                    // for (int k = i; k >= 0; --k)
                    // {
                    //     if (dp_[k][j - 1] == 1)
                    //     {
                    //         dp_[i][j] = 1;
                    //         break;
                    //     }
                    // }

                    // improvement
                    // dp[i][j]     = dp[i][j - 1] || dp[i - 1][j - 1] || ... || dp[0][j - 1] (1)
                    // dp[i - 1][j] =                 dp[i - 1][j - 1] || ... || dp[0][j - 1] (2)
                    // use (2) to replace (1)
                    dp_[i][j] = dp_[i][j - 1] || dp_[i - 1][j];
                }
            }
        }

        return dp_[m][n];
    }

private:
    int dp_[2005][2005];
};
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